Sample size and power |
James Dean Brown University of Hawai'i at Manoa |
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In fact, in a follow-up power analysis on the production tests, the observed power (1 - _), which is the probability of correctly rejecting the null hypothesis (Tabachnick & Fidell, 1996: 36-37), was 0.50 for the immediate posttest and 0.11 for the delayed posttest, both of which were fairly low (for more information about power analysis, see Cohen, 1988: Lipsey, 1990). This suggests that the design (i.e., n-size, distributions, and treatment magnitude) may not have been strong enough to detect significant differences.
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The bottom line with regard to power analysis is that there is much to be gained in our understanding of the statistical results of our studies if only we will ask our statistical programs to calculate power.[ p. 34 ]
In a more direct answer to the original question, if the power of a statistical test is sufficient (i.e., is .80 or higher), the sample size is probably sufficient for the common research purposes discussed here. If the power statistic is not larger enough (i.e., is .79 or lower), the researcher might want to consider increasing the sample size and thereby just possibly raise the power of the study. Indeed, it is even possible to use the power statistic to estimate how much larger the sample should be. For an example of this use of power, see Gorsuch (1999, pp. 189-196). [For more on this and related topics, see Cohen, 1988; Kline, 2005; Kraemer & Thiemann, 1987; Lipsey, 1990; Murphy & Myors, 2004; Rosenthal, Rosnow, & Rubin, 2000; and Thompson, 2006.]Where to Submit Questions: |
Please submit questions for this column to the following address: |
JD Brown Department of Second Language Studies University of Hawai'i at Manoa 1890 East-West Road Honolulu, HI 96822 USA |
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