anova_table: implement SE calculation for different sample sizes

[wleoncio]

Summary

According to the following code, the anova_table() function is not able to calculate the standard error of the intraclass correlation when the sample sizes are different.

lsasim/R/anova_table.R

Lines 39 to 44 in 844c889

	if (stats::var(ds$n_j) == 0) {
	se_rho <- calc_se_rho(rho_hat, ds$n_j, ds$N)
	} else {
	se_rho <- NA
	warning("SE not yet implemented for different sample sizes")
	}

Theoretical references must be provided to implement this.

MRE

The following was performed on lsasim 2.0.2.9004.

remotes::install_github("tmatta/lsasim", "844c889a")
library(lsasim)
set.seed(12334)
n7 <- list(school = 10, student = ranges(10, 50))
r5 <- cluster_gen(n7, rho = c(0.005, 0.01, 0.85))
anova_table(r5)

[wleoncio]

@mollyolaf, @Kondwani84, @ylinglw, do any of you know where I could find the equation to calculate the standard error of rho (the intraclass correlation) when each sampling unit has a different size?

[wleoncio]

Reference: Donner (1986), equation (6.1)