Wald Ratio standard error

Author

Gibran Hemani

Published

May 8, 2025

Background

library(MendelianRandomization)
library(dplyr)

Attaching package: 'dplyr'
The following objects are masked from 'package:stats':

    filter, lag
The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union
library(ivreg)
library(twopartm)

simulate_sumstats <- function(bgx, bxy, nx, ny, af) {
    g_a <- rbinom(nx, 2, af)
    g_b <- rbinom(ny, 2, af)
    xpred_a <- bgx * g_a
    xe_a <- rnorm(nx, 0, sqrt(1-var(xpred_a)))
    x_a <- xpred_a + xe_a

    xpred_b <- bgx * g_b
    xe_b <- rnorm(ny, 0, sqrt(1-var(xpred_b)))
    x_b <- xpred_b + xe_b
    ypred <- bxy * x_b
    ye <- rnorm(ny, 0, sqrt(1-var(ypred)))
    y <- ypred + ye

    modx <- summary(lm(x_a ~ g_a))
    bgx_hat <- modx$coefficients[2, 1]
    segx_hat <- modx$coefficients[2, 2]

    mody <- summary(lm(y ~ g_b))
    bgy_hat <- mody$coefficients[2, 1]
    segy_hat <- mody$coefficients[2, 2]
    bgy_pval <- mody$coefficients[2, 4]
    bgy_pval_pnorm <- 2 * pnorm(-abs(bgy_hat / segy_hat))

    modiv <- summary(ivreg(y ~ x_b | g_b))
    return(list(
        bgx = bgx_hat,
        segx = segx_hat,
        bgy = bgy_hat,
        segy = segy_hat,
        bgy_pval = bgy_pval,
        bgy_pval_pnorm = bgy_pval_pnorm,
        b = modiv$coefficients[2, 1],
        se = modiv$coefficients[2, 2],
        pval = modiv$coefficients[2, 4]
    ))
}

wr_delta1 <- function(sim_result) {
    biv_b <- sim_result$bgy / sim_result$bgx
    biv_se <- sim_result$segy / sim_result$bgx
    biv_pval <- 2 * pnorm(-abs(biv_b / biv_se))
    return(tibble(
        b = biv_b,
        se = biv_se,
        pval = biv_pval,
        method = "delta1"
    ))
}

wr_bootstrap <- function(sim_result, nboot = 1000) {
    biv_b <- sim_result$bgy / sim_result$bgx
    biv_boot <- rnorm(nboot, sim_result$bgy, sim_result$segy) / rnorm(nboot, sim_result$bgx, sim_result$segx)
    biv_se <- sd(biv_boot)
    biv_pval <- 2 * pnorm(-abs(biv_b / biv_se))

    return(tibble(
        b = biv_b,
        se = biv_se,
        pval = biv_pval,
        method = "bootstrap"
    ))
}

wr_delta2 <- function(sim_result) {
    bgx <- sim_result$bgx
    segx <- sim_result$segx
    bgy <- sim_result$bgy
    segy <- sim_result$segy

    biv_b <- bgy / bgx
    # temp <- sqrt((segy^2 / bgy^2) + segx^2 / bgx^2)
    # biv_se <- biv_b * temp
    biv_se <- sqrt(bgy^2 * segx^2 + bgx^2 * segy^2) / bgx^2
    biv_pval <- 2 * pnorm(-abs(biv_b / biv_se))
    return(tibble(
        b = biv_b,
        se = biv_se,
        pval = biv_pval,
        method = "delta2"
    ))
}

wr_fieller <- function(sim_result) {
    vcov <- matrix(c(sim_result$segy^2, 0, 0, sim_result$segx^2), nrow = 2)
    tryCatch({
        f <- FiellerRatio(xest = sim_result$bgy, yest = sim_result$bgx, V = vcov)
        se <- (f[1] - f[2]) / 1.96
        pval <- 2 * pnorm(-abs(f[1] / se))
        return(tibble(
            b = f[1],
            se = se,
            pval = pval,
            method = "fieller"
        ))    
    },
    error = function(e) {
        message("Error in FiellerRatio: ", e$message)
        return(tibble(
            b = NA,
            se = NA,
            pval = NA,
            method = "fieller"
        ))
    })
}

