Question

A Sleep researcher coducts an experiment to determine whether a hypnotic drug called Drowson, Which is advertised as a remedy for insomnia, Actually does promote sleep. In addition, the researcher is interested in whether a tolerance to the drug develops with chronic use. The design of the experiment is a 2 X 2 factorial independent groups design.

One of the variables is the concentration of Drowson. There are two levels: 1- zero concentration (placebo) and 2- the manufacturer’s minimum recommended dosage. The other variable concerns the previous use of Drowson. Again there are two levels: 1- Subjects with no previous use and 2- chronic users. Sixteen individuals with Sleep- onset insomnia (difficulty in falling a sleep) Who Have Had no previous use of Drowson Are randomly assigned to the two concentration conditions, such that there are eight subjects in each condition.

Sixteen chronic users of Drowson are also assigned randomly to the two conditions, eight subjects per condition. All subjects take their prescribed “medication” for 3 consecutive nights, and the Time To Fall asleep is recorded.

No previous use(Placebo):

45 53

48 58

62 55

70 64

No Previous use(Min. Recommended Dosage):

30 47

33 35

40 31

50 39

Chronic Users(Placebo):

47 68

52 64

55 58

62 59

Chronic users(Min. Recommended Dosage):

52 46

60 49

58 50

68 55

Test all the null hypotheses at both .05 and .01 level.

Answer 1

Step 1: Enter and Name the Data. As usual, you have three choices for entering the data: 1) by typing the scores directly into the Data Editor; 2) by downloading from the web the saved data file for this example, and 3) by opening the saved data file (for this example) that resides on your computer.

Entering the scores by typing them directly into the Data Editor.   If you choose to type in the data, remember to name the grouping variables Row and Column, and the other variable Time. If you have any questions, please follow the instructions in the illustrative example for Chapter 16, substituting the variables and scores for this problem.

Entering the scores by downloading from the web, the saved data file for this example. To enter the scores using this option, click here, and then click Open from the drop-down menu.

Entering the scores by opening the saved data file (for this example) that resides on your computer. If you choose to open the saved data file, the name of the file is Ch16prob1. To enter the data and name the variables for this problem, please follow the instructions in the illustrative example for Chapter 16.

When the data are entered and named correctly, the Data Editor, Data View should look like Figure 16.1.1.

Figure 1.1. Data Editor with Row, Column and Time scores entered.

Step 2: Conclusion Regarding the Main Effect of Previous Use, Main Effect of