Related Experiment Video
Updated: Aug 16, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Multiple correlation: exact power and sample size calculations
Abstract:
This article discusses power and sample size calculations for observational studies in which the values of the independent variables cannot be fixed in advance but are themselves outcomes of the study. It reviews the mathematical framework applicable when a multivariate normal distribution can be assumed and describes a method for calculating exact power and sample sizes using a series expansion for the distribution of the multiple correlation coefficient. A table of exact sample sizes for level .05 tests is provided. Approximations to the exact power are discussed, most notably those of Cohen (1977). A rigorous justification of Cohen's approximations is given. Comparisons with exact answers show that the approximations are quite accurate in many situations of practical interest. More extensive tables and a computer program for exact calculations can be obtained from the authors.
More Related Videos
Related Concept Videos
Sample Size Calculation
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...
One-Way ANOVA: Equal Sample Sizes
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
One-Way ANOVA: Unequal Sample Sizes
Bonferroni Test
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
Fisher's Exact Test
Microsoft Excel: Pearson's Correlation

