Confusion of empirical and statistical aspects that lead to controversy

Gaito, John

doi:10.3758/bf03330357

Cited by 2 publications

(1 citation statement)

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“…(A two-tailed test, on the other hand, is an unbiased split-tailed test.) R.J. Harris therefore agrees with Gaito (1987) and Howell (1987, p. 70) that a one-tailed test is never appropriate in a research setting, though it might be reasonable in some applied settings. Nevertheless, onetailed tests are much more common than all other forms of biased, splittailed tests.…”

Section: Split-tailed (Including One-tailed) Testssupporting

confidence: 67%

The Minimally Important Difference Significant Criterion for Sample Size

Harris¹,

Quade²

1992

Journal of Educational Statistics

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Key words: power, sample sizeFor a wide range of fests of single-df hypotheses, the sample size needed to achieve 50% power ii readily approximated by setting N such chat atignificance test tonducted donatataat fit one's assumptions perfectly just barely achieves statistical significance at one's chosen alpha levele If thIfffect size assumed in establishing gne's N is the minimally important effect sizs (i.e., that effect size such that populatioonifferences or correlations smaller than that are not of any practical or theoretical significance, whethee statistically significant or not), then 50% power is optimall becaussehe probability of rejecting the null hypothesis should de greater than .5 when the population difference is of practtcal lo theoretical aignificance but lower that .5 whew it is not. Moreover, ,he ectual power of tht test in this casc will be considerably higher than .5, exceeding . 95 for a population difference two or more times as large es the minimally important difference (MID). This misimally important difference significant (MIDS) criterion extends naturally to specific comparisons following (or substituting for) )verall testesuch as theANOVA F and chi-square for contingency tables, although ghe power of thf overall test (i.e., the probability of finding some statisticalllyignificant specific An earlier version of this article was presented at the meeting of the Society for Multivariate Experimental Psychology (SMEP), Berkeley, 10/31/85. The application to proving the modified H Q was presented at the SMEP meetings in Newportt RI, 10/26/90. Matters of style and extreme bias against one-tailed tests should be attributed to the first author (RJH), who prepared the original manuscript. Contributions of the second author (DQ) include: (a) checking several of the claims of this article via Monte Carlo runs on a PC; (b) checking how seriously the various findings are affected by using integer, rather than fractional, N; (c) discovering that simply adding two or three observations to the nMmS, computed as if cr were known, yields a very close approximation to n M mS for the variance-estimated case; and (d) the insight that the TV needed to prove H 0m is simply four times n M iDs when H 0 is true, which inspired RJH's development of the more general expressions for « PH OM. Thanks, too, to Mary B. Harris for comments contributing to the readability of this article.

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Section: Split-tailed (Including One-tailed) Testssupporting

confidence: 67%