**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, 5^{th} 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.