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- 1. CARLOS ALBIZU UNIVERSITYSAN JUAN CAMPUS<br />MASTER SYLLABUS<br />RMIC- 822: ANALYSIS OF VARIANCE<br />CREDITS: 3CONTACT HOURS: 45<br />COURSE DESCRIPTION<br />This course explores the principles and applications of Analysis of Variance for the treatment of research data in psychology. One, two and three factors Analysis of Variance; Multiple Comparisons (planned versus post hoc comparisons); Analysis of Covariance; Random, Mixed and Fixed Models Analysis of Variance; Analysis of Variance for proportional and non proportional samples, and Analysis of Variance for ordinal scaled variables are among the topics included.<br />PREREQUISITES <br />PSYF-568 Inferential Statistics<br />COURSE OBJECTIVES<br />The course pretends to empower the student with relevant statistical methods of analysis of variance as it applies to behavioral research; It also will enable the student to differentiate among the statistical procedures for analysis of variance suitable for different research situations, to evaluate the advantages and disadvantages of analysis of variance, to properly apply analysis of variance's procedures to actual research data, and to read and properly interpret analysis of variance's results.<br />REQUIRED TEXT BOOKS<br /> <br />Gravetter, F.J., & Wallnau, L.B. (2009). Statistics for the behavioral sciences (8th ed.) Belmont, CA: Cengage Learning (ISBN-13: 978-0-495-60220-0). <br />Shavelson, R. (1996). Statistical reasoning for the behavioral sciences. (3rd ed). Mass.: <br />Allyn and Bacon (ISBN 0-205-18460-X).<br />ITINERARY OF CLASS UNITS<br />Unit 1: Introduction <br />Unit 2: Analysis of Variance: One factor-fixed effect model.<br />Unit 3: Analysis of Variance: One factor-randomized effect model.<br />Unit 4: Multiple comparisons: Tukey and HSD.<br />Unit 5: Multiple comparisons: Scheffé<br />Unit 6: MID TERM EXAM.<br />Unit 7: Analysis of Variance: Repeated measures design (One factor).<br />Unit 8: Analysis of Variance: (Two factors-fixed model).<br />Unit 9: Analysis of Variance: (Two factors-fixed model).<br />Unit 10: Fixed model, randomized model and mixed effect model.<br />Unit 11: Multiple comparisons (Turkey, and HSD)<br />Unit 12: Multiple comparisons (Scheffé)<br />Unit 13: Analysis of Covariance<br />Unit 14: FINAL EXAM <br />COURSE CONTACT HOURS <br />Professors who teach the course must divide the contact hours the following way:<br />Face-to-face time in the classroom must not be less than 40.0 hours (16 classes, 2.5 hours each class).<br />For the remaining hours (≥ 5 hours), students will conduct statistics written assignments or homework outside the classroom. These assignments or homework will include, but are not limited to: statistics homework assignments, some using statistical software. <br />METHODOLOGY<br />Weekly conferences by the professor, discussion of assigned readings, small group discussions, as well as practical assignments and applications of statistical procedures, are among the methodologies to be considered during the course. <br />EDUCATIONAL TECHNIQUES<br />The specific educational techniques will be selected by the professor who offers the course. These techniques should include, but not limited to: debates, practical demonstrations, films/videos, simulations, slide shows and forums.<br />EVALUATION <br />The specific methodology will be selected by the professor who offers the course. These methodologies could include, but are not limited to: class participation, literature reviews, exams, class presentations and practical applications of statistical procedures.<br />RESEARCH COMPETENCIES:<br />Develop an overview and understanding of the statistical procedures for analysis of variance and the critical thinking necessary to analyze research data.<br />Develop knowledge in ANOVA statistical techniques used in answering research questions within the field of clinical psychology.<br />Develop competence on how ANOVA simple and complex research designs are important for addressing decision-oriented problems in applied research.<br />Develop competence in applying analysis of variance/covariance models that focuses on acquiring new knowledge.<br />Develop competence in identifying which procedures of analysis of variance and post hoc procedures are the most relevant to the substantive area in which a student intend to conduct research. <br />Develop knowledge of the principles and statistical assumptions underpinning ANOVA factorial designs to analyze complex data sets. <br />Develops a general understanding using SPSS software package for testing hypotheses in ANOVA & ANCOVA research designs.<br />ATTENDANCE POLICY <br />Class attendance is mandatory for all students. After two unexcused absences, the student will be dropped from the class, unless the professor recommends otherwise. When a student misses a class, he/she is responsible for the material presented in class. <br />AMERICANS WITH DISABILITIES ACT (ADA)<br />Students that need special accommodations should request them directly to the professor during the first week of class.