One-Tailed vs Two-Tailed Tests

Statistics · Axiom Academy

LESSON One-Tailed vs Two-Tailed Tests Understanding the directionality of hypothesis tests and when to use each type 1. Two-Tailed Tests: Testing for Any Difference Two-tailed tests are used when you want to detect any difference from the null hypothesis value, whether higher or lower. The alternative hypothesis is non-directional. In a two-tailed test, you split the significance level (α) between both tails of the distribution. If α = 0.05, then each tail contains 0.025 of the probability. 2. Right-Tailed Tests: Testing for Greater Than Right-tailed tests (upper-tailed) are used when you specifically want to test if a parameter is greater than the null hypothesis value. All of α is placed in the right tail. Example: Testing if a new drug increases recovery time, or if a training program improves test scores. 3. Left-Tailed Tests: Testing for Less Than Left-tailed tests (lower-tailed) are used when you specifically want to test if a parameter is less than the null hypothesis value. All of α is placed in the left tail. Example: Testing if a new manufacturing process reduces defect rates, or if a diet decreases cholesterol levels. 4. Calculating p-values for Each Test Type The p-value calculation differs based on the test type. The p-value represents the probability of observing data as extreme as (or more extreme than) what you observed, assuming H₀ is true. Sum both tails beyond the test statistic: Find area beyond |z| in both directions Area to the right of test statistic:

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