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How Many Subjects Does It Take To Do A Regression Analysis.

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    Common rules for minimum sample size in multiple regression are unreliable. Power analyses suggest researchers should consider effect size and number of predictors for accurate sample size determination.

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    Area of Science:

    • Statistics
    • Psychometrics

    Background:

    • Rules-of-thumb for minimum sample size in multiple regression are widely used but lack empirical support.
    • Existing guidelines often fail to account for crucial factors like effect size and the number of predictors.

    Purpose of the Study:

    • To evaluate the validity of common rules-of-thumb for determining minimum sample size in multiple regression analyses.
    • To compare rules-of-thumb against power analyses for hypothesis testing of multiple and partial correlations.

    Main Methods:

    • Comparison of established rules-of-thumb with results derived from power analyses.
    • Evaluation of rules based on constant subject numbers or subject-to-predictor ratios.
    • Assessment of rules considering the number of predictors (m) and sample size (N).

    Main Results:

    • Rules-of-thumb based on constant minimum subjects or subject-to-predictor ratios were not supported.
    • Limited support was found for specific rules like N ≥ 50 + 8m (multiple correlation) and N ≥ 104 + m (partial correlation).
    • These supported rules-of-thumb can overestimate sample size needs and assume medium effect sizes.

    Conclusions:

    • Researchers should move beyond simplistic rules-of-thumb for sample size determination in multiple regression.
    • A more nuanced approach incorporating effect size alongside the number of predictors is recommended.
    • Utilizing methods that integrate effect size is crucial for accurate sample size estimation.