<br />COURSE UNITS<br />UNIT 1: INTRODUCTION <br />Upon successful completion of this unit, students should gain understanding of the <br />relationship of the analysis of variance and statistical tests, as well as of the logic behind this particular methodology.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Discuss the role of analysis of variance in inferential statistical.<br />Discuss the fundamental concepts of analysis of variance.<br />Identify the limitations of analysis of variance in behavioral research.<br />Discuss the logic behind the analysis of variance.<br />Analyze the consequences of violating the assumptions underlying the analysis of variance.<br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 1- 3Introduction to Analysis of Variance <br />Shavelson, R. (1996) <br />Chapter 13- One-way Analysis of variance <br />UNIT 2: ANALYSIS OF VARIANCE: ONE FACTOR-FIXED EFFECT MODEL <br />Upon successful completion of this unit, students should gain understanding of the statistical procedures for one factor analysis of variance (fixed effect model), and its relation to the Student test.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Identify the relationship between the F test and the t test (one factor-fixed model-two levels).<br />Identify the differences between the fixed effect model and the randomized effect model.<br />Discuss the concepts of variability between groups and within groups.<br />Explain how variability between groups and within groups represents the variance of the population, when the null hypothesis is true.<br />Explain the concept of variability within groups as a measurement of error.<br />Explain the process of variability between groups as a measurement of error.<br />Discuss the concept of the Proportion of F as the result of the division between the variability between groups with the variability within groups.<br />Explain the concept of total variance as the result of the sum of variability within and variability between groups.<br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 13- Introduction to Analysis of Variance <br />Shavelson, R. (1996) <br />Chapter 13-One-way Analysis of variance <br />UNIT 3: ANALYSIS OF VARIANCE: ONE FACTOR-RANDOMIZED EFFECT MODEL<br />Upon successful completion of this unit, students should gain understanding of <br />the statistical procedures for one factor analysis of variance-randomized effect model, and of the logical theory behind this particular model.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Discuss the logic and theory behind one factor analysis of variance-randomized effect model.<br />Identify the differences between the fixed effect model and the randomized effect model.<br />Explain the computational procedures for calculating an analysis of variance with randomized effect model and fixed effect model with one factor.<br />Analyze the defining formulas for the sum of squares total in one factor-analysis of variance: randomized effect model and fixed effect model.<br />Recognize the formulas for calculating sum of squares between groups and sum of squares within groups for one factor analysis, randomized effect model and fixed effect model.<br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 13– Introduction to Analysis of Variance <br />Shavelson, R. (1996) <br />Chapter 13-One-way Analysis of variance <br />UNIT 4: MULTIPLE COMPARISONS: TUKEY AND HSD<br />Upon successful completion of this unit, students should again an understanding of the statistical procedures behind the analysis of variance, and how to perform and interpret results obtained from multiple comparisons procedures.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Discuss the concepts of degrees of freedom for Sum of Squares Total, Sum of Squares Between Groups, and Sum of Squares Within Groups.<br />Discuss the concepts of mean squares. Total, between groups and within groups.<br />Compute the F ratio.<br />Use an F table to determine the critical value of the F statistic.<br />Present results from an analysis of variance in a Summative Table.<br />Explain when it is necessary to compute multiple comparisons.<br />Mention the uses and limitations of Tukey and HSD.<br />Perform multiple comparisons: Tukey and HSD.<br />Use the studentized table to obtain the critical value.<br />Interpret results from multiple comparison analysis.<br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 13- Introduction to Analysis of Variance <br />Shavelson, R. (1996) <br />Chapter 13-One-way Analysis of variance <br />UNIT 5: MULTIPLE COMPARISONS: SCHEFFÉ <br />Upon successful completion of this unit, students should gain an understanding of <br />the statistical procedures for multiple comparison: Scheffé.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Compare the different procedures for multiple comparisons (Scheffé and Tukey), including their advantages and limitations.