Browsing by Author "Alliger, George M."

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    Correcting for range restriction when the population variance is unknown
    (1984) Alexander, Ralph A.; Alliger, George M.; Hanges, Paul J.
    Correction of correlations diminished by range restriction is a commonly suggested psychometric technique. Such corrections may be appropriate in applied settings, such as educational or personnel selection, or in more theoretical applications, such as meta-analysis. However, an important limitation on the practice of range restriction corrections exists-an estimate of the unrestricted population variance is required. This article outlines and examines the accuracy of a method for estimating the unrestricted variance of a variable from the restricted sample itself. This method is based on the observation that it is possible to table a function of the truncated normal distribution that will allow the extent or point of truncation to be estimated (Cohen, 1959). The correlation of the truncated variable with other variables may then be corrected by standard restriction of range formulas. The method also allows for correction of the mean of the restricted variable.
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    Correcting for restriction of range in both X and Y when the unrestricted variances are unknown
    (1985) Alexander, Ralph A.; Hanges, Paul J.; Alliger, George M.
    Correction of correlation coefficients that have arisen from range restricted populations is commonly suggested and practiced in research on testing and measurement. Until recently, that research has operated under two important limitations. First, the majority of the research has dealt with range restriction on one variable only, and second, the correction formulas have assumed that the variance of the variable(s) in the unrestricted population was known. This article presents a method for estimating such corrections from the data in the restricted sample and applies the method to a recently developed approximation for restriction on both and Y. The procedure is evaluated and found to produce sufficiently accurate results to be useful in many practical range restriction settings.
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    Correction for restriction of range when both X and Y are truncated
    (1984) Alexander, Ralph A.; Carson, Kenneth P.; Alliger, George M.; Barrett, Gerald V.
    The effect of range restriction on one variable in a bivariate normal distribution on the X-Y correlation and the problem of estimating unrestricted from restricted correlations has been widely studied for more than half a century. The behavior of correction formulas under truncation of both X and Y, however, remains largely unresearched. The performance of the correction formula for unidimensional truncation (Thorndike, 1947, Case 2) and an approximation procedure for correcting for bidimensional truncation proposed by Wells and Fruchter (1970) were investigated. The Thorndike correction formula undercorrects in most circumstances. The Wells and Fruchter procedure performs quite well under most conditions but often results in a slight overcorrection. The performance of the Wells and Fruchter and Thorndike formulas are also compared under truncation on X or Y alone. In these circumstances the Wells and Fruchter correction is either equal or markedly superior to the traditional correction. Based on overall performance in recapturing the unbiased population values under both unidimensional and bidimensional truncation, the Wells and Fruchter correction is recommended as the preferred procedure in many practical settings.