Properties of the Spearman Correction for Attenuation for Normal and Realistic Non-Normal Distributions

Abstract

Results are presented of a computer simulation study of the Spearman correction for attenuation using a design originally suggested by Spearman (1904). Two parallel measures were generated for each of two variables with predetermined distribution shapes, correlations between true scores, and population reliability coefficients. The resulting data consisted of error scores, observed scores, sample reliability coefficients, and sample validity coefficients. The correction for attenuation was performed, and means, variances, and relative frequency distributions of both the uncorrected and corrected validity coefficients were analyzed for normal and non-normal distributions. For varying sample sizes and for all population distributions, the means of the corrected sample correlations were very close to the correlation between true scores, provided that the population reliability coefficients were fairly high. The variability of the corrected sample correlations was substantial, even for larger sample sizes. For lower reliability values, there was pronounced overcorrection, combined with extreme variability, especially for smaller sample sizes. Under these conditions, corrections exceeding 1.00 were frequent. The correction for attenuation appears to be useful only if the reliability coefficients of both measures are relatively high and sample size is relatively large. The properties of the correction for attenuation appear to be independent of the shape of the population distribution of test scores, at least for distributions commonly encountered in psychological and educational research.