PSY 530 Analysis of Variance

Announcements | Goals | Required Books | Course Requirements | Assignments | Exams
Examples and Computer Info |

Last updated 09/14/2004

Instructor:
David MacKinnon 

Goals

At the end of the course I expect that you will:

1. be able to compute a variety of ANOVA designs by hand.
2. be able to write computer programs to analyze a variety of ANOVA designs.
3. understand the theoretical rationale for ANOVA.
4. be able to identify ANOVA designs from description of experiments.
5. be able to interpret two-way and higher-way interactions.
6. be able to conduct statistical techniques to identify the source of statistical significance in a
multiple group design.
7. understand how repeated measures and random effects are incorporated in ANOVA.
8. know where to look for information on any ANOVA design that you may encounter in your research.

Required Books

Keppel, G. & Wickens, T. D. (2004). Design and Analysis: A researchers handbook (Fourth Edition) . Englewood Cliffs, New Jersey: Prentice Hall.

Page, M. C., Braver, S. L., & MacKinnon, D. P. (2003). Levine's Guide to SPSS for Analysis of Variance (Second Edition) . Hillsdale, NJ: Lawrence Erlbaum.

Readings on special topics will be available in the Graduate Reading room.

Optional:
Abelson, R. P. (1995). Statistics as a Principled Argument . Hillsdale, NJ: Lawrence Erlbaum. 
SAS and SPSS computer programs

Course Requirements

1. Exams There will be three exams during the course and a final exam. 
2. Discussion Students are expected to participate in class discussions and ask for clarification. 
3. Homework There will be approximately ten homework problem sets depending on material 
covered. The lowest homework score will be dropped. Some homework problem sets may be 
worth twice as many points as others. Some homework problem sets may be required. 

Grading

1. Exams during the semester 54% 
2. Final Exam 22% 
3. Homework 22% 
4. Class Participation 2%
Final grades will be based on the percentage out of 100. 

Active and Cooperative Learning

This class will employ active learning strategies. The purpose of these methods is to engage students in a way that increases retention of the material. It is also more fun and less boring than more traditional lecture-only formats. These strategies will include splitting students into groups of two to five persons.

Resources

The instructor and teaching assistant will be available during office hours. Students are also encouraged to study in small groups and to use any available resources to increase their learning in the course. Some of these resources include other books on analysis of variance, other graduate students, faculty members, and self-study books.

Computer Work

Students will learn how to conduct ANOVA analyses using the Statistical Analysis System (SAS) and Statistical Programs for the Social Sciences (SPSS) computer software. We will use the statistical computing laboratory in room 153 in the Psychology Building. You will be instructed in how to logon and use this system. The computer work for the course will be writing and running programs and interpreting output.

Syllabus

The course will cover analysis of variance (ANOVA) including between subjects, within subjects, mixed designs and designs with random factors. Analysis of variance is the most commonly used analysis method for experimental data in the social sciences. Students will learn the theoretical rationale and methods to compute analysis of variance by hand and with computer software. MS Word Version.

August 24 and 26 (HW1 Out) 
Introduction, History, Research Design, Variability 

Required Reading 
Chapter 1: Experimental Design 
Chapter 2: Sources of Variability and Sums of squares 
Handouts 
August 31 and September 2 (HW1 In; HW2 Out)
Sampling Distributions, One-way Between Subjects ANOVA, Analytical Comparisons 


Required Reading 
Chapter 3: Variance Estimates and the F Ratio
Chapter 4: Analytical Comparisons among Means 
September 7 and 9 (HW2 In; HW3 Out)
Analytical comparisons and Trend Analysis 

Required Reading 
Chapter 4 continued
Chapter 5: Trend Analysis 
September 14 and 16 (HW3 In: Review Questions Out) 
Correction for Experimentwise Error Rates, Assumptions, Review 

Required Reading 
Chapter 6: Simultaneous Comparisons 
Chapter 7: The Linear Model and Its Assumptions 
September 21 and 23 (HW4 Out) 
Assumption, Effect Size, and Power 


