2. Identifying Experimental Design Elements Experiment vs. Observational Study Experimental units –Homogeneous or blocked Treatment Factor(s) A and Levels, Controls Classification Factors and Levels Response Variables Covariates

3. Married with Problems Completely randomized one-way experiment Units – 59 troubled married couples, assumed homogeneous A= marriage therapy, 2 levels –Insight, Behavior Modification –No control Response variables –Y 1 = commitment after 6 months –Y 2 = commitment after 4 years

4. Stress Management for Heart Patients Completely randomized one-way experiment Units – 107 primarily white men with heart trouble, homogeneous A = heart treatment, 3 levels –Standard, Standard plus exercise, Standard plus group therapy for stress management –Standard provides control Response variables: –Y 1 = subsequent heart problems in 3 to 5 years –Y 2 = subsequent incidences of ischemia, chest pain –Y 3 = psychological post test –Y 4 = cholesterol level –Y 5 = lipid levels Covariates: Personality pre-test, Physical pre-tests, Mental stress pre-tests

5. Sunscreen to Prevent Solar Keratoses Randomized block experiment with one treatment factor, two classification factors, and repeat tests within blocks Units – 588 men and women over 40 years of age with 1 to 30 solar keratoses, blocked by gender and self-reported skin types –2x3 = 6 blocks A= sun cream, two levels –Screen, Placebo –Placebo is the control Treatments are randomly assigned within blocks – blind experiment Y =[y ij ], i=1,2,3; j=1,2,3, –i:3 subsequent time periods –j:total lesions, remissions, new lesions Covariates: number of initial keratoses, amount of cream applied

6. Antihistamines and Driving Ability Randomized block experiment with one treatment factor and no repeat tests within blocks Units=40 allergy sufferers ages 25 to 45, each serving as their own block A=drug, four levels –Placebo, Diphenhydramine, Fexofenadine, and Alcohol for.10 blood level –Placebo is the control Treatments are randomly sequenced for each person - ? Blind Response variables: –Y 1 = driving coherence measure –Y 2 = steering ability –Y 3 = ability to avoid a crash –Y 4 = assessment of drowsiness

7. Hypoparathyrodism during Intoxication Randomized block experiment with one treatment factor and no repeat tests within blocks Units=24 normal men and women who consume 1 to 2 drinks daily, each serving as their own block A=Alcohol, two levels –Alcohol, Fruit juice –Fruit juice is the control Treatments are randomly sequenced for each block - ? blind Y = [y ij ] i=1,…,8; j = 1, …, 3 –i: 8 repeated observations 7pm to 10 am –j: blood serum levels of calcium, magnesium, and phosphate Covariates –Two base line blood serum levels of calcium, magnesium, and phosphate

8. Welch’s Grape Juice for Babies Experiment Units=eighteen 6 months old babies and ten 18 months old babies, non-homogeneous; 16 served as their own blocks; ? others blocked by ages A=Juice, two levels –White grape juice, apple juice –No control Treatments are randomly assigned (or sequenced) within blocks Response variables –Y i = hydrogen gas in breath at 30 minute intervals, i=1…5

9. Ethical Considerations in these Experiments Controls Business sponsored research Drug and alcohol consumption Other issues

10. Analysis Definitions Repeated measures – –each subject receives all treatments, equivalent to a randomized block design with subjects as blocks or a single treatment evaluated at different points in time MANOVA - multiple response variables with possibility of treatment factors, classification factors, blocks, and covariates Profile analysis –application of MANOVA, multiple response variables on the same scale –single response variable measured on each subject through time, alternative to univariate repeated measures

11. Analysis of these Designs Married with problems –Profile analysis or repeated measures (single response repeated through time) Stress management for heart patients –MANOVA (multiple response variables – on different scales) Sunscreen to prevent solar keratoses –Multiple profile analyses or multiple repeated measures (multiple response variables on the same scale repeated through time)

12. Analysis continued Antihistamines and driving ability –Multiple repeated measures or MANOVA (multiple response variables repeated for all treatments on each subject) Hypoparathyrodism during intoxication –Multiple profile analyses or multiple repeated measures or MANOVA (multiple response variables on the same scale repeated through time and repeated for all treatments on each subject ) Welch’s grape juice for babies ???????