Three criteria for the use of one-tailed tests.

Abstract

Examination of the recent literature on the question of when to use one-tailed tests of significance in psychological research reveals a state of unresolved disagreement. A variety of differing opinions (1, 2, 5, 7, 8, 9, 10, pp. 62-63) have been presented, ranging from Burke's (2) exhortation that psychologists should never report one-tailed tests in the public literature to Jones' (8) statement that we may not only do so, but, in certain instances, we will be in error if we fail to do so. It is by no means necessary for psychologists to agree on all matters of importance to them. Disagreement regarding methodological considerations, however, especially when they bear on how and when propositions shall be accepted as true or rejected as false, should not be permitted to persist indefinitely. The argument is not settled by noting, as Burke (2) does, that the increased use of one-tailed tests may result in the one-tailers scoring a sociological victory almost before the controversy has begun. Actually, this observation by Burke does not coincide completely with the fact that many responsible investigators have continued to employ two-tailed tests (in situations calling for one-tailed tests according to Jones' view) long after the opening of the one-tailed avenue. 1 An example of an experiment with an explicit directional hypothesis, but employing a two-tailed test, is reported by Davitz (3). This experimenter reasoned that the injection of tetraethylammonium prior to extinction trials would inhibit the punishing effect of the emotional response under study and, consequently, would result in faster extinction in the experimental animals than in a placeboinjected control group. Instead, Davitz found In attempting to arrive at a set of acceptable criteria for the use of onetailed tests, it is important to note that the argument is not one of mathematical statistics but primarily one of experimental logic. Burke and Jones would agree that one-tailed tests should be used to test one-tailed hypotheses; their disagreement concerns when one-tailed hypotheses should and should not be made. Before proceeding to the proposed criteria, it would be of value to consider the difference between oneand two-tailed hypotheses from a viewpoint that has not been stressed by previous writers. All concerned agree that a given mean difference in the hypothesized direction is more significant under a one-tailed hypothesis (in the correct direction) than under a two-tailed hypothesis. This is due to the fact that there are exactly twice as many chances of

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