Sample Size Requirements for Accurate Estimation of Squared Semi-Partial Correlation Coefficients.

Area of Science:

• Statistics
• Quantitative Psychology
• Biostatistics

Background:

• The squared multiple correlation coefficient (ρ(2)) is a common metric for variable importance in regression.
• Alternative importance measures include adjusted squared multiple correlation coefficients.
• Both approaches estimate the population squared multiple correlation coefficient difference (Δρ(2)), also known as the squared semi-partial correlation coefficient.

Purpose of the Study:

• To determine the sample size required for accurate estimation of the squared semi-partial correlation coefficient (Δρ(2)).
• To identify key factors influencing the necessary sample size in regression analysis.

Main Methods:

• The study focused on estimating the population squared multiple correlation coefficient difference (Δρ(2)).
• Sample size requirements were analyzed based on desired accuracy levels.

Main Results:

• Sample size adequacy for estimating Δρ(2) is highly dependent on the population squared multiple correlation coefficient (ρ(2)), the population increase in ρ(2), and the desired accuracy.
• The number of predictors demonstrated a minimal impact on the required sample size.

Conclusions:

• Accurate estimation of variable importance in regression necessitates careful sample size planning.
• The findings provide guidance for researchers to select appropriate sample sizes for regression studies, ensuring reliable estimates of Δρ(2).