DESIGN OF EXPERIMENTS



STA 5206 Syllabus






Prerequisites: STA 4322 or STA 3164 or STA 3033 or (STA 3163 and STA 4321).
Terms Offered: Fall
Text: Fundamental Concepts in the Design of Experiments, 5th ed.,by C. R. Hicks and K. V. Turner, Jr.

1. INTRODUCTION. Research design principles. The planning of an experiment. Basic terminology and concepts in experimental designs.

2. THE COMPLETELY RANDOMIZED DESIGN (CRD). The one-factor experiment in a CRD. Randomization. Linear statistical model. Null and research hypotheses and corresponding reduced and full models. Least squares method of estimation of the parameters involved in a linear model. Analysis of variance (ANOVA). The F statistic to test a model hypothesis. The significant level of a test. Standard error of a treatment mean. Interval estimation of treatment means. Unequal subclass frequencies case. Central and non-central F distributions. Power of the F-test and determination of the number of replications. Expected values and expected mean squares (EMS).

3. TREATMENT COMPARISONS. Linear contrasts and orthogonal contrasts: Estimation of and hypothesis testing. Quantitative factors and response curves: hypothesis testing and estimation. Multiple comparisons and error rates. Bonferroni, Scheffe, MCB and Dunnett methods. Other pairwise comparisons: Fisher's Least Significant Difference (LSD), Tukey's Honestly Significant Difference (HSD), and Student-Newman-Keuls (SNK) multiple range test.

4. VALIDITY OF MODEL ASSUMPTIONS. The effects of departures from assumption. Examination of residuals. The normality assumption. The homogeneity of variances assumption. Outliers. Transformations.

5. RANDOM EFFECTS MODELS. A statistical model for variance components. ANOVA and EMS. Estimation of variance components. Intraclass correlation. Unequal subclass frequencies. The power of the F test and determination of the number of replications. Subsampling. Unequal subclass and/or unequal subsampling frequencies.

6. FACTORIAL EXPERIMENTS. Two-factor factorial experiment. Simple effects, main effects, and interaction effects. Linear statistical model. Additivity. ANOVA. One and two quantitative factors and response curves. Three-factor factorial. ANOVA. Unequal subclass frequencies.

7. FACTORIAL, NESTED AND NESTED FACTORIAL EXPERIMENTS. Random and mixed models. ANOVA, EMS and F-tests. Determination of number of replications. EMS algorithms for balanced designs with equal subclass frequencies.

8. RANDOMIZED COMPLETE BLOCK DESIGN (RCB). Blocking as a means to increase the precision of the comparisons among treatments. One blocking criterion. Randomization. Linear model. ANOVA. Multiple comparisons. Relative efficiency. A quick check of blocking efficiency.

9. LATIN SQUARE DESIGN. Two-way blocking. Standard Latin squares. Randomization. Linear model. ANOVA. Relative efficiency. Multiple Latin squares and Latin rectangles, their linear models and corresponding ANOVA tables.

10. FACTORIAL EXPERIMENTS FITTED IN COMPLETE BLOCK DESIGNS. Randomization. Linear models and ANOVA tables.