Why does minitab 18 not assume equal variances

Why does minitab 18 not assume equal variances software#
Why does minitab 18 not assume equal variances code#

Menu location: Analysis_Parametric_Unpaired t. Open topic with navigation Unpaired (Two Sample) t Test Under the null hypothesis, the P-value of a test with a continuous test statistic should be standard uniform (with bars roughly the height of the green line).Unpaired (Two Sample) t Test - StatsDirect

Result in this problematic situation, but a great improvement over the catastrophic result of the standard ANOVA.Р”В«elow are histograms of simulated P-values for the two tests. Lead to massive false 'discovery' of population differences, where there are none.Р”В«y contrast, the Welch ANOVA has a rejection rate ofР”Р„bout 5.7% where the 5% level is intended. Quite wrongly assuming equal population variances, the standard ANOVA has an actual rejection rate of about 25%Р”Р‡or a test intended to be at the 5% level.

Why does minitab 18 not assume equal variances code#

To make sure we assess precisely the versions of ANOVA implemented in R, we simulate 100,000 datasets, run both ANOVAs in R, and look at the 200,000 resulting P-vales.Р”В«ecause R formats each ANOVA, only for us to use the P-value in each case, the code is inefficient and runs slowly. In particular, we use sample sizes 5, 10, and 15, and respective population SDs Here we use simulation to investigate the behavior of a standard ANOVA (assuming equal population variances) in an analogous situation and compare the behavior the behavior of the Welch ANOVA in the same situation. Specifically, if population means are the same, the true significance level can be inflated considerably. If sample sizes differ and the population from which the smaller sample was chosen has a larger variance than the other population. The two-sample pooled t test is known to behave badly

So we may see other answers here voicing different opinions.Р”Р„ddendum: In response to a Comment, here is an example of simulation investigating

The Satterthwaite one-way ANOVA is still a matter of personal opinion (even if fairly widespread). But I don't think one can say yet that it is 'standard practice' to use the Satterthwaite ANOVA.Р”Р„t this point, I would have to admit that strong preference for A couple of limited simulation studies I have seen and my own experience have made me feel comfortable using the Satterthwaite ANOVA by default. However, the Satterthwaite (or Welch) ANOVA, implemented in R as oneway.test, is relatively new, and there has not been the same level of scrutiny of the Satterthwaite ANOVA as there has been of the Satterthwaite 2-sample t test. But some statisticians do make an exception to standard practice when sample sizes are very small and sample standard deviations are similar.Р”Р‡or one-way ANOVA. This means that the power of the Welch 2-sample t test is somewhat smaller than the power of the pooled test, often not enough smaller to matter for practical purposes. Satterthwaite DF, which is often smaller than the DF $n_1 + n_2 - 2$ of the pooled 2-sample t test (never larger).

Why does minitab 18 not assume equal variances software#

I believe some other statistical software (For example, I know that the Welch test is the default inР”В«oth R and Minitab. Specifically request the pooled version of the test if desired. Welch test is the default 2-sample t test, so that one must In some statistical software packages the Prior evidence (say, from data of the same type) that population To use the Welch two-sample t test, unless there is strong For two-sample t tests, I think it is now standard practice