Equivalence of standard deviations with different sample sizesA customer is looking into understanding testing for equivalence for standard deviation. The help documentation is a bit confusing on testing for equivalence for standard deviation and there is no example (only for equivalence of means).
Does anyone have a good example of this?
Also, how does sample size affect this test? The sample sizes are quite different, without knowing what "quite" means specifically. S
And, to follow up on the sample sizes, how do unequal sample sizes come into play in, for example, the unequal variance test, Welch's test for means with unequal variance, the Games-Howell test (found through the add-in for a comparison of more than 2 means with unequal variances) and the equivalence of means test?
Re: Equivalence of standard deviations with different sample sizesThe sample size could impact the variance of the data set in general, however there is no requirement to have same sample size for testing equivalence of variances across groups. Different sample sizes will result into unbalanced ANOVA. If the sample sizes among the groups is "quite different", it is highly likely that the test of unequal variances is significant. In this case, using Welch's ANOVA is recommended.
Regular ANOVA assumes equal variances and uses pooled standard deviation for the F-test. Welch's ANOVA does not assume equal variances; it uses individual variance for each group to conduct the F-test.
Re: Equivalence of standard deviations with different sample sizesThanks, Rashmi, for your response.
Since Welch's test does not require equal sample sizes, I assume that is the same then for the Games-Howell test, which I understand is a Welch-corrected Tukey Kramer pair-to-pair comparison test, correct?
With the unequal variance assumption and unequal sample size assumption, it seems this Games-Howell test is a very practical and relevant tool for comparing means. Why is this not by default in JMP - anyone know?
Also, does anyone have a good example of how to do and interpret the equivalence test for the standard deviation (not for the mean)?
Re: Equivalence of standard deviations with different sample sizesGames-Howell test is a non-parametric test equivalent to Tukey Kramer. It works well when the variances are unequal. Kruskal-Wallis test is a non-parametric equivalent to ANOVA. These are good options for unequal variances. However, non-parametric tests usually require all groups to have large sample sizes.
I found this example for interpreting equivalence test for variances (test is for variance instead if standard deviation).
Example of the Unequal Variances Option
Re: Equivalence of standard deviations with different sample sizesI use the Process Phases data table from the Training Starter (JMP 17 > JMP > Equivalence Improvements). The scripts saved to the data table seem to make sense when shown in order.
Re: Equivalence of standard deviations with different sample sizesI forgot to look in the training starter! Would be great to have an example in the JMP documentation for customers as well.