<br />Perform multiple comparisons using the Scheffé method.<br />Identify the procedure to determine the critical value for the Scheffé test.<br />Perform complex comparisons using Scheffé: comparing two means with three means.<br />Interpret results from multiple comparison analysis.<br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 13- Introduction to Analysis of Variance <br />Shavelson, R (1996) <br />Chapter 13- One-way Analysis of variance <br />UNIT 6: MID TERM EXAM<br />UNIT 7: ANALYSIS OF VARIANCES: REPEATED MEASURES DESIGN (ONE <br /> FACTOR)<br />Upon successful completion of this unit students should gain understanding <br />of the statistical procedures for analysis of variance: repeated measures design.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Identify the differences between repeated measures designs and independent sample designs.<br />Analyze the basic steps to calculate the Sum of Squares Total, Sum of Squares Between Subjects, Factor and Residual.<br />Analyze the basic steps to calculate the Mean Squares Total, Between Subjects, Factor and Residual.<br />Perform an analysis of variance for a repeated measures design.<br />Perform multiple comparisons, using Tukey, HSD or Scheffé with a repeated measures design.<br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 14- Repeated-Measures ANOVA <br />Shavelson, R. (1996) <br />Chapter 15- Randomized-Blocks Analysis of Variance <br />UNIT 8: ANALYSIS OF VARIANCE (TWO FACTORS-FIXED MODEL)<br />Upon successful completion of this unit students should gain understanding <br />of the statistical procedures for two factors analysis of variance, the F ratio for Factor A, B and the interaction effect (AB). <br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Discuss the advantages of the two factors analysis of variance.<br />Discuss the assumptions underlying the two factors analysis of variance.<br />Discuss the concept of interaction and its implication for theory.<br />Discuss the concepts of factors, levels of the factors, main effects and interaction effects.<br />Analyze examples of interaction and lack of interaction.<br />Construct and interpret graphs for interaction effects.<br />Analyze and interpret examples of interactions between two variables.<br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 15-Two-Factor ANOVA <br />Shavelson, R. (1996) <br />Chapter 14-Factorial Analysis of Variance <br />UNIT 9: ANALYSIS OF VARIANCE (TWO FACTORS-FIXED MODEL)<br />Upon successful completion of this unit, students will gain understanding of the statistical procedures for two factors analysis of variance, the F ratio for Factor A, B and the interaction effect.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Analyze the basic steps to reach the Sum of Squares for Factor A, Factor B and for interaction (AB), and for within groups.<br />Determine and calculate the degrees of freedom for each factor (A and B) and for within groups.<br />Analyze the basic steps to determine the Mean Squares for Factor A, Factor B, and within groups.<br />Perform an analysis of variance (two factors).<br />Analyze and interpret examples of interactions between two variables.<br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 15-Two-Factor ANOVA <br />Shavelson, R. (1996) <br />Chapter 14-Factorial Analysis of Variance <br />UNIT 10: FIXED MODEL, RANDOMIZED MODEL AND MIXED EFFECT MODEL<br />Upon a successful completion for this unit, students should gain understanding of the statistical procedures for two factors analysis of variance when both are random factors, as well as when one factor is fixed and the other is random. Besides, the students should gain an understanding of the underlying theory.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit student should be able to:<br />Discuss the theory underlying the two factors analysis of variance when both are random factors and, when one is fixed and the other random.<br />Identify the proper statistical procedures for estimating mean squares for two factors analysis of variance, when both are random factors and when one is fixed and the other random.<br />Discuss the conclusions that can be derived from the two factors analysis of variance when both are random factors and, when one is fixed and the other random.<br />Familiarize with reading and interpreting, results from two factors analysis of variance when both are random factors and, when one is fixed and the other is random. <br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 15-Two-Factor ANOVA <br />Shavelson, R. (1996) <br />Chapter 14-Factorial Analysis of Variance <br />UNIT 11: MULTIPLE COMPARISONS (TUKEY, AND HSD)<br />Upon successful completion of this unit, students will gain an understanding of the <br />statistical procedures for multiple comparisons; Tukey and HSD, for two factors analysis of variance.