Using the Extreme Groups Strategy When Measures Are Not Normally Distributed

Abstract

The extreme groups research strategy is a twostage measurement procedure that may be employed when it is relatively simple and inexpensive to obtain data on a psychological variable (X) in the first stage of investigation, but it is quite complex and expensive to measure subsequently a second variable (Y). This strategy is related to the selection of upper and lower groups for item discrimination analysis (Kelley, 1939) and to the treatments x blocks design in which participants are first "blocked" on the X variable and then only the extreme (highest and lowest means) blocks are compared on the Y variable, usually by a t test or an analysis of variance. Feldt (1961) showed analytically that if the population correlation coefficient between X and Y is p = .10, the power of the t test is maximized if each extreme group consists of 27% of the population tested on the X variable. However, Feldt's derivation assumes that the X and Y variables are normally distributed. The present study employed a monte carlo simulation to explore the question of how to optimize power in the extreme groups strategy when sampling from non-normal distributions. The results showed that the optimum percent for the extreme group selection was approximately the same for all population shapes except for the extremely platykurtic (uniform) distribution. The power of the extreme groups strategy under conditions of normality was compared to the power of other research strategies, and an extension of the extreme groups approach was developed and applied in an example. Index terms: construct validation; extreme-group design; monte carlo technique; non-normal distributions; statistical power; upper-lower index.The extreme groups research strategy is a two-stage procedure that sometimes is employed when it is relatively simple and inexpensive to measure a psychological variable (X) in the first stage of investigation, but it is quite complex and expensive to obtain data subsequently on a second variable (Y). This situation often exists in the early stages of validating a concept such as was done, for example, by Taylor (1951) with the Manifest Anxiety Scale and by Glass (1977) with the Type A Behavior Pattern. This approach is related to the treatments x blocks experimental design (Myers, 1979) in which participants are first &dquo;blocked&dquo; on the X variable and then only the extreme (highest and lowest means) blocks are used in collecting data on the Y variable. The means of the two blocks then are compared, usually by a t test or an analysis of variance (ANOVA). Feldt (1961) showed analytically that if the population correlation coefficient between X and Y is p = .10, the power of the t test is maximized if each extreme group consists of 27 Vo of the population tested on the X variable. As p increases, the optimum percent decreases slightly; for example, at p = .8, power is greatest when 23% of each tail of the X distribution is used. This is similar to the result obtained by Kelley (1939) in the selection of upper and lower groups for item ...

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