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Under what conditions is the one-way ANOVA test equivalent to, worst, and better than the t-test...

Under what conditions is the one-way ANOVA test equivalent to, worst, and better than the t-test ?

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Answer #1

If there are only two groups then one-way ANOVA test and t-test are equivalent provided two population variances are equal.

If there are more than two groups, then one-way ANOVA is better than t-test provided population variances of all groups are equal. Becaue type I error rate for ANOVA is less than total type I error rate for all t tests required.

If  there are only two groups and population variances are not equal, then t test for unequal variance (ie Walch's t test) is better than ANOVA.

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