Welch's rectified degree of freedom — WelchDegreeOfFreedom • superb

When variance across groups are heterogeneous, the Student t distribution with n - 1 df is not the exact distribution. However, (Welch 1947) , using methods of moments, was able to find the best-fitting t distribution. This distribution has degree of freedom reduced based on the sample sizes and the variances of the group tests. The present function returns the rectified degree of freedom

WelchDegreeOfFreedom(dta, cols, groupingcols)

Arguments

dta: A data frame containing within-subject measures, one participant per line;
cols: A vector indicating the columns containing the measures.
groupingcols: A vector indicating the columns containing the groups.

Value

df the degrees of freedom rectified according to Welch (1947).

References

Welch BL (1947). “The generalization of student's' problem when several different population variances are involved.” Biometrika, 34(1/2), 28--35. doi:10.1093/biomet/34.1-2.28 .

Examples

# creates a small data frames with 4 subject's scores for 5 measures:
dta <- data.frame(cbind(
        DV.1 = c(3., 6., 2., 2., 5.),
        DV.2 = c(4., 5., 4., 4., 3.),
        DV.3 = c(2., 7., 7., 8., 6.),
        DV.4 = c(6., 8., 4., 6., 5.),
        grp  = c(1., 1., 2., 2., 2.)
    ))
# performs the test (here rectified df = 1.898876)
WelchDegreeOfFreedom(dta, "DV.1","grp")
#> [1] 1.898876