Statistics

SRM 502 Homework Assignment 7

Answer the following questions. For “hand calculations” feel free to use anything like Excel to make the calculations easier and quicker. Use SAS only when directed.

1. An anesthesiologist studied the effects of codeine and acupuncture on dental pain relief. Each of 32 patients was randomly assigned either to no treatment, codeine only, acupuncture only, or both codeine and acupuncture, with 8 patients in each group. Effectiveness of pain relief was measured on a scale from 0 to 3.0.

(a) Write an appropriate two-factor ANOVA model equation to assess the impact of codeine (Factor A) and acupuncture (Factor B) on pain relief.

(b) Construct an ANOVA table, and perform a test of the significance of the interaction of these two factors. The data are available in the file “Pain”, with measures of pain relief followed by levels of codeine, followed by levels of acupuncture. Now assume patients were blocked into 8 pain tolerance groups (1 = lowest, 8 = high- est) of four patients per group, with one patient from each group randomly assigned to each of the four treatment combinations.

(c) Using pain tolerance as a blocking variable, write an appropriate ANOVA model equa- tion to assess the effect of codeine and acupuncture on pain relief.

(d) Construct an ANOVA table, and perform a test of the significance of the interaction of codeine and acupuncture. Data are available in the file “BlockedPain”, with pain relief followed by tolerance group, followed by codeine, followed by acupuncture.

(e) Compare your answers from parts b and d, specifically considering model MSE.

2. Three states ( factor A) participated in a health awareness study. Each state independently devised a health awareness program. Three cities ( factor b) within each state were chosen at random from all the cities in the state and five households within each city were randomly selected to evaluate the effectiveness of the program. All members of the selected households were investigated before and after participation in the program and a composite index was formed for each household measuring the impact of the health awareness program. The data on health awareness follow ( the larger the index, the greater the awareness).

State 1 2 3 City 1 2 3 1 2 3 1 2 3

1 42 26 34 47 56 68 19 18 16

Household 2 42 26 34 47 56 68 19 18 16 3 56 38 51 58 43 51 36 40 28 4 35 42 60 39 65 49 24 27 45 5 28 53 44 65 59 57 33 23 21

(a) Write an appropriate nested two-factor ANOVA model.

(b) List the hypotheses of interest regarding state and city effects on health index.

(c) Using SAS, perform tests for these two hypotheses of interest, and interpret both in terms of the original problem. Use α = .05.

3. For each of the following three descriptions,

(a) Determine the dependent and independent variables.

(b) Determine which independent variable is nested within the other.

(c) Sketch a representation of the data structure that makes the nesting clear. Do this in any way that makes sense to you!

i. Education researchers recorded the individual students’ standardized reading scores for five classrooms selected from four different schools in a district. They are interested in the effects of schools and of classrooms on these scores.

ii. A hospital is investigating basic supply expenditures. Three nurses are selected from each of four different floors and surveyed about supply usage once a month for a year. Nurses work only on a single floor. It is of interest to know the effect of the individual and also of the floor on average supply usage.

iii. Public health researchers are interested in rating residents on a “health index” scored on a scale from 1 to 100. Three states participated in their study, with three cities selected from each state. Researchers recorded the health index value for five households in each city, and are interested in the effect of the state and the city on these values.

4. For each of the following two descriptions,

(a) Determine the dependent and independent variables.

(b) Determine which variable is the subject, and which describes the within-subjects factor.

i. Marketing researchers would like to know the effect of color on individual responses to food advertisements. Individuals are each presented with three food ads with three different color schemes, and asked the rate their likelihood of purchasing the advertised food.

ii. Researchers are interested in the number of minutes required to complete a computer task. Each individual performs the task on a desktop and a laptop (in varying orders), and minutes required for completion is recorded.

iii. Four female and four male subjects participated in a 12 week strength training pro- gram designed to improve jumping ability. The subjects jumping ability was measured with 3 different jumps (squat jump, countermovement jump, 20 cm drop jumps) at the following time points: pre, 6 weeks and post.

5. Four female and four male subjects participated in a 12 week strength training program designed to improve jumping ability. The subjects jumping ability was measured with 3 different jumps (squat jump, countermovement jump, 20 cm drop jumps) at the following time points: pre, 6 weeks and post. The results follow.

Jumps squat countermovement 20 cm drop

Gender Pre 6 week Post Pre 6 week Post Pre 6 week Post F 20 21 28 22 23 29 22 22 30 F 21 21 27 20 20 29 21 22 29 F 19 18 25 19 22 27 19 21 28 F 20 21 28 21 21 28 22 23 31 M 19 21 28 20 20 27 21 22 30 M 18 19 27 19 19 28 20 21 29 M 21 22 29 20 21 30 22 23 30 M 22 23 30 23 25 31 23 26 32

Use SAS to answer the following questions.

(a) What type of design is used here?

(b) Is there a significant JUMP effect?

(c) Did the training program improve jumping ability equally across the three jumping techniques?

(d) Did the training program improve jumping ability?

(e) Is there a difference between males and females?

(f) Did the training program effect males and females equally?

(g) Did the training program effect males and females equally across the three jumping styles?

6. a paper manufacturer wants to analyze the effect of three pulp preparation methods (factor A) and four cooking temperatures (factor B) on the tensile strength of the paper. The ex- perimenter wants to perform three replicates of this experiment on three different days each consisting of 12 runs (3 × 4). It would be economical to randomly select any of the prepa- ration methods, make the blend and divide it into four samples and cook each of them with one of the four cooking temperatures. Then the second method is used to prepare the pulp and so on. The experimenter decides to run one replicate on each of the three days. The data are in tensile.xlcx. Use SAS to answer the following questions.

(a) What type of design is used here? Specify the whole plot and split plot factors?

(b) Write an appropriate ANOVA model equation to assess the impact of pulp preparation and cooking temperature on tensile strength.

(c) Construct an ANOVA table.

(d) Perform a test of the significance of the interaction of the two factors. Use α = .05.

(e) Test separately whether or not factor A and factor B main effects are present. Use α = .05.