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Numerical evaluation of cytologic data. VII. Multivariate significance tests
Analytical and Quantitative Cytology
|March 1, 1981
Summary
This study examines multivariate analysis, including Hotelling's T2 test, Wilks' lambda, and Box's M statistic. It assesses the risk of incorrectly identifying chance differences as significant, highlighting limitations in determining the cause of observed variations.
Area of Science:
- Statistics
- Multivariate Analysis
Background:
- Multivariate analysis is frequently employed to detect subtle differences between samples.
- Assessing the significance of these differences often involves managing the risk of Type I errors (false positives).
Purpose of the Study:
- To present methods for evaluating the probability of Type I errors in multivariate analysis.
- To discuss the sensitivity and specificity of common multivariate test statistics.
Main Methods:
- Numerical examples are provided for three key multivariate test statistics.
- Hotelling's T2 test, Wilks' lambda, and Box's M statistic are examined.
- The focus is on assessing the chance that observed differences are due to random variation.
Main Results:
- The study evaluates the Type I error rate (alpha) for selected multivariate tests.
- Hotelling's T2 test measures inter-group significance.
- Wilks' lambda assesses group separation, and Box's M tests equality of variance-covariance matrices.
Conclusions:
- While multivariate tests are sensitive to detecting differences, they may lack specificity.
- These statistics help identify significant variations but do not definitively determine their causes.
- Understanding the limitations of test power is crucial for accurate interpretation.