Required Reading 
Chapter 7: The Linear Model and Its Assumptions 
Chapter 8: Effect Size, Power, and Sample Size 
First Exam September 21 
September 28 and 30 (HW4 In; HW5 Out) 
Effect Size and Power, Two Factor Design 


Required Reading 
Chapter 8: Effect Size, Power, and Sample Size 
Chapter 9: Using Statistical Software 
Chapter 10 Introduction to the Factorial Design 
Computer Handouts 
October 5 and 7 (HW5 In; HW6 Out) 
Factorial Design 


Required Reading 
Chapter 10: Introduction to Factorial Designs 
Chapter 11: The Overall Two-Factor Analysis 
Computer Readings 
October 12 and 14 (HW6 In; Review Questions Out) 
Detailed Analysis of Main Effects and Simple Effects 


Required Reading 
Chapter 12: Main Effects and Simple Effects 
Chapter 13: The Analysis of Interaction Components 


October 19 and 21 (HW7 Out) 
Three Factor Between Subjects Design 


Required Reading 
Chapter 21: The Overall Three-factor Design 
Chapter 22: The Three-Way Analytical Analysis 
Second Exam October 19 
October 26 and 28 (HW7 In; HW8 Out)
The General Linear Model, Unequal Sample Sizes, and the Within-Subjects Design 


Required Reading 
Chapter 22: The Three-Way Analytical Analysis 
Chapter 14: The General Linear Model 
Chapter 16: The Single-Factor Within Subjects Design 
Computer handouts and problems 
November 2 and 4 (HW8 In; HW9 Out) 
Within-subjects Designs continued 


Required Reading 
Chapter 16 continued 
Chapter 17: Further Within-Subject Topics 
Chapter 18: The Two-Factor Within-subjects Design 
November 9 (HW 9 In; Review Questions Out) and 11 (Veteran's Day, No class) 
Mixed Designs 


Required Reading 
Chapter 19: The Mixed Design: Overall Analysis 
Chapter 20: The Mixed Design: Analytical Analysis 
November 16 and 18 (HW10 Part I Out) 
Mixed Designs continued and Higher-order designs 

Required Reading 
Chapters 19 and 20 continued 
Chapter 26: Higher-Order Designs 
Chapter 24: Random Factors and Generalization 
Third Exam November 16 
November 23 (HW10 Part II Out) and 25 (No Class, Thanksgiving) 
Higher order designs and Special Topics 


Required Reading 
Chapter 24 continued 
Computer Handouts and Projects 
November 30 and December 2 (HW10 In; Review Questions Out) 
Higher order designs and Special Topics 


Required Reading 
Chapter 25: Nested Factors 
Chapter 24 and 26 continued 
Readings 
December 7 
Special Topics and Review 


Required Reading 
None 
Final Exam Thursday December 9 7:40-9:30 
*Note: The syllabus may change. 

Assignments

Homework #1                                          Optional Homework #1
Homework #2                                          Optional Homework #2
Homework #3
Homework #4

Exams

Exam 1 - Tuesday, September 21 Exam 2 - Tuesday, October 19 Exam 3 - Tuesday, Nov. 16 Final - Thursday, Dec. 9, 7:40-9:30am

Exam 1 review questions Answers to Exam 1 Review Exam 2 review questions Exam 3 review questions

Examples and Computer Handouts

Running Programs - Step by step 
SAS Programming Examples
SPSS Programming Examples
Effect Size and Power in the Two-Factor Mixed Design
Link that allows you to do power calculations (scroll towards the bottom).

ANOVA Books

Bogartz, R. S. (1994). An Introduction to the Analysis of Variance. Westport, Connecticut: Praeger.

Box, J. F. (1978). R. A. Fisher, the life of a scientist. New York: Wiley. Written by Fisher's daughter.

*Cortina, J. M. & Nouri, H. (2000). Effect size for ANOVA designs . Thousand Oaks, CA: Sage.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2 nd ed.). Hillsdale, NJ: Erlbaum. Classic power book.

