1 / 7

Residual Analysis for ANOVA Models

Residual Analysis for ANOVA Models. KNNL – Chapter 18. Residuals. 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

wetherington
Download Presentation

Residual Analysis for ANOVA Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related