Overview
This lecture explains the differences between one-tailed (directional) and two-tailed (non-directional) hypothesis tests, including when to use each and how to interpret test direction.
One-Tailed Tests (Directional Tests)
- One-tailed tests can be right-tailed (upper-tailed) or left-tailed (lower-tailed).
- Right-tailed tests are used when the alternative hypothesis claims the population parameter is greater than the hypothesized value.
- Keywords for right-tailed tests: more, higher, increased, above, over, beyond, exceed.
- The critical region for a right-tailed test is at the extreme right of the distribution; the critical value is positive.
- Left-tailed tests are used when the alternative hypothesis claims the parameter is less than the hypothesized value.
- Keywords for left-tailed tests: lower, smaller, decreased, below, under, reduced.
- The critical region for a left-tailed test is at the extreme left; the critical value is negative.
- Direction is indicated in the alternative hypothesis, not the null hypothesis.
- The problem context determines the correct direction; terms like “better” must be interpreted carefully.
Two-Tailed Tests (Non-Directional Tests)
- Two-tailed tests are used when the alternative hypothesis specifies the parameter is different (not equal) to the hypothesized value.
- Two-tailed tests look for deviations in both directions (greater than or less than).
- Keywords: different from, changed, deviate from, inconsistent with.
- Two-tailed tests have two critical values: one positive (right) and one negative (left).
- If the test statistic falls beyond either critical value, reject the null hypothesis.
Key Terms & Definitions
- One-tailed test — Hypothesis test evaluating deviation in only one direction (right or left).
- Right-tailed test (Upper-tailed) — Tests if a parameter is greater than a certain value.
- Left-tailed test (Lower-tailed) — Tests if a parameter is less than a certain value.
- Two-tailed test — Hypothesis test evaluating deviations in both directions (greater and lesser).
- Critical value — The threshold at which the null hypothesis is rejected.
- Critical (rejection) region — Area(s) under the curve where the null hypothesis is rejected.
Action Items / Next Steps
- Review textbook examples on identifying test direction based on alternative hypotheses.
- Practice determining the correct test type for different research questions.