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Perform multiple comparisons using Tukey and HSD to determine significance of treatments or main effects.<br />Analyze and interpret examples of interactions between two variables.<br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 15-Two-Factor ANOVA <br />Shavelson, R. (1996) <br />Chapter 14-Factorial Analysis of Variance <br />UNIT 12: MULTIPLE COMPARISONS (SHEFFÉ)<br />Upon successful completion of this units, students will gain an understanding of the <br />statistical procedures for multiple comparisons; Scheffé, for two factors analysis of variance.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Perform multiple comparisons using Scheffé to determine significance of treatments of main effects.<br /> Analyze and interpret examples of interactions between two variables.<br />Use multiple comparisons methods to identify differences within cells. <br />ASSIGNED READINGS:<br />Gravetter, F. J. & Wallnau, L. B. (2009) <br />Chapter 15-Two-Factor ANOVA <br />Shavelson, R. (1996) <br />Chapter 14-Factorial Analysis of Variance <br />UNIT 13: ANALYSIS OF COVARIANCE<br />Upon successful completion of this unit, students should gain an understanding of <br />the statistical procedures for the analysis of Covariance, as well as of the purpose and underlying logic.<br />LEARNING OBJECTIVES:<br />Upon successful completion of this unit students should be able to:<br />Discuss the purpose and underlying logic of the analysis of Covariance. <br />Interpret readings and results from the analysis of Covariance.<br />ASSIGNED READINGS:<br />Shavelson, R. (1996) <br />Chapter 17-Analysis of Covariance <br />UNIT 14: FINAL EXAM<br />REFERENCES<br />Ashcraft, A.S. (1998, April). Ways to evaluate the assumption of multivariate normality. <br />Paper presented at the annual meeting of the Southwestern Psychological <br />Association, New Orleans. (ERIC Document Reproduction Service No. ED 418 095).<br />Bryman, A., & Cramer, D. (2008). Quantitative data analysis with SPSS 14, 15 & 16: A guide for social scientists. New York, NY : Routledge<br />Buser, K.P. (1995, April). Dangers in using ANCOVA to evaluate special education <br />program effects. Paper presented at the annual meeting of the American <br />Educational Research Association, San Francisco. (ERIC Document Reproduction Service No. ED 384 654).<br />Capraro, M. M. (2005). An introduction to confidence intervals for both statistical estimates <br />and effect sizes. Research in the Schools, 12(2), 22–32.<br />Chambers, J., Cleveland, W. , Kleiner, B. , & Tukey, P. (1983). Graphical methods for data analysis. Monterey, CA: Wadsworth.<br />Cohen, J. (1992). A power primer. Psychological Bulletin, 112, 155–159.<br />Cohen, J. (1994). The earth is round (p < .05). American Psychologist, 49, 997– 1003. <br />Coladarci, T., Cobb, C. D., Minium, E. W., & Clarke, R. C. (2004). Fundamentals of <br />statistical reasoning in education. Hoboken, NJ: John Wiley & Sons.<br />Cole, D.A., Maxwell, S.E., Arvey, R. & Salas, E. (1994). How the power of MANOVA can <br />both increase and decrease as a function of the intercorrelations among the dependent variables. Psychological Bulletin, 115(3), 465-474.<br />Cortina, J. M. & Nouri, H. (2000). Effect size for ANOVA designs. Series: Quantitative Applications in the Social Sciences, 129. Sage Publications, Inc.<br />Cronbach, L. J. & Shavelson, R. J. (2004). My current thoughts on coefficient alpha and <br />successor. Procedures in Educational and Psychological Measurement. 64(3), 391-418.<br />González, R. (2008). Data analysis for experimental design. Guilford Press.<br />Glass, G. V. & Hophins, K. D. (1996). Statistical methods for education and psychology <br />(3rd ed). Mass.: Allyn and Bacon.<br />Gravetter, F. J. & Wallnau, L. B. (2009). Statistics for the behavioral sciences (8th ed.). <br />Belmont, CA: Wadsworth Publishing, <br />Green, S.B., & Salkind, N.J. 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Conditions under which mean square ratios in repeated measurements <br />designs have exact F-distributions. Journal of the American Statistical Association, <br />65, 1582-1589.<br />Huynh, H. (1979). Validity conditions in repeated measures designs. Psychological <br />Bulletin, 86, 964-973.<br />Johnson, E.S. (1978). An introduction to experimental design in psychology: A case <br />approach (2nd ed.). New York: Harper & Row.<br />Kachigan, S. K. (1991). Multivariate Statistical Analysis: A Conceptual Introduction (2nd ed.). Radius Press: New York.<br />Keppel, G. & Wickens, T. D. (2004). Design and analysis: A researcher’s handbook. Upper <br />Saddle River, NJ: Pearson Prentice Hall<br />Keselman, H.J. (1977). The Tukey multiple-comparison test: 1953-1976. Psychological <br />Bulletin, 84, 1050-1056.<br />Keselman, H. J., Huberty, C. J., Lix, L. M. , Olejnik, S., Cribbie, R., Donahue, <br />B., Kowalchuk, R. K., Lowman, L. L., Petoskey, M. D., Keselman, J. C., & Levin, J. 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