Test of Significance: One-tailed and Two-tailed

What is the difference between a one-tailed and a two-tailed test of significance? Under what circumstances would each be used?

According to Aron, Aron, & Coups (2009), a one – tailed test is a hypothesis – testing procedure where the region for rejection of the null hypothesis is on one side of the distribution. Also according to Aron, Aron, & Coups (2009), a two – tailed test is a hypothesis – testing procedure where the region for rejection of the null hypothesis is on both sides of the distribution. One – tailed tests are for directional hypothesis (predicting a particular difference); two – tailed tests are for non directional hypothesis (predicting no particular difference).

Suppose researchers are testing a new drug, Drug Z, and its effects. If the hypothesis was, “Drug Z is just as effective as similar drugs on the market.”, a one – tailed test would be appropriate. In testing this hypothesis, the researchers are concerned with whether or not Drug Z is at least equal to the other drugs. They are not concerned with the significance levels above or below the other drugs. However, if researchers were testing how Drug Z compared with other drugs a two – tailed test would be appropriate. In this study, the researchers would want to know how significantly above or below the effectiveness of other drugs that Drug Z was.

Aron, A., Aron, E. N., & Coups, E. J. (2009). Statistics for psychology (5th ed). Upper Saddle River, NJ: Pearson/Prentice Hall.

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