Ezekiel’s classic estimator of the population squared multiple correlation coefficient: Monte Carlo-based extensions and refinements

Abstract

Ezekiel’s adjusted R² is widely used in linear regression analysis. The present study examined the statistical properties of Ezekiel’s measure through a series of Monte Carlo simulations. Specifically, we examined the bias and root mean squared error (RMSE) of Ezekiel’s adjusted R² relative to (a) the sample R² statistic, and (b) the sample R² minus the expected value of R². Simulation design factors consisted of sample sizes (N?=?50, 100, 200, 400), number of predictors (2, 3, 4, 5, 6), and population squared multiple correlations (ρ² = 0, .10, .25, .40, .60). Factorially crossing these design factors resulted in 100 simulation conditions. All populations were normal/Gaussian, and for each condition, we drew 10,000 Monte Carlo samples. Regarding systematic variation (bias), results indicated that with few exceptions, Ezekiel’s adjusted R² demonstrated the lowest bias. Regarding unsystematic variation (RMSE), the performance of Ezekiel’s measure was comparable to the other statistics, suggesting that the bias-variance tradeoff is minimal for Ezekiel’s adjusted R². Additional findings indicated that sample size-to-predictor ratios of 66.67 and greater were associated with low bias and that ratios of this magnitude were accompanied by large sample sizes (N?=?200 and 400), thus suggesting that researchers using Ezekiel’s adjusted R² should aim for sample sizes of 200 or greater in order to minimize bias when estimating the population squared multiple correlation coefficient. Overall, these findings indicate that Ezekiel’s adjusted R² has desirable properties and, in addition, these findings bring needed clarity to the statistical literature on Ezekiel’s classic estimator.     

I’ll just watch: Do the pro-social effects of coordination really generalize to non-actors?

ABSTRACT

Moving in time together has been shown to cultivate pro-social effects in co-actors, such as cooperation and helping. But less is known about who these effects apply to – whether they are restricted only to co-actors, or whether they generalize to those not involved in the coordination. One difference between past work finding generalized vs. restricted effects is whether these “outsiders” were present for the coordination or not. The present study explores whether the pro-social effects of coordination are seen towards observers as well as co-actors, and whether the absence or presence of observers during the coordination is a determining factor. Results show that greater cooperation following coordination is only seen amongst co- actors, regardless of whether the observers were present during the task or not. Findings are discussed in the context of the literature and alternative explanations for research showing generalized effects are suggested.     

Providing more or less detailed information in job advertisements—Does it matter?

Job advertising is a common and useful recruitment marketing method that is available to a wide range of candidates and offers a practical way to widen the applicant pool. Frequently, retail advertisements only briefly introduce job requirements, but others provide more detailed information. Existing message studies, however, are inconclusive about the effectiveness of message specificity. A scenario‐based experiment that included 164 participants revealed that the type of decision maker (maximizer or satisficer) moderates the specificity effects in recruitment messages. After receiving a detailed job message, more satisficers stop their search process, but only maximizers perceive the company as more attractive and increase intentions toward the advertised job. A follow‐up qualitative study involving 30 participants provided further insights.