Sample size for multiple regression: obtaining regression coefficients that are accurate, not simply significant

Area of Science:

• Statistics
• Quantitative Psychology
• Econometrics

Background:

• Traditional sample size planning often focuses on statistical power.
• Accurate parameter estimation is crucial for reliable regression models.
• Existing methods may not adequately address the precision of effect size estimates.

Purpose of the Study:

• To present a novel sample size planning approach emphasizing Accuracy in Parameter Estimation (AIPE) for multiple regression.
• To provide methods for determining sample sizes that yield narrow confidence intervals for regression coefficients.
• To contrast AIPE with traditional power analytic approaches.

Main Methods:

• Developed an AIPE method to calculate sample size based on a specified expected confidence interval width for standardized regression coefficients.
• Introduced an enhanced AIPE formulation to guarantee confidence interval width with a certain probability.
• Discussed implications for standardized coefficients and random predictors.

Main Results:

• The AIPE approach provides a direct link between sample size and the precision of parameter estimates.
• The enhanced formulation offers a probabilistic guarantee on the achieved precision.
• Sample size recommendations are tailored to achieve specific confidence interval widths.

Conclusions:

• AIPE offers a valuable alternative to power analysis for sample size planning in multiple regression.
• This approach enhances the interpretability and reliability of regression findings.
• Researchers can achieve desired estimation accuracy by applying AIPE methods.