In meta-analysis, effect sizes often need to be converted into a common metric. For this purpose conversion formulas have been constructed; some are exact, others are approximations whose accuracy has not yet been systematically tested. We performed Monte Carlo simulations where samples with pre-specified population correlations between the…

The authors examined 2 approaches for determining the required sample size of Welch's test for detecting equality of means when the greatest difference between any 2 group means is given. It is shown that the actual power obtained with the sample size of the suggested approach is consistently at least as great as the nominal power. However, the…

In the present Monte Carlo simulation study, the authors compared bias and precision of 7 sampling error corrections to the Pearson r[superscript 2] under 6 x 3 x 6 conditions (i.e., population ρ values of 0.0, 0.1, 0.3, 0.5, 0.7, and 0.9, respectively; population shapes normal, skewness = kurtosis = 1, and skewness = -1.5 with kurtosis =…

Often researchers face situations where comparative studies between two or more programs are necessary to make causal inferences for informed policy decision-making. Experimental designs employing randomization provide the strongest evidence for causal inferences. However, many pragmatic and ethical challenges may preclude the use of randomized…

Research pertaining to the distortion of the squared canonical correlation coefficient has traditionally been limited to the effects of sampling error and associated correction formulas. The purpose of this study was to compare the degree of attenuation of the squared canonical correlation coefficient under varying conditions of score reliability.…

When two or more univariate population means are compared, the proportion of variation in the dependent variable accounted for by population group membership is eta-squared. This effect size can be generalized by using multivariate measures of association, based on the multivariate analysis of variance (MANOVA) statistics, to establish whether…

One of the main objectives in meta-analysis is to estimate the overall effect size by calculating a confidence interval (CI). The usual procedure consists of assuming a standard normal distribution and a sampling variance defined as the inverse of the sum of the estimated weights of the effect sizes. But this procedure does not take into account…

Most psychology journals now require authors to report a sample value of effect size along with hypothesis testing results. The sample effect size value can be misleading because it contains sampling error. Authors often incorrectly interpret the sample effect size as if it were the population effect size. A simple solution to this problem is to…

Eta-Squared (ES) is often used as a measure of strength of association of an effect, a measure often associated with effect size. It is also considered the proportion of total variance accounted for by an independent variable. It is simple to compute and interpret. However, it has one critical weakness cited by several authors (C. Huberty, 1994;…

The meta-analytic random effects model assumes that the variability in effect size estimates drawn from a set of studies can be decomposed into two parts: heterogeneity due to random population effects and sampling variance. In this context, the usual goal is to estimate the central tendency and the amount of heterogeneity in the population effect…

This paper suggests that statistical significance testing and effect size are two sides of the same coin; they complement each other, but do not substitute for one another. Good research practice requires that both should be taken into consideration to make sound quantitative decisions. A Monte Carlo simulation experiment was conducted, and a…

Monte Carlo studies explored the sampling characteristics of Cohen's d and three approximations to Cohen's d when used as average effect size measures in meta-analysis. Reviews of 10, 100, and 500 studies (M) were simulated, with degrees of freedom (df) varied in seven steps from 8 to 58. In a two independent groups design, samples were obtained…

The standardized group mean difference, Cohen's "d", is among the most commonly used and intuitively appealing effect sizes for group comparisons. However, reporting this point estimate alone does not reflect the extent to which sampling error may have led to an obtained value. A confidence interval expresses the uncertainty that exists between…