Assume John is conducting a one-way ANOVA with three groups. Naturally he specifies the null hypothesis as Mean1=Mean2=Mean3. After learned about the t-test, he claims that the ANOVA can also be accomplished by three separate t-tests on the three pairs of means. In other words, the null hypotheses in the three t-tests would be: Mean1=Mean2; Mean2=Mean3; Mean1=Mean3. He further argues that the t-tests are preferred since they help to identify which mean(s) is(are) significantly different from other(s) while the one-way ANOVA could not without further tests.

Do you agree with John?

Prove your agreement and show your work

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