Two-way ANOVA AWS
11
SPSS ACTIVITY
Two-way ANOVA Forty-eight college students participated in a study to examine the effects of two different diets and three dosages of a drug developed to curb hunger. Twenty-four of the subjects were randomly assigned to diet 1, and the other 24 were assigned to diet 2. Within each diet condition, 8 subjects were randomly assigned to each of the three drug dosages. The sensation of hunger was measured with a questionnaire at the end of five weeks. The questionnaire was designed so that high scores indicated that the sensation of feeling hungry was low. Table 11.9 gives the resulting data.
Procedures and Questions A. To analyze these data, we will use a two-way ANOVA, since we have two
independent variables. Be sure to enter the data correctly, based on the level of measurement of each variable. Your SPSS Data View file will contain three variables: Dosage with three levels, Diet with two levels, and Questionnaire scores). n Enter the data, and then go to Analyze→General Linear Model→ Univariate. This will bring up the main dialog window. n Move the Diet and Dosage variables into the Fixed Factors box, and move the Questionnaire score variable into the Dependent Variable box. n Click on Options, and move all of the factors in the left-hand box into the right-hand box (Display Means for). Also, check the Descriptive statistics box under Display. TABLE
11.9
Data set.
DOSAGE
Diet
.1 gram
.2 gram
.3 gram
Diet 1
26 41 28 92
14 16 29 31
41 26 19 59
82 86 45 37
36 39 59 27
87 99 122 104
Diet 2
51 96 97 22
35 36 28 76
39 104 130 122
114 92 87 64
42 52 156 144
133 124 68 142
Click Continue. Click on Plots, and move Diet to the Horizontal Axis box and Dosage to the Separate Lines box. Click Add. This graph will be required to answer a later question. n Click Continue and OK.
n n
Use the resulting analysis to answer the following questions: Q
1. What are the two independent variables in this experiment? 2. What is the dependent variable? 3. What are the levels of measurement for each of the three variables? 4. What type of design is this? 5. State the null hypothesis and an alternative hypothesis for each of the main effects and the interaction, in terms of the experiment. 6. What are the six cell means? Be sure to identify which mean is in which cell. 7. What are the two diet means? 8. What are the three dosage means? 9. What is the sum of squares total? (Hint: In SPSS two-way ANOVA, the total sum of squares is not in the row labeled Total.) 10. What is the sum of the explained variance? 11. What is the F-ratio for diet? Is it statistically significant? 12. What is the F-ratio for dosage? Is it statistically significant? 13. What is the F-ratio for interaction? Is it statistically significant? 14. State your answer to question 11 in terms of the experiment. 15. State your answer to question 12 in terms of the experiment. 16. State your answer to question 13 in terms of the experiment. 17. For which independent variable in this experiment is it necessary to perform a multiple comparisons calculation? 18. Describe the Profile Plots graph briefly. What does it indicate about any interaction between diet and dosage? 19. Which diet best curbs appetite? 20. Which drug dosage best curbs appetite?
SPSS ACTIVITY
Two-way ANOVA Forty-eight college students participated in a study to examine the effects of two different diets and three dosages of a drug developed to curb hunger. Twenty-four of the subjects were randomly assigned to diet 1, and the other 24 were assigned to diet 2. Within each diet condition, 8 subjects were randomly assigned to each of the three drug dosages. The sensation of hunger was measured with a questionnaire at the end of five weeks. The questionnaire was designed so that high scores indicated that the sensation of feeling hungry was low. Table 11.9 gives the resulting data.
Procedures and Questions A. To analyze these data, we will use a two-way ANOVA, since we have two
independent variables. Be sure to enter the data correctly, based on the level of measurement of each variable. Your SPSS Data View file will contain three variables: Dosage with three levels, Diet with two levels, and Questionnaire scores). n Enter the data, and then go to Analyze→General Linear Model→ Univariate. This will bring up the main dialog window. n Move the Diet and Dosage variables into the Fixed Factors box, and move the Questionnaire score variable into the Dependent Variable box. n Click on Options, and move all of the factors in the left-hand box into the right-hand box (Display Means for). Also, check the Descriptive statistics box under Display. TABLE
11.9
Data set.
DOSAGE
Diet
.1 gram
.2 gram
.3 gram
Diet 1
26 41 28 92
14 16 29 31
41 26 19 59
82 86 45 37
36 39 59 27
87 99 122 104
Diet 2
51 96 97 22
35 36 28 76
39 104 130 122
114 92 87 64
42 52 156 144
133 124 68 142
Click Continue. Click on Plots, and move Diet to the Horizontal Axis box and Dosage to the Separate Lines box. Click Add. This graph will be required to answer a later question. n Click Continue and OK.
n n
Use the resulting analysis to answer the following questions: Q
1. What are the two independent variables in this experiment? 2. What is the dependent variable? 3. What are the levels of measurement for each of the three variables? 4. What type of design is this? 5. State the null hypothesis and an alternative hypothesis for each of the main effects and the interaction, in terms of the experiment. 6. What are the six cell means? Be sure to identify which mean is in which cell. 7. What are the two diet means? 8. What are the three dosage means? 9. What is the sum of squares total? (Hint: In SPSS two-way ANOVA, the total sum of squares is not in the row labeled Total.) 10. What is the sum of the explained variance? 11. What is the F-ratio for diet? Is it statistically significant? 12. What is the F-ratio for dosage? Is it statistically significant? 13. What is the F-ratio for interaction? Is it statistically significant? 14. State your answer to question 11 in terms of the experiment. 15. State your answer to question 12 in terms of the experiment. 16. State your answer to question 13 in terms of the experiment. 17. For which independent variable in this experiment is it necessary to perform a multiple comparisons calculation? 18. Describe the Profile Plots graph briefly. What does it indicate about any interaction between diet and dosage? 19. Which diet best curbs appetite? 20. Which drug dosage best curbs appetite?
