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With k = 2 treatments, are post hoc tests necessary when the null hypothesis is rejected?...

With k = 2 treatments, are post hoc tests necessary when the null hypothesis is rejected? Explain your reasoning

Math   Statistics-And-Probability   
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Answer #1

If we want to test the equality of k treatment effects then null hypothesis is all the k treatment effects are equal. Suppose null hypothesis is rejected and conclusion is atleast one pair of treatment effect differ significantly. Obviously, we will be curious to know that which pairs are differing significantly. This procedure of testing equality of various pairs of treatment effects is called as post hoc tests.

Suppose k=2

That is we are testing equality of two treatment effects and suppose in this case, null hypothesis is rejected. That means two treatment effects are differing significantly. It is clear that the two treatments that we are testing have significantly different effects. There is no need to test that again. So when k=2, post hoc tests are not necessary.

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