Confidence Intervals, Power Calculation, and Sample Size Estimation for the Squared Multiple Correlation Coefficient under the Fixed and Random Regression Models: A Computer Program and Useful Standard Tables
Open Access
- 1 August 2001
- journal article
- Published by SAGE Publications in Educational and Psychological Measurement
- Vol. 61 (4) , 650-667
- https://doi.org/10.1177/00131640121971419
Abstract
In this article, the authors introduce a computer package written for Mathematica, the purpose of which is to perform a number of difficult iterative functions with respect to the squared multiple correlation coefficient under the fixed and random models. These functions include, among others, computation of confidence interval upper and lower bounds, power calculation, calculation of sample size required for a specified power level, and providing estimates of shrinkage in cross validating the squared multiple correlation under both the random and fixed models. Attention is given to some of the technical issues regarding the selection of, and working with, these two types of models as well as to issues concerning the construction of confidence intervals.Keywords
This publication has 11 references indexed in Scilit:
- In praise of the null hypothesis statistical test.American Psychologist, 1997
- The appropriate use of null hypothesis testing.Psychological Methods, 1996
- Power analysis and determination of sample size for covariance structure modeling.Psychological Methods, 1996
- What is the probability that null hypothesis testing is meaningless?American Psychologist, 1995
- The earth is round (p < .05).American Psychologist, 1994
- Multiple indicators of children's reading habits and attitudes: Construct validity and cognitive correlates.Journal of Educational Psychology, 1992
- Multiple correlation: Exact power and sample size calculations.Psychological Bulletin, 1989
- A Note on the Estimation of the Level of Predictive Precision of a Fitted Linear EquationPsychometrika, 1977
- A Tale of Two RegressionsJournal of the American Statistical Association, 1974
- A Cross-Validation Approach to Sample Size Determination for Regression ModelsJournal of the American Statistical Association, 1974