Question

Which of the following is always true regarding the relationship between the one- and two-tailed significance tests? Select all that are true.

  

If the one-tailed test is significant, then the two-tailed test at the same α will also be significant.

   

If the two-tailed test is significant, then the one-tailed test at the same α will also be significant (in the appropriate direction).

   

If the two-tailed test is significant, then the one-tailed test at the same α may or may not be significant (in the appropriate direction).

   

If the one-tailed test is significant, then the two-tailed test at the same α may or may not be significant

Answer 1

Let us explain with the help of an example of z test

Test statistic = z

Test criteria , test is significant

if absolute value of test statistic, I z I > zc

Let

Two tailed Critical value of z is , zc = 1.96

One ( left or right) tailed critical value of z is , zc = 1.65  

Two tailed test is significant if, I z I  > 1.96

Then certainly, I z I > 1.65

( but in the appropriate direction , that is if z = 2.36 , it is significant at two tailed and also significant at right tailed test , but not at left tailed test . Similarly if z = -2.36 , it is significant at two tailed and also significant at left tailed test , but not at right tailed test)

But if one tailed test is significant , that is I z I >1.65

Then , I z I may or may not be greater than 1.96

( If z = 1.80 , it is significant at one tail , but not significant at two tail)

Thus true relationships are

If the two tailed test is significant , then one tailed test at the same will also be significant ( in the appropriate direction)

If the one tailed test is significant , then two tailed test at the same may or may not be significant .