a <- simulate_sumstats(0.5, 0.3, 100000, 10000, 0.5)
a
$bgx
[1] 0.4961796

$segx
[1] 0.00419403

$bgy
[1] 0.1463906

$segy
[1] 0.01392041

$bgy_pval
[1] 9.903398e-26

$bgy_pval_pnorm
[1] 7.270415e-26

$b
[1] 0.2939658

$se
[1] 0.02688236

$pval
[1] 1.121262e-27
wr_delta1(a)
# A tibble: 1 × 4
      b     se     pval method
  <dbl>  <dbl>    <dbl> <chr> 
1 0.295 0.0281 7.27e-26 delta1
wr_delta2(a)
# A tibble: 1 × 4
      b     se     pval method
  <dbl>  <dbl>    <dbl> <chr> 
1 0.295 0.0282 1.13e-25 delta2
wr_fieller(a)
# A tibble: 1 × 4
      b     se     pval method 
  <dbl>  <dbl>    <dbl> <chr>  
1 0.295 0.0281 9.70e-26 fieller
wr_bootstrap(a)
# A tibble: 1 × 4
      b     se     pval method   
  <dbl>  <dbl>    <dbl> <chr>    
1 0.295 0.0301 9.45e-23 bootstrap
params <- expand.grid(
    bgx = seq(0.01, 0.1, by = 0.01),
    bxy = c(0, 0.1, 0.2),
    nx = c(10000, 100000),
    ny = c(10000, 100000),
    af = c(0.01, 0.4),
    sim=1:10
)

full_sim <- function(bgx, bxy, nx, ny, af, sim) {
    args <- tibble(bgx = bgx, bxy = bxy, nx = nx, ny = ny, af = af)
    a <- simulate_sumstats(bgx, bxy, nx, ny, af)
    r1 <- tibble(
        b = a$b,
        se = a$se,
        pval = a$pval,
        method = "ivreg"
    )

    res <- bind_rows(
        r1, 
        wr_delta1(a),
        wr_delta2(a),
        wr_fieller(a),
        wr_bootstrap(a)
    )
    return(bind_cols(args, res))
}

full_sim(0.1, 0.2, 10000, 10000, 0.5, 1)
# A tibble: 5 × 9
    bgx   bxy    nx    ny    af     b    se  pval method   
  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>    
1   0.1   0.2 10000 10000   0.5 0.183 0.155 0.240 ivreg    
2   0.1   0.2 10000 10000   0.5 0.184 0.160 0.249 delta1   
3   0.1   0.2 10000 10000   0.5 0.184 0.163 0.257 delta2   
4   0.1   0.2 10000 10000   0.5 0.184 0.161 0.253 fieller  
5   0.1   0.2 10000 10000   0.5 0.184 0.176 0.294 bootstrap
do.call(full_sim, params[1,])
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
# A tibble: 5 × 9
    bgx   bxy    nx    ny    af      b     se   pval method   
  <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl> <chr>    
1  0.01     0 10000 10000  0.01  1.94   5.10   0.704 ivreg    
2  0.01     0 10000 10000  0.01  0.601 -0.726  0.407 delta1   
3  0.01     0 10000 10000  0.01  0.601  0.851  0.480 delta2   
4  0.01     0 10000 10000  0.01 NA     NA     NA     fieller  
5  0.01     0 10000 10000  0.01  0.601 76.4    0.994 bootstrap
dim(params)
[1] 2400    6
library(furrr)
Loading required package: future
Registered S3 method overwritten by 'future':
  method               from      
  all.equal.connection parallelly
plan(multicore, workers = 4)
opt <- furrr::furrr_options(seed = TRUE)
res <- furrr::future_pmap(params, full_sim, .options = opt, .progress = TRUE)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Notice: The denominator is not significantly different from zero, and the confidence set of the ratio is combining [-inf,bound1] and [bound2,inf].
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
Error in FiellerRatio: The denominator is not significantly different from zero, and the confidence set of ratio does not exclude any value at all. (unbounded CI)
length(res)
[1] 2400
r <- bind_rows(res)

library(ggplot2)

