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Multiple correlation: exact power and sample size calculations.

C Gatsonis, A R Sampson

    Psychological Bulletin
    |November 1, 1989
    PubMed
    Summary
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    Calculating power and sample size for observational studies is complex when variables are outcomes. This study provides exact methods and validates approximations for accurate statistical power calculations.

    Area of Science:

    • Statistics
    • Biostatistics
    • Epidemiology

    Background:

    • Power and sample size calculations are crucial in research design.
    • Traditional methods often assume fixed independent variables, which is not always feasible in observational studies.
    • Accurate calculations are essential for reliable research findings.

    Purpose of the Study:

    • To develop and present methods for calculating statistical power and sample size in observational studies.
    • To address scenarios where independent variables are study outcomes, not predetermined.
    • To provide a rigorous framework and practical tools for researchers.

    Main Methods:

    • Review of mathematical frameworks for power and sample size calculations.
    • Application of a series expansion for the distribution of the multiple correlation coefficient.

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  • Comparison of exact calculations with existing approximations, including Cohen's (1977).

    • Main Results:

    • A method for exact power and sample size calculation is described.
    • A table of exact sample sizes for significance level .05 tests is provided.
    • Cohen's approximations for power are rigorously justified and shown to be accurate in many practical situations.

    Conclusions:

    • The presented methods offer accurate solutions for power and sample size in complex observational studies.
    • Validated approximations provide practical and reliable alternatives for researchers.
    • Tools for exact calculations are available to aid study design.