# WelchDegreeOfFreedom: Welch's rectified degree of freedom In superb: Summary Plots with Adjusted Error Bars

## Description

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

## Usage

 `1` ```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).

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## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```# 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") ```

superb documentation built on June 23, 2021, 9:08 a.m.