Applied Statistics Analysis of Variance and Regression

The late Olive Jean Dunn, PhD, was Professor Emerita of Biostatistics and Biomathematics at the University of California, Los Angeles.

Virginia A. Clark, PhD, is Professor Emerita of Biostatistics and Biomathematics at the University of California, Los Angeles.

1. Data Screening.

1.1 Variables and Their Classification.

1.2 Describing the Data.

1.3 Departures from Assumptions.

1.4 Summary.

2. One-Way Analysis of Variance Design.

2.1 One-Way Analysis of Variance with Fixed Effects.

2.2 One-Way Analysis of Variance with Random Effects.

2.3 Designing an Observational Study or Experiment.

2.4 Checking if the Data Fit the One-Way ANOVA Model.

2.5 What to Do if the Data Do Not Fit the Model.

2.6 Presentation and Interpretation of Results.

2.7 Summary.

3. Estimation and Simultaneous Inference.

3.1 Estimation for Single Population Means.

3.2 Estimation for Linear Combinations of Population Means.

3.3 Simultaneous Statistical Inference.

3.4 Inference for Variance Components.

3.5 Presentation and Interpretation of Results.

3.6 Summary.

4. Hierarchical or Nested Design.

4.1 Example.

4.2 The Model.

4.3 Analysis of Variance Table and F Tests.

4.4 Estimation of Parameters.

4.5 Inferences with Unequal Sample Sizes.

4.6 Checking If the Data Fit the Model.

4.7 What to Do If the Data Don't Fit the Model.

4.8 Designing a Study.

4.9 Summary.

5. Two Crossed Factors: Fixed Effects and Equal Sample Sizes.

5.1 Example.

5.2 The Model.

5.3 Interpretation of Models and Interaction.

5.4 Analysis of Variance and F Tests.

5.5 Estimates of Parameters and Confidence Intervals.

5.6 Designing a Study.

5.7 Presentation and Interpretation of Results.

5.8 Summary.

6 Randomized Complete Block Design.

6.1 Example.

6.2 The Randomized Complete Block Design.

6.3 The Model.

6.4 Analysis of Variance Table and F Tests.

6.5 Estimation of Parameters and Confidence Intervals.

6.6 Checking If the Data Fit the Model.

6.7 What to Do if the Data Don't Fit the Model.

6.8 Designing a Randomized Complete Block Study.

6.9 Model Extensions.

6.10 Summary.

7. Two Crossed Factors: Fixed Effects and Unequal Sample Sizes.

7.1 Example.

7.2 The Model.

7.3 Analysis of Variance and F Tests.

7.4 Estimation of Parameters and Confidence Intervals.

7.5 Checking If the Data Fit the Two-Way Model.

7.6 What To Do If the Data Don't Fit the Model.

7.7 Summary.

8. Crossed Factors: Mixed Models.

8.1 Example.

8.2 The Mixed Model.

8.3 Estimation of Fixed Effects.

8.4 Analysis of Variance.

8.5 Estimation of Variance Components.

8.6 Hypothesis Testing.

8.7 Confidence Intervals for Means and Variance Components.

8.8 Comments on Available Software.

8.9 Extensions of the Mixed Model.

8.10 Summary.

9. Repeated Measures Designs.

9.1 Repeated Measures for a Single Population.

9.2 Repeated Measures with Several Populations.

9.3 Checking if the Data Fit the Repeated Measures Model.

9.4 What to Do if the Data Don't Fit the Model.

9.5 General Comments on Repeated Measures Analyses.

9.6 Summary.

10. Linear Regression: Fixed X Model.

10.1 Example.

10.2 Fitting a Straight Line.

10.3 The Fixed X Model.

10.4 Estimation of Model Parameters and Standard Errors.

10.5 Inferences for Model Parameters: Confidence Intervals.

10.6 Inference for Model Parameters: Hypothesis Testing.

10.7 Checking if the Data Fit the Regression Model.

10.8 What to Do if the Data Don't Fit the Model.

10.9 Practical Issues in Designing a Regression Study.

10.10 Comparison with One-Way ANOVA.

10.11 Summary.

11. Linear Regression: Random X Model and Correlation.

11.1 Example.

11.2 Summarizing the Relationship Between X and Y.

11.3 Inferences for the Regression of Y and X.

11.4 The Bivariate Normal Model.

11.5 Checking if the Data Fit the Random X Regression Model.

11.6 What to Do if the Data Don't Fit the Random X Model.

11.7 Summary.

12. Multiple Regression.

12.1 Example.

12.2 The Sample Regression Plane.

12.3 The Multiple Regression Model.

12.4 Parameters Standard Errors, and Confidence Intervals.

12.5 Hypothesis Testing.

12.6 Checking If the Data Fit the Multiple Regression Model.

12.7 What to Do If the Data Don't Fit the Model.

12.8 Summary.

13. Multiple and Partial Correlation.

13.1 Example.

13.2 The Sample Multiple Correlation Coefficient.

13.3 The Sample Partial Correlation Coefficient.

13.4 The Joint Distribution Model.

13.5 Inferences for the Multiple Correlation Coefficient.

13.6 Inferences for Partial Correlation Coefficients.

13.7 Checking If the Data Fit the Joint Normal Model.

13.8 What to Do If the Data Don't Fit the Model.

13.9 Summary.

14. Miscellaneous Topics in Regression.

14.1 Models with Dummy Variables.

14.2 Models with Interaction Terms.

14.3 Models with Polynomial Terms.

14.4 Variable Selection.

14.5 Summary.

15. Analysis of Covariance.

15.1 Example.

15.2 The ANCOVA Model.

15.3 Estimation of Model Parameters.

15.4 Hypothesis Tests.

15.5 Adjusted Means.

15.6 Checking If the Data Fit the ANCOVA Model.

15.7 What to Do if the Data Don't Fit the Model.

15.8 ANCOVA in Observational Studies.

15.9 What Makes a Good Covariate.

15.10 Measurement Error.

15.11 ANCOVA versus Other Methods of Adjustment.

15.12 Comments on Statistical Software.

15.13 Summary.

16. Summaries, Extensions, and Communication.

16.1 Summaries and Extensions of Models.

16.2 Communication of Statistics in the Context of Research Project.

Appendix A.

A.1 Expected Values and Parameters.

A.2 Linear Combinations of Variables and Their Parameters.

A.3 Balanced One-Way ANOVA, Expected Mean Squares.

A.4 Balanced One-Way ANOVA, Random Effects.

A.5 Balanced Nested Model.

A.6 Mixed Model.

A.7 Simple Linear Regression—Derivation of Least Squares Estimators.

A.8 Derivation of Variance Estimates from Simple Linear Regression.

Appendix B.

Index.

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