Misprescription and misuse of one‐tailed tests

Abstract

One-tailed statistical tests are often used in ecology, animal behaviour and in most other fields in the biological and social sciences. Here we review the frequency of their use in the 1989 and 2005 volumes of two journals (Animal Behaviour and Oecologia), their advantages and disadvantages, the extensive erroneous advice on them in both older and modern statistics texts and their utility in certain narrow areas of applied research. Of those articles with data sets susceptible to one-tailed tests, at least 24% in Animal Behaviour and at least 13% in Oecologia used one-tailed tests at least once.They were used 35% more frequently with nonparametric methods than with parametric ones and about twice as often in 1989 as in 2005. Debate in the psychological literature of the 1950s established the logical criterion that one-tailed tests should be restricted to situations where there is interest only in results in one direction. 'Interest' should be defined; however, in terms of collective or societal interest and not by the individual investigator. By this 'collective interest' criterion, all uses of one-tailed tests in the journals surveyed seem invalid. In his book Nonparametric Statistics, S. Siegel unrelentingly suggested the use of one-tailed tests whenever the investigator predicts the direction of a result.That work has been a major proximate source of confusion on this issue, but so are most recent statistics textbooks. The utility of one-tailed tests in research aimed at obtaining regulatory approval of new drugs and new pesticides is briefly described, to exemplify the narrow range of research situations where such tests can be appropriate.These situations are characterized by null hypotheses stating that the difference or effect size does not exceed, or is at least as great as, some 'amount of practical interest'. One-tailed tests rarely should be used for basic or applied research in ecology, animal behaviour or any other science.

Fluctuating Asymmetry of Human Populations: A Review

“…Studies of fluctuating asymmetry are especially vulnerable to these abuses, which include p-hacking ( [295], but see [296]), overuse of one-tailed tests [297,298], confirmation bias [299], lack of effect-size estimates and confidence intervals [295], poor experimental design, small sample sizes, low statistical power, and lack of replication. p-hacking, the testing of statistical hypotheses until a significant effect is found, is especially problematic, because fluctuating asymmetry is, almost by definition, characterized by "small effects hidden in noisy data" [295].…”

Choosing between two semi-finalists: On academic performance gap, sex category, and decision question

“…(As customary, we use two-tailed tests as a way to compensate for the effects of Type-1 error in this case; see Lombardi and Hurlbert, 2009 Table 2 and Fig. 1, men and women are very similar in their responses to Condition (2).…”

A practical guide to statistical methods for comparing means from two-stage sampling

“…Other problems beyond mis-specification in hypothesis testing include the arbitrary specification of a value for the significance level˛and ignoring the power of a test. These concerns are discussed in greater detail in Balleurka et al (2005), Boruch (2007), Lombardi andHurlbert (2009), Nickerson (2000), Parkhurst (2001), and Ziliak and McCloskey (2008). We employ hypothesis testing with the arbitrary significance level of˛= 0.05 in this study only as a device to compare analytical methods; our focus on Type I error rates (the rate of rejecting a true null hypothesis) is not meant to imply our endorsement of hypothesis testing as a means of assessing hypotheses.…”