How are directional and non-directional hypotheses related to the test?

How are directional and non-directional hypotheses related to the test?

• A. Directionality does not affect the test.
• B. Directional uses one-tailed, non-directional uses two-tailed.
• C. Both use the same critical values.
• D. A directional hypothesis uses a one-tailed test, non-directional uses a two-tailed test.

Answer: (D)

Whether the hypothesis specifies a direction determines the type of test you use. If the prediction is in a specific direction, you use a one-tailed test because all the alpha is placed in that single tail. The decision rule then uses a single critical value, and you reject the null if the statistic crosses that boundary in the predicted direction. If there is no stated direction—only that there will be a difference—you need to consider extreme outcomes in both directions, so you use a two-tailed test with alpha split between the two tails; there are two critical cutoffs, and you reject if the statistic falls beyond either one. This also affects p-values: a one-tailed p-value only considers extremity in the predicted direction, while a two-tailed p-value doubles the one-sided value to account for both tails. So a directional hypothesis maps to a one-tailed test, while a non-directional hypothesis maps to a two-tailed test.

Whether the hypothesis specifies a direction determines the type of test you use. If the prediction is in a specific direction, you use a one-tailed test because all the alpha is placed in that single tail. The decision rule then uses a single critical value, and you reject the null if the statistic crosses that boundary in the predicted direction. If there is no stated direction—only that there will be a difference—you need to consider extreme outcomes in both directions, so you use a two-tailed test with alpha split between the two tails; there are two critical cutoffs, and you reject if the statistic falls beyond either one. This also affects p-values: a one-tailed p-value only considers extremity in the predicted direction, while a two-tailed p-value doubles the one-sided value to account for both tails. So a directional hypothesis maps to a one-tailed test, while a non-directional hypothesis maps to a two-tailed test.