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A test for serial correlation in univariate repeated-measures analysis.

E M Hearne, G M Clark, J P Hatch

    Biometrics
    |March 1, 1983
    PubMed
    Summary
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    Univariate F tests in time-factor experiments may be invalid if covariance matrices violate assumptions. This study investigates the serial correlation pattern, finding inflated Type I error rates, and presents a new likelihood ratio test.

    Area of Science:

    • Biostatistics
    • Psychometrics
    • Statistical Analysis

    Background:

    • Time-factor experiments with one grouping and one repeated-measures factor are common in biostatistics and psychometrics.
    • Univariate procedures for F tests with repeated measures require specific covariance matrix assumptions for validity.
    • Violations of these assumptions can impact the accuracy of statistical inference.

    Purpose of the Study:

    • To investigate the robustness of univariate F tests when covariance matrices exhibit a serial correlation (simplex) pattern.
    • To quantify the inflation of Type I error rates under these specific covariance matrix conditions.
    • To introduce a likelihood ratio test for detecting the serial correlation pattern.

    Main Methods:

    • Simulation study examining F test validity under serial correlation patterns.

    Related Experiment Videos

  • Analysis of Type I error rates for repeated-measures effects.
  • Development and presentation of a likelihood ratio test for the serial correlation pattern.

    • Main Results:

    • The study found that for certain serial correlation patterns, the estimated actual probability level of the main-effect repeated-measures F test can exceed three times the nominal 0.05 level.
    • This indicates a significant inflation of Type I error rates, compromising test validity.
    • A likelihood ratio test for the serial correlation pattern was developed.

    Conclusions:

    • Standard univariate procedures may be unreliable in time-factor experiments when covariance matrices follow a serial correlation pattern.
    • Researchers should be cautious about assumption violations and consider alternative analyses or tests.
    • The proposed likelihood ratio test offers a method for assessing the presence of the serial correlation pattern.