STA 6208 Spring 2012 Take-Home (Data Analysis) Exam

STA 6208 – Spring 2012 – Take-Home (Data Analysis) Exam

Split-Plot Experiment:

Masters golf tournament. 11 Years (Blocks). 4 Rounds per year. 3 Famous Golfers. Each golfer plays each round (in same order) each year. Note: Y=score is discrete, and clearly not normally distributed, but conduct analysis as a split-plot experiment. Variables/Columns: Golfer Name 1-10 Golfer ID 18 Year 20-26 Round 34 score 40-42

 Give the ANOVA table, as well as Bonferroni comparisons among rounds and golfers.

Repeated Measures: (Note: Do not use Improvement Indicator)

Dataset: dog_zylkene.dat

Source: C. Beata, E. Beaumont-Graff, C. Diaz, M. Marion, N. Massal, N. Marlois, G. Muller, C. Lefranc (2007). "Effects of Alpha-Casozepine (Zylkene) versus Selegiline Hydrochloride (Selgian, Anipryl) on Anxiety Disorders in Dogs," Journal of Veterinary Behavior, Vol. 2, 175-183

Description: Repeated measures at 5 time points of emotional distress (low scores are better) of dogs receining zylkene (trt=1) or selgian anipryl (trt=0).

Variables/Columns dog id 7-8 period 1 eded 15-16 period 2 eded 23-24 period 3 eded 31-32 period 4 eded 39-40 period 5 eded 47-48 improvement indicator 56 treatment 64

 Give the ANOVA table, as well as Bonferroni comparisons among time periods. Is there a treatment by time interaction?

Crossover Design

Dataset: apple_carrover.dat Source: W. Hoofnagle (1965). "Experimental Designs in Measuring the Effectiveness of Promotion," Journal of Marketing Research, Vol.II, pp.154-162

Description: Apple sales by Treatment (color quality), period, and store in a 3-period crossover design

Trt 1=75-100% good red color (highly colored) Trt 2=50-75% (partly colored) Trt 3=50-100% (combination) variables/columns Store 8 /* 9 stores */ period 16 /* 1=Oct-Nov11, 2=Nov13-Nov25, 3=Nov27-Dec09 */ sequuence 24 treatment 32 trt1 39-40 /* 1 if trt=1, -1 if trt=3 */ trt2 47-48 /* 1 if trt=2, -1 if trt=3 */ Carryover 56 /* 0 if period=1, trt in period-1 ow */ Carry1 63-64 /* 1 if carryover=1, -1 if carryover=3 */ Carry2 71-72 /* 1 if carryover=2, -1 if carryover=3 */ sales 77-80  Give the ANOVA table, testing for treatment effects, controlling for carryover and vice versa. Which effects, if any are significant?

Analysis of Covariance in a Latin Square

Dataset: mcapple.dat

Source: S. Banks (1965), "Latin Square Experiments," Journal of Advertising Research, Vol5, #3, pp. 37-46

Description: Results of an experiment based on a latin square design relating daily apple sales (pounds) to merchandising practices (based on pricing by size and whether in cellophane packaging) over 4 days in 4 stores in Fall 1950. Customer flow is included as a covariate.

Variables/Columns Store 8 Day 16 Merchandising Practice 24 /* A=2lb/NoCell,B=2/Cell, C=4/NoCell, D=4/Cell*/ Customer Flow 30-32 Apple Sales (Pounds) 48-50

 Test for merchandising practice effects, controlling for customer flow, store, and day effects.

Response Surface Design

Dataset: cotton_bleach.dat

Source: P.K. Lavric, F. Kovac, P.F. Tavcer, P. Hauser, D. Hinks (2007). "Enhanced PAA Bleaching of Cotton by Incorporating a Cationic Bleach Activator," Coloration Technology, Vol. 123, #4, pp230-236

Description: 4-Factor Design to determine effects on whiteness of cotton. Factors: Temperature (40-80C) Bleach Activator - TBBC (0-3 %owf) pH (6.5-8.5) Paracetic Acid - PAA (ml/l) Response: Whiteness Index

Note: Polynomial Regression fit on coded levels, not raw levels

Variables/Columns Run # 7-8 Temperature 15-16 TBBC 20-24 pH 30-32 PAA 39-40 Coded Temp 47-48 Coded TBBC 55-56 Coded pH 63-64 coded PAA 71-72 Whiteness Index 77-80

 Fit a full model (including main effects, 2-way interactions, and quadratic terms), and then any reduced models that explain the variation. On graph paper, show the design points for each pair of factors.