Determining Sample Size for Accurate Estimation of the Squared Multiple Correlation Coefficient

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Existing resources primarily focus on sample size determination for hypothesis testing.
• Sample size requirements for hypothesis testing differ significantly from those for accurate parameter estimation.
• Accurate estimation of effect sizes is increasingly important in research.

Purpose of the Study:

• To provide researchers with methods for determining appropriate sample sizes for accurate parameter estimation.
• To specifically address sample size determination for the squared multiple correlation coefficient.
• To highlight the inadequacy of hypothesis testing sample size methods for estimation purposes.

Main Methods:

• Development of regression equations for sample size calculation.
• Focus on estimating the squared multiple correlation coefficient.
• Inclusion of models with up to 20 predictor variables.

Main Results:

• Regression equations are presented to determine the minimum sample size for estimating the squared multiple correlation coefficient.
• Calculated sample sizes for estimation are compared to those required for hypothesis testing.
• The findings demonstrate that sample sizes for estimation are often larger than for hypothesis testing.

Conclusions:

• Researchers must consider the study's purpose (hypothesis testing vs. estimation) when determining sample size.
• Current methods for hypothesis testing sample sizes are insufficient for accurate parameter estimation.
• New guidelines are necessary for sample size determination in estimation contexts, particularly for effect sizes like the squared multiple correlation coefficient.