1. Factorial Design of Experiments

2. An Economy of Design Two or more levels of each factor (variable) are administered in combination with the two or more levels of every other factor

3. An Economy of Design Such higher-order designs are called Completely Randomized Factorial ANOVA Factorial designs are of much greater power to reject the null hypothesis

4. Effects and the Structure of Analysis of Variance SS total = SS between + SS within SS between is broken down (partitioned) (treatment A) (treatment B) (interaction AB) SS total = SS A + SS B + SS AB + SS within

5. The Variances Variance between groups = estimate of treatment + error Variance within groups = estimate of error F = estimate of treatment + error / estimate of error F = Variance between groups /Variance within groups

6. Individual Differences As Error Error has remained unchanged The grand mean tells us the general “level” of our measurements and is usually not of great intrinsic interest. Treatment has been divided into three parts (A, B, AB) so there are now three F’s to calculate.

7. The Table of Variance SourceSSdfdf MSFetap Between conditions57319.0 7.60.86.01 Treatment A27127.010.80.76.01 Treatment B27127.010.80.76.01 Interaction AB 31 3.0 1.20.36.30 Within conditions208 2.5 Total7711 7.0

8. Computational Procedures: Equal and Unequal Sample Sizes In completely randomized factorial ANOVA, special care must be taken when the number of sampling units varies from condition to condition Two ways to handle unequal sample sizes Multiple-regression procedures Unweighted means analysis