This is pretty small print. You may also see this as the Satterthwaite-Welch correction/equation
Details #
This is a more general extension of Welch’s correction which is a way of modifying the degrees of freedom (d.f.) to be used in some parametric tests where the statistical model assumes equal variances in the populations from which the samples analysed were taken. If the p value for the statistic of interest is worked out using this value for the d.f. it will be more robust if the populations actually don’t have the same variances. Whereas the correction is generally called Welch’s when it’s applied to the between groups t-test, the terms “Satterthwaite”, “Satterthwaite-Welch” or “Welch-Satterthwaite” are seen when the same equation is used in multi-group ANOVA, MANOVA, Confirmatory Factor Analyis (CFA) or structural relations modelling analyses. As far as I can see the same equation is being used in all these situations and is giving you an approximate p value that is generally more robust than would be the case if the correction weren’t applied.
This is all very much about p values and firmly located in the Null Hypothesis Significance Testing (NHST) paradigm. If you see it in reports it is probably not inappropriate and means that the p values you are seeing should be understood as approximate and interpreted with all the usual attention to whether other assumptions beyond one of equal variances (homscedasticity) behind the particular analyses reported may also be unlikely to have been satisfied. Sadly, that “usual” is really “rarely” but that’s another story.
Try also #
- Analysis of Variance (ANOVA)
- Degrees of freedom (d.f.)
- Heteroscedasticity
- Homoscedasticity
- MANOVA
- Null Hypothesis Significance Testing (NHST) paradigm
- Welch’s t
Chapters #
Not covered in the OMbook.
Online resources #
None likely from me I think.
Dates #
First created 11.ii.26, link to d.f. added 12.ii.26.
