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Residual Analysis for ANOVA Models

Explore detecting and addressing model deviations in ANOVA through residual analysis. Identify issues like non-constant variance, outliers, and omitted predictors. Learn remedial actions such as weighted least squares and transformations to handle non-normal data.

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Residual Analysis for ANOVA Models

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  1. Residual Analysis for ANOVA Models KNNL – Chapter 18

  2. Residuals

  3. Model Departures Detected With Residuals and Plots • Errors have non-constant variance • Errors are not independent • Existence of Outlying Observations • Omission of Important Predictors • Non-normal Errors • Common Plots • Residuals versus Treatment • Residuals versus Treatment Mean • Aligned Dot Plot (aka Strip Chart) • Residuals versus Time • Residuals versus Omitted Variables • Box Plots, Histograms, Normal Probability Plots

  4. Tests for Constant Variance H0:s12=...=st2

  5. Remedial Measures • Normally distributed, Unequal variances – Use Weighted Least Squares with weights: wij = 1/si2 • Non-normal data (with possibly unequal variances) – Variance Stabilizing Transformations and Box-Cox Transformation • Variance proportional to mean: Y’=sqrt(Y) • Standard Deviation proportional to mean: Y’=log(Y) • Standard Deviation proportional to mean2: Y’=1/Y • Response is a (binomial) proportion: Y’=2arcsin(sqrt(Y)) • Non-parametric tests – F-test based on ranks and Kruskal-Wallis Test

  6. Effects of Model Departures • Non-normal Data – Generally not problematic in terms of the F-test, if data are not too far from normal, and reasonably large sample sizes • Unequal Error Variances – As long as sample sizes are approximately equal, generally not a problem in terms of F-test. • Non-independence of error terms – Can cause problems with tests. Should use Repeated Measures ANOVA if same subject receives each treatment

  7. Nonparametric Tests

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