Attaching package: 'ggplot2'
The following object is masked from 'package:twopartm':

    margin
r %>% filter(se < 1 & se > 0) %>%
ggplot(aes(x = bgx, y=se)) +
    geom_boxplot(aes(fill=method, linetype=as.factor(af))) +
    facet_grid(bxy ~ nx + ny) +
    scale_colour_brewer(palette = "Set1") 

library(tidyr)
r %>% 
    filter(se < 1 & se > 0) %>%
    group_by(method) %>%
    mutate(sim = 1:n()) %>%
    ungroup() %>%
    select(-c(b, pval, bgx, bxy, nx, ny, af)) %>%
    pivot_wider(names_from = method, values_from = c(se)) %>%
    select(-c(sim)) %>%
    pairs

sessionInfo()
R version 4.5.0 (2025-04-11)
Platform: aarch64-apple-darwin20
Running under: macOS Sonoma 14.6.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: Europe/London
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] tidyr_1.3.1                   ggplot2_3.5.2                
[3] furrr_0.3.1                   future_1.40.0                
[5] twopartm_0.1.0                ivreg_0.6-5                  
[7] dplyr_1.1.4                   MendelianRandomization_0.10.0

loaded via a namespace (and not attached):
 [1] gtable_0.3.6        shape_1.4.6.1       rjson_0.2.23       
 [4] xfun_0.52           htmlwidgets_1.6.4   lattice_0.22-7     
 [7] numDeriv_2016.8-1.1 vctrs_0.6.5         tools_4.5.0        
[10] generics_0.1.3      parallel_4.5.0      tibble_3.2.1       
[13] DEoptimR_1.1-3-1    pkgconfig_2.0.3     Matrix_1.7-3       
[16] data.table_1.17.0   RColorBrewer_1.1-3  arrangements_1.1.9 
[19] lifecycle_1.0.4     compiler_4.5.0      farver_2.1.2       
[22] MatrixModels_0.5-4  codetools_0.2-20    carData_3.0-5      
[25] SparseM_1.84-2      quantreg_6.1        htmltools_0.5.8.1  
[28] yaml_2.3.10         lazyeval_0.2.2      glmnet_4.1-8       
[31] gmp_0.7-5           Formula_1.2-5       plotly_4.10.4      
[34] pillar_1.10.2       car_3.1-3           iterpc_0.4.2       
[37] MASS_7.3-65         iterators_1.0.14    abind_1.4-8        
[40] foreach_1.5.2       parallelly_1.44.0   robustbase_0.99-4-1
[43] tidyselect_1.2.1    digest_0.6.37       listenv_0.9.1      
[46] purrr_1.0.4         labeling_0.4.3      splines_4.5.0      
[49] fastmap_1.2.0       grid_4.5.0          colorspace_2.1-1   
[52] cli_3.6.5           magrittr_2.0.3      survival_3.8-3     
[55] utf8_1.2.5          withr_3.0.2         scales_1.4.0       
[58] rmarkdown_2.29      httr_1.4.7          globals_0.18.0     
[61] zoo_1.8-14          evaluate_1.0.3      knitr_1.50         
[64] lmtest_0.9-40       viridisLite_0.4.2   rlang_1.1.6        
[67] Rcpp_1.0.14         glue_1.8.0          jsonlite_2.0.0     
[70] R6_2.6.1