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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.

For those who have not recognized the disparate natures of tests of statistical hypotheses and tests of scientific hypotheses, one-tailed statistical tests of null hypotheses such as ∂ ≤ 0 or ∂ ≥ 0 have often seemed a reasonable procedure. We earlier reviewed the many grounds for not regarding them as such. To have at least some power for detection of effects in the unpredicted direction, several authors have independently proposed the use of lopsided (also termed split-tailed, directed or one-and-a-half-tailed) tests, two-tailed tests with α partitioned unequally between the two tails of the test statistic distribution. We review the history of these proposals and conclude that lopsided tests are never justified. They are based on the same misunderstandings that have led to massive misuse of one-tailed tests as well as to much needless worry, for more than half a century, over the various so-called 'multiplicity problems'. We discuss from a neo-Fisherian point of view the undesirable properties of multiple comparison procedures based on either (i) maximum potential set-wise (or familywise) type I error rates (SWERs), or (ii) the increasingly fashionable, maximum potential false discovery rates (FDRs). Neither the classical nor the newer multiple comparison procedures based on fixed maximum potential set-wise error rates are helpful to the cogent analysis and interpretation of scientific data.

Pigeons were trained to learn an instrumental oddity-from-sample discrimination involving visual forms. One group, the "few examples" group, dealt with 5 patterns in 40 different combinations. Another group, the "many examples" group, dealt with 20 patterns in 160 different combinations. After both groups had reached asymptotic performance and had learned to operate under partial reinforcement conditions, they were tested for transfer under extinction conditions with two different groups of 5 novel patterns, each in 40 combinations. All animals showed significant above chance transfer to both of these novel stimulus sets. Transfer performance with test stimuli of similar geometric design to training stimuli was better than performance with stimuli of markedly different design. The transfer performance of the "many examples" group was marginally better than that of the "few examples" group, even though the latter's performance on the training stimuli was better throughout. It is concluded that pigeons can learn to employ an oddity concept and that this may be promoted by the use of many training exemplars. Furthermore, it is inferred that pigeons may normally use a mixture of strategies to solve oddity and identity problems.

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