CIs based on non-central t-distribution may not be correct due to numerical issues

[metinbulus]

Describe the bug
CIs based on non-central t-distribution may not be correct due to numerical issues.

To Reproduce
Steps to reproduce the behavior:

effectsize:::.get_ncp_t(t = 55, df_error = 1e6, conf.level = 0.95)
[1] 48.400 63.525
effectsize:::.get_ncp_t(t = 56, df_error = 1e6, conf.level = 0.95)
[1] 61.6 61.6

Screenshots

Specifiations (please complete the following information):

• R Version 4.1.0
• effectsize Version 0.8.6

[mattansb]

Are you using the latest version of effectsize? The optimization of the NCP bounds was revised sometime last year.

library(ggplot2)

effectsize:::.get_ncp_t(t = 55, df_error = 1e6, conf.level = 0.95)
#> [1] 53.03854 56.96143
effectsize:::.get_ncp_t(t = 56, df_error = 1e6, conf.level = 0.95)
#> [1] 54.03849 57.96149

x <- 1:150
ci <- sapply(x, effectsize:::.get_ncp_t, df_error = 1e6, conf.level = 0.95)

data.frame(cbind(x, t(ci))) |> 
  ggplot(aes(x)) + 
  geom_line(aes(y = V3), linetype = "solid") + 
  geom_line(aes(y = V2), linetype = "dashed")

^{Created on 2025-12-17 with reprex v2.1.1}

[metinbulus]

Awesome, updated the package, which solved the issue. Now it fails at df = 2.

> effectsize:::.get_ncp_t(t = 56, df_error = 2, conf.level = 0.95)
Error in stats::optim(par = 1.1 * rep(t, 2), fn = function(x) { : 
  function cannot be evaluated at initial parameters

[mattansb]

Do you typically have such large t-value with df=2? 😉

Should be fixed here #692