One-Tailed Test

Directional and Nondirectional Testing

Suppose the researcher wants to examine whether males or females exhibit differences in the level of verbal aggressiveness. If one simply asks the research question, “Does a difference exist between men and women?” then the question, as framed, permits an answer that could have either men or women testing as greater in the level of verbal aggressiveness. Such a test, associated with the use of a research question, typically is tested by a nondirectional test, because a two-tailed t-test would be considered significant if the value was greater than the critical value (e.g., 1.96) or less than the other critical value (e.g., −1.96). In this case, one of the groups will be designated as Group 1 and the other as Group 2, and the mean of the first group could be significantly greater than the second group (1.96). The mean of the first group could be significantly smaller than the second group (−1.96). The designation of either group (males or females) as Group 1 or Group 2 is arbitrary; the key is that the distance between the means of the groups (the difference score) represents a value greater than expected due to random chance (p value is less than .05).

The one-tailed test or directional test is usually associated with a hypothesis where any direction becomes specified in advance. For example, suppose the researcher has a hypothesis that males report higher levels of verbal aggressiveness compared with females. In this statement, the test is only concerned about one direction and confirmation of the hypothesis specifies which group has a greater mean. Suppose one designates males as Group 1. Then, the difference between the means (Group 1 minus Group 2) should be positive and significant (a p value of less than .05). In a one-tailed (or directional) test, the value for p = .05 becomes smaller (1.64). The reason for the smaller value is that the probability level is calculated based on the percentage of area under a curve (much like a traditional calculus formulation), and instead of having 2.5% of the value in each end of the curve (less than −1.96 and greater than 1.96), the entire value is now appearing in one tail (1.64).

[Page 1127]Directional tests do not exist in statistics, like chi-square or the F test, because the tests are nondirectional. The reason for post hoc tests in many statistics becomes necessary because a significant effect only indicates a difference but fails to specify the direction of the difference. The post hoc test provides an examination of individual cells and provides a basis to decide which effects, if any, should be considered significantly different. The issue of the one- or two-tailed test involves the issue of deciding whether a directional hypothesis is warranted or not, something not necessary in the usual F statistic, which cannot be negative (mathematically, the value of F is technically t2 and, therefore, it cannot be negative—unless imaginary numbers are a part of the system).

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