Crowder, M.J. and Hand, D.J. (1990). Monographs on Statistics and Applied Probability 41: Analysis of repeated measures . New York : Chapman and Hall.

Edgington, E. S. (1986). Randomization tests (2 nd ed.). New York: Marcel Dekker.

Edwards, A. L. (1979). Multiple regression and the analysis of variance and covariance . San Francisco: Freeman. ANOVA in regression models.

Edwards, L. K. (Ed.) (1993). Analysis of Variance in the Behavioral Science . New York: Marcel Dekker. Chapters by different authors on current issues in analysis of variance.

Fienberg, S.E. & Hinkley, D.V. (1980). R.A. Fisher: An appreciation . New York: Springer-Verlag. Call #QA276.16.r18 Science Library). Chapters by different authors on Fisher's contributions to many areas of statistics.

Fisher, R. A. (1925). Statistical methods for research workers . Edinburgh: Oliver and Boyd. First book on ANOVA.

Fisher, R. A. (1935). The design of experiments. Edinburgh: Oliver and Boyd. First book on design.

Fisher, R. A. (1959). Statistical Methods and Scientific Inference . New York: Hafner. Call #QA9F54. Classic book more focused on inference and design rather than ANOVA. Clear explanations of many.

Hand, D.J. & Taylor, C.C. (1991). Multivariate analysis of variance and repeated measures . New York: Chapman and Hall.

Hays, W. L. (1973). Statistics for the social sciences . New York: Holt, Rhinehart, and Wilson.

Iverson, G.R. & Norpoth, H. (1976). Analysis of Variance : Sage University Paper series on Quantitative Applications in the Social Sciences. 07-001. Beverly Hills and London: Sage.

*Jackson, S. & Brashers, D.E. (1994). Random factors in ANOVA. Thousand Oaks, CA:Sage.

Keppel, G. (1991). Design and analysis: A researcher's handbook (3 rd ed.) . Englewood Cliffs, New Jersey: Prentice-Hall. Clear substantive and quantitative introduction to analysis of variance.

Keppel, G. & Zedeck, S. (1989). Data analysis for research designs: Analysis of variance and multiple regression/correlation approaches . New York: W.H. Freeman. Covers both ANOVA and regression based analysis for experimental and nonexperimental designs.

*Kirk, R.E. (1995). Experimental Design: Procedures for the Behavioral Sciences. Pacific Grove, CA: Brooks/Cole. Excellent book. Good section on transformations.

Mason, R. L., Gunst, R. F., & Hess, J. L. (1989). Statistical design & analysis of experiments , New York: Wiley.

Mead, R. (1991). The design of experiments: Statistical principals for practical application . Cambridge, UK: Cambridge University Press. Linear models approach to ANOVA. Good resource.

*Murphy, K. R. & Myors, B. (1998). Statistical power analysis: A simple and general model for traditional and modern hypothesis tests . Hillsdale, NJ: Erlbaum. General way to compute power based on the noncentral F.

*Rosenthal, R., Rosnow, R. L., & Rubin, D. B. (2000). Contrasts and effect sizes in behavioral research: A correlational approach . Cambridge, UK: Cambridge University Press.

Salsburg, D. (2001). The lady tasting tea: How statistics revolutionized science in the twentieth century. Freeman: New York. Good overview of statistics.

Scheffe, H. (1959). The Analysis of Variance , New York: Wiley. Call #QA 276.S34 Science Library. Classic and mathematically sophisticated book.

Winer, B.J., Brown, D.R., & Michels, K.M. (1991). Statistical Principles in Experimental Design (3 rd Edition) . New York: McGraw-Hill. Excellent book. Good resource. The third edition by the last two authors was completed after Winer died.

*Woodward, J. A., Bonett, D.G. & Brecht. M.L. (1990). Introduction to linear models and experimental design , : New York : Harcourt Brace Jovanovich. Excellent book describing the linear model approach to ANOVA.

*books which were considered for Psy 530.

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