Transformations for within-subject designs: A Monte Carlo investigation.

Explored the use of transformations to improve power in within-S designs in which multiple observations are collected for each S in each condition, such as reaction time (RT) and psychophysiological experiments. Often, the multiple measures within a treatment are simply averaged to yield a single number, but other transformations have been proposed. Monte Carlo simulations were used to investigate the influence of those transformations on the probabilities of Type I and Type II errors. With normally distributed data, Z and range correction transformations led to substantial increases in power over simple averages. With highly skewed distributions, the optimal transformation depended on several variables, but Z and range correction performed well across conditions. Correction for outliers was useful in increasing power, and trimming was more effective than eliminating all points beyond a criterion. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Sampling variance in attenuated correlation coefficients: A Monte Carlo study.

Research in validity generalization has generated renewed interest in the sampling error of the Pearson correlation coefficient. The standard estimator for the sampling variance of the correlation was derived under assumptions that do not consider the presence of measurement error or range restriction in the data. The accuracy of the estimator in attenuated or restricted data has not been studied. This article presented the results of computer simulations that examined the accuracy of the sampling variance estimator in data containing measurement error. Sample sizes of n?=?25, n?=?60, and n?=?100 are used, with the reliability ranging from .10 to 1.00, and the population correlation ranging from .10 to 0.90. Results demonstrated that the estimator has a slight negative bias, but may be sufficiently accurate for practical applications if the sample size is at least 60. In samples of this size, the presence of measurement error does not add greatly to the inaccuracy of the estimator. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A Monte Carlo evaluation of three formula estimates of cross-validated multiple correlation.

To determine the stability of regression equations, researchers have typically employed a cross-validation design in which weights are developed on an estimation subset of the sample and then applied to the members of a holdout sample. The present study used a Monte Carlo simulation to ascertain the accuracy with which the shrinkage in R–2 could be estimated by 3 formulas developed for this purpose. Results indicate that R. B. Darlington's (see record 1968-08053-001) and F. M. Lord (1950) and G. E. Nicholson's (1960) formulas yielded mean estimates approximately equal to actual cross-validation values, but with smaller standard errors. Although the Wherry estimate is a good estimate of population multiple correlation, it is an overestimate on population cross-validity. It is advised that the researcher estimate weights on the total sample to maximize the stability of the regression equation and then estimate the shrinkage in R–2 that he/she can expect when going to a new sample with either the Lord-Nicholson or Darlington estimation formulas. (17 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Sampling variance in the correlation coefficient under range restriction: A Monte Carlo study.

Validity generalization methods require accurate estimates of the sampling variance in the correlation coefficient when the range of variation in the data is restricted. This article presents the results of computer simulations examining the accuracy of the sampling variance estimator under sample range restrictions. Range restriction is assumed to occur by direct selection on the predictor. Sample sizes of 25, 60, and 100 are used, with the selection ratio ranging from .10 to 1.0 and the population correlation ranging from .10 to .90. The estimator is found to have a slight negative bias in unrestricted data. In restricted data, the bias is substantial in sample sizes of 60 or less. In all sample sizes, the negative bias increases as the selection ratio becomes smaller. Implications of the results for studies of validity generalization are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)