Question

A researcher did a one-tailed hypothesis test using an alpha level of .01, H0 was rejected. A colleague analyzed the same data but used a two-tailed test with α=.05, H0 was failed to reject. Can both analyses be correct? Explain your answer.

I searched for this but found another answer which did not accurately reflect the original one-tailed using .01.

Answer 1

Case 1) A researcher did a one-tailed hypothesis test using an alpha level of .01, H0 was rejected.

That means p-value for this one-tailed test is less than or equak to alpha level of 0.01

Case 2) A colleague analyzed the same data but used a two-tailed test with α=.05, H0 was failed to reject.

That means p-value for thia two-tailed test is greater than alpha level of 0.05.

Explanation 1) : Let consider case 1) result is correct

We know, for two-tailed test,

p-value = 2 * p-value of one tailed test

And largest p-value for one-tailed test should be 0.01

Therefore, largest p-value for two-tailed test should be,

p-value = 2 * 0.01 = 0.02 which is less than alpha level of 0.05

And since, p-value = 0.02 less than alpha level of 0.05, we should reject H0.

Therefore, case 2) result would not be correct.

Explanation 2) Lets consider case 2) result is correct.

In this case p-value is greater than alpha level of 0.05

Suppose the largest p-value for two-tailed test is 0.05,

then p-value for one-tailed should be, p-value = 0.05/2 = 0.025

which is greater than alpha level of 0.01 and we should fail to reject H0.

That means case 1) would no be correct.

Conclusion : From above explanations we can conclude that both analyses should not be correct at the same time. Either of the analyses correct.