DIRECTIONAL DECISIONS FOR 2-TAILED TESTS - POWER, ERROR RATES, AND SAMPLE-SIZE

One imposing directional decisions on nondirectional tests will overes timate power, underestimate sample size, and ignore the risk of Type I II error (getting the direction wrong) if traditional calculations-tho se applying to nondirectional decisions-are used. Usually trivial with the z test, the errors might be important where ct is large and effec t size is small or with tests using other distributions. One can avoid the errors by using calculations that apply to directional decisions or by using a directional two-tailed test at the outset, a conceptuall y simpler solution. With a revised concept of power, this article show s calculations for the test; explains how to find its power, Type III error risk, and sample size in statistical tables for traditional test s; compares it to conventional one- and two-tailed tests and to one- a nd two-sided confidence intervals; and concludes that when a significa nce test is planned it is the best choice for most purposes.