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.     

What did mummy say? Dyadic interactions between young "hard to manage" children and their mothers

Thirty preschoolers rated as hard to manage on Goodman's (R. Goodman, 1997) Strengths and Difficulties Questionnaire (SDQ), and a group of matched control children were observed and recorded on audiotape at home, interacting with their mothers (Time 1). At the 18-month follow-up home visits (Time 2), the children and mothers were filmed across 4 observation settings. Mother–child interactions were rated on affect, control, responsiveness and connectedness of communication. At Time 1, mothers of the hard to manage group used more negative control and engaged in fewer connected conversations than did mothers in the control group. At Time 2, mothers of the hard to manage group displayed higher levels of negative control and lower levels of positive control. These results are discussed in terms of the importance of examining connected communication and different observation contexts when examining dyadic mother–child interactions.     

MMPI-2 subgroups in a sample of chronic pain patients

MMPI-2 scores of 307 female and 161 male chronic pain patients were analyzed by gender using a multivariate clustering method. Two subgroups were found for both sexes replicating previous results. The major subgroup corresponded to the classical "Conversion V" and the minor corresponded to the "Generally elevated" profile. The results also indicated a satisfactory internal consistency and a high discriminant validity of the Swedish version of the MMPI-2.     

Predictive Genetic Testing for Hereditary Breast and Ovarian Cancer: Psychological Distress and Illness Representations 1 Year Following Disclosure

This prospective study evaluates emotional functioning and illness representations in 68 unaffected women (34 carriers/34 noncarriers) 1 year after predictive testing for BRCA1/2 mutations when offered within a multidisciplinary approach. Carriers had higher subjective risk perception of breast cancer than noncarriers. Carriers who did not have prophylactic oophorectomy had the highest risk perception of ovarian cancer. No differences were found between carriers and noncarriers regarding perceived seriousness and perceived control of breast and ovarian cancer. Mean levels of distress were within normal ranges. Only few women showed an overall pattern of clinically elevated distress. Cancer-specific distress and state-anxiety significantly decreased in noncarriers from pre- to posttest while general distress remained about the same. There were no significant changes in distress in the group of carriers except for ovarian cancer distress which significantly decreased from pre- to posttest. Our study did not reveal adverse effects of predictive testing when offered in the context of a multidisciplinary approach.     

辩证分析兴奋性氨基酸对神经细胞的双重作用

兴奋性氨基酸（ＥＡＡｓ） 广泛分布于中枢神经系统,参与多种生理过程包括学习、记忆和伤害感受等。然而,ＥＡＡｓ 受体的过度兴奋却可引发一系列细胞事件,最终导致神经元的损伤与死亡。许多神经退行性疾病如早老性痴呆、癫痫和肌侧索硬化症等都与ＥＡＡｓ 的兴奋毒作用有关。目前的研究表明,由ＥＡＡｓ 受体过度兴奋所引发的细胞内钙超载是导致神经元死亡的最终途径     

Examination of the MMPI-2 Restructured Clinical (RC) Scales in a Sample of Bariatric Surgery Candidates

The current study examined the MMPI-2 Restructured Clinical (RC) scales (Tellegen et al., MMPI-2 Restructured Clinical (RC) scales: Development, validation, and interpretation. Minneapolis: University of Minnesota Press, 2003) in a sample of 1,091 bariatric surgery candidates. The RC scales were developed to address concerns about limited discriminant validity of the Clinical scales. Internal consistency and external validity analyses were conducted to evaluate the RC scales in this setting. Results indicated that the RC scales are generally more internally consistent than the Clinical scales and display significantly better convergent and discriminant validity in predicting a variety of behavioral, psychological, and developmental variables relevant to preoperative bariatric psychological evaluations. Implications of the results and recommendations for future research with the RC scales in medical settings are discussed.