One-Tailed Versus Two-Tailed Tests

When is a one-tailed test appropriate?

Only when there is a clear, theory-based expectation about the direction of the effect, and the opposite direction is considered irrelevant.

How does the p-value of a one-tailed test compare to that of a two-tailed test?

The one-tailed p-value is half the size of the two-tailed p-value (assuming the effect is in the expected direction).

What happens in a one-tailed test if the result is in the opposite direction of the hypothesis?

The researcher fails to reject the null, even if the difference is large, because the result is in the non-hypothesized direction.

In a t-distribution with 10 degrees of freedom and p = .05, what are the critical t-values for a two-tailed test?

±2.228

What is the main difference between a one-tailed and a two-tailed test?

A one-tailed test checks for an effect in one specific direction, while a two-tailed test checks for an effect in either direction.

In the same situation, what is the critical t-value for a one-tailed test?

1

Why must the critical value in a two-tailed test be more extreme than in a one-tailed test?

Because the .05 significance level is divided, placing .025 in each tail, requiring stronger evidence to reject the null.

Why is a two-tailed test considered more conservative than a one-tailed test?

Because the region of rejection is split between both tails, requiring a more extreme test statistic to reject the null.

When is a two-tailed test appropriate?

When the researcher wants to detect any difference, regardless of direction, and has no strong directional hypothesis.