East Carolina University
Department of Psychology
One-Tailed NHST
In Psychology, the norm is to employ non-directional rather than directional tests of hypotheses. Some have teased us about this, noting that theory in Psychology is so retarded that it cannot even predict the direction of associations between variables. Directional hypotheses are met with suspicion, as some will expect that the prediction was made a posteriori, after observing the data. This suspicion is likely to be greatest with the p value is less than .05 for the directional test and over .05 for the nondirectional test.
IMHO, there are cases where a strong argument could be made for the use of directional tests, three of which are detailed below.
When testing a directional hypothesis logically derived from a formal theory. The null is that the theory incorrectly predicts the direction, the alternative is that it correctly predicts the direction. Given sufficient power, if the null cannot be rejected, one suggests that the theory needs revision.
When a result in one direction, while conceivable, would seem to be nonsensical. My favorite example here is the research done by Porter et al. in 1983. Mothers were presented with two containers, one containing a garment worn by their newborn infant for about a day, the other containing a garment worn by another newborn infant for about a day. The mothers were asked to sniff through a portal in each box and try to identify the one containing their own baby's garment. Sixteen of twenty mothers correctly identified the box with their own baby's garment. By a one-tailed binomial test, p = .006. Using the traditional .05 criterion of statistical significance, this would also have been statistically significant with a non-directional test. What, however, would Porter et al. have done if only four of twenty mothers had correctly identified their own baby's garment. Would they have discarded the directional test, gone with a non-directional test, and then come up with explanation of why mothers prefer the smell of a stranger's baby?
When testing the null that a squared quantity has a value of zero -- for example, R2 = 0. Unless you dealing with imaginary numbers, such a parameter cannot have a value less than zero, so a one-tailed test is the only way to go.
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This page most recently revised on the 29th of January, 2013.