A New Formula for Predicting the Shrinkage of the Coefficient of Multiple Correlation

Wherry, Robert J.

doi:10.1214/aoms/1177732951

Cited by 249 publications

(151 citation statements)

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“…The P-values ranged from 0.22 to 0.88 indicating no evidence against the assumption of normality of the residuals. The percentage of variance in the dependent variable (CMJ height) explained by the independent variable(s) in a regression was determined by Wherry's (1931) adjusted R squared value. This represents an attempt to estimate the proportion of variance that would be explained by the model had it been derived from the population (young physically active males) from which the sample was taken.…”

Section: Methodsmentioning

confidence: 99%

Determinants of countermovement jump performance: a kinetic and kinematic analysis

McErlain-Naylor

King

Pain

2014

Journal of Sports Sciences

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This study aimed to investigate the contributions of kinetic and kinematic parameters to inter-individual variation in countermovement jump (CMJ) performance. Two-dimensional kinematic data and ground reaction forces during a CMJ were recorded for 18 males of varying jumping experience.Ten kinetic and eight kinematic parameters were determined for each performance, describing peak lower-limb joint torques and powers, concentric knee extension rate of torque development, and CMJ technique. Participants also completed a series of isometric knee extensions to measure rate of torque development and peak torque. CMJ height ranged from 0.38 -0.73 m (mean 0.55 ± 0.09 m). CMJ peak knee power, peak ankle power, and take-off shoulder angle explained 74% of this observed variation. CMJ kinematic (58%) and CMJ kinetic (57%) parameters explained a much larger proportion of the jump height variation than the isometric parameters (18%), suggesting that coachable technique factors and the joint kinetics during the jump are important determinants of CMJ performance. Technique, specifically greater ankle plantar-flexion and shoulder flexion at take-off (together explaining 58% of the CMJ height variation), likely influences the extent to which maximal muscle capabilities can be utilised during the jump.

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Section: Methodsmentioning

confidence: 99%

Determinants of countermovement jump performance: a kinetic and kinematic analysis

McErlain-Naylor

King

Pain

2014

Journal of Sports Sciences

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“…An informal derivation of this was offered by Diamond (1959, p. 130) First Cohen (1965) and then Winer et al (1991, p. 124) pointed out that the statistic £2 is exactly equivalent to the "shrunken" estimate ofthe multiple correlation coefficient originally proposed by Wherry (1931). Hays (1963, p. 381-385) took an alternative approach based on the deviation of the mean of the ith population from the overall mean, t, = J1i -J1.…”

Section: N -K) Ss(total)mentioning

confidence: 99%

Measures of effect size

Richardson

1996

Behavior Research Methods, Instruments, & Computers

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Twodifferent approaches have been used to derive measures of effect size. One approach is based on the comparison of treatment means, The standardized mean difference is an appropriate measure of effect size when one is merely comparing two treatments, but there is no satisfactory analogue for comparing more than two treatments. The second approach is based on the proportion of variance in the dependent variable that is explained by the independent variable. Estimates have been proposed for both fixed-factor and random-factor designs, but their sampling properties are not well understood. Nevertheless, measures of effect size can allow quantitative comparisons to be made across different studies, and they can be a useful adjunct to more traditional outcome measures such as test statistics and significance levels.Most psychological researchers appreciate in abstract terms at least that statements describing the outcomes of tests of statistical inference need to be distinguished from statements describing the importance of the relevant findings in theoretical or practical terms. The latter may have more to do with the magnitude of the effects in question than their level of statistical significance. Cohen (1965) remarked that in research concerned with comparisons among treatment means, investigators nonetheless typically confined themselves to reporting test statistics such as t or F and did not attempt to derive measures of effect size. More specifically, Craig, Eison, and Metze (1976) surveyed the articles in three different psychological journals that had employed Student's t test; none of these reported a measure of effect size, and in many instances the "significant" effects proved on inspection to be relatively slight in magnitude. Craig et al. concluded that "researchers and journal editors as a whole tend to (over)rely on 'significant' differences as the definition of meaningful research" (p. 282). This situation does not seem to have altered in the intervening time.This paper reviews research on the development and practical value of different measures of effect size. Classically, two different approaches have been taken in deriving such measures. One approach is based on the comparison of different treatment means, and the other approach evaluates the proportion of the variance in the dependent variable that is explained by the independent variable. Winer, Brown, and Michels (1991) noted that the first approach tends to be used in fixed-effects de-The author is grateful to Jacob Cohen, Richard Schweickert, and two anonymous reviewers for their comments on previous versions of this paper. Correspondence should be addressed to 1.T. E. Richardson, Department of Human Sciences, Brunei University, Uxbridge, Middlesex UB8 3PH, United Kingdom (e-mail: john.richardson@ brunel.ac.uk).Copyright 1996 Psychonomic Society, Inc. 12 signs, where the treatments employed exhaust the population of interest. The second approach is typically used in random-effects designs, in which the treatments are regarded as a sample f...

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“…Averaging over uncertainty in the regression coefficients leads to a lower value for R 2 , as with the classical "adjusted R 2 " measure (Wherry, 1931). We discuss this connection further in Section 3.1.1.…”

Section: Proportion Of Variance Explained At Each Levelmentioning

confidence: 85%

Bayesian Measures of Explained Variance and Pooling in Multilevel (Hierarchical) Models

2006

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Explained variance (R 2 ) is a familiar summary of the fit of a linear regression and has been generalized in various ways to multilevel (hierarchical) models. The multilevel models we consider in this paper are characterized by hierarchical data structures in which individuals are grouped into units (which themselves might be further grouped into larger units), and there are variables measured on individuals and each grouping unit. The models are based on regression relationships at different levels, with the first level corresponding to the individual data, and subsequent levels corresponding to between-group regressions of individual predictor effects on grouping unit variables. We present an approach to defining R 2 at each level of the multilevel model, rather than attempting to create a single summary measure of fit. Our method is based on comparing variances in a single fitted model rather than comparing to a null model. In simple regression, our measure generalizes the classical adjusted R 2 . We also discuss a related variance comparison to summarize the degree to which estimates at each level of the model are pooled together based on the level-specific regression relationship, rather than estimated separately. This pooling factor is related to the concept of shrinkage in simple hierarchical models. We illustrate the methods on a dataset of radon in houses within counties using a series of models ranging from a simple linear regression model to a multilevel varying-intercept, varying-slope model. Terms of use: Documents in

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A New Formula for Predicting the Shrinkage of the Coefficient of Multiple Correlation

Cited by 249 publications

References 0 publications

Determinants of countermovement jump performance: a kinetic and kinematic analysis

Determinants of countermovement jump performance: a kinetic and kinematic analysis

Measures of effect size

Bayesian Measures of Explained Variance and Pooling in Multilevel (Hierarchical) Models

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