This article presents a simple, computer-assisted method of determining the extent to which increases in reliability increase the power of the F test of equality of means. The method uses a derived formula that relates the changes in the reliability coefficient to changes in the noncentrality of the relevant F distribution. A readily available computer applet translates the noncentrality parameter into the power value of the F test.
Charter, R.A. ( 1997). Effect of measurement error on tests of statistical significance . Journal of Clinical and Experimental Neuropsychology, 19, 458-462.
2.
Cleary, T.A., & Linn, R.L. ( 1969). Error of measurement and the power of a statistical test . British Journal of Mathematical and Statistical Psychology , 22, 49-55.
3.
Cleary, T.A., Linn, R.L., & Walster, G.W. ( 1970). The effect of reliability and validity on power of statistical tests. Sociological Methodology, 2, 130-138.
4.
Feldt, L.S. ( 1973). What size samples for methods/materials experiments? Journal of Educational Measurement, 10, 221-226.
5.
Feldt, L.S., & Brennan, R.L. ( 1989). Reliability. In R. L. Linn (Ed.), Educational measurement (3rd ed., pp. 105-146). New York, NY: American Council on Education and Macmillan.
6.
Gulliksen, H. ( 1950). Theory of mental tests. New York, NY: Wiley.
7.
Hoover, H.D., Dunbar, S.B., & Frisbie, D.A. ( 2003). Iowa tests of basic skills, manual of norms and score conversions. Itasca, IL: Riverside .
8.
Humphreys, L.G., & Drasgow, F. ( 1989). Some comments on the relation between reliability and statistical power. Applied Psychological Measurement, 13, 419-425.
Nicewander, W.A., & Price, J.M. ( 1983). Reliability of measurement and the power of statistical tests. Psychological Bulletin, 94, 524-533.
11.
Patnaik, P.B. ( 1949). The non-central χ2 and F-distributions and their applications. Biometrika, 36, 202-232.
12.
Pearson, E.S., & Hartley, H.O. ( 1951). Charts of the power function for analysis of variance tests, derived from the non-central F distribution. Biometrika , 38, 112-130.
13.
Scheffé, H. ( 1959). The analysis of variance. New York, NY: Wiley.
14.
Severo, N., & Zelen, M. ( 1960). Normal approximation to the chi-square and non-central F probability functions. Biometrika, 47, 411-416.
15.
Sutcliffe, J.P. ( 1958). Error of measurement and the sensitivity of a test of significance. Psychometrika, 23, 9-17.
16.
Sutcliffe, J.P. ( 1980). On the relationship of reliability to statistical power . Psychological Bulletin, 88, 509-515.
17.
Tiku, M.L. ( 1960). Laguerre series forms of non-central χ2 and F distributions . Biometrika, 52, 415-427.
18.
Walster, G.W., & Cleary, T.A. ( 1970). Statistical significance as a decision rule. Sociological Methodology, 2, 246-254.
19.
Williams, R.H., & Zimmerman, D.W. (1989). Statistical power analysis and reliability of measurement. Journal of General Psychology , 116, 359-369.
20.
Zimmerman, D.W., & Williams, R.H. (1986). Note on the reliability of experimental measures and the power of significance tests. Psychological Bulletin, 100, 123-124.
21.
Zimmerman, D.W., Williams, R.H., & Zumbo, B.D. ( 1993). Reliability of measurement and power of significance tests based on differences. Applied Psychological Measurement , 17, 1-9.
