1 Nov 2006 10:15
Re: F-test vs.T-test-on-differences
Hello Benjamin! I think there is some misunderstanding here. The t-test is a test for the differences between the means of two distributions. If you center your data like you propose the difference is 0 so the t-statistic will always behave very much like under the nullhypothesis (not exactly as the distributions might differ in variances and other properties, but the t-test is NOT meant to detect those). The F-test on the other hand specifically tests for difference in variances, so it is clearly the more appropriate test in your case (and if you are worrried about non-normality you might determine p-values by a resampling method like bootstrap). I think what might have confused you is that there are TWO F-tests: a) the one for testing differences between variances (lets call that F1) b) the F-test that is being used in Analysis of Variance (ANOVA) (lets call it F2) Despite its name ANOVA is a method to compare MEANS not VARIANCES. With two groups you have the trivial case of a one-way ANOVA and if you calculate the F-statistic F2 for that it is just a transformation of the usual t-statistic, i.e. the test will yield the same p-values. So F1 and F2 are very different statistics for very different things, but both have a F-distribution under normality assumptions so their names are the same (there are plenty of chi-square tests out there as well!) Hope this helps Claus Benjamin Otto wrote: > Dear community,(Continue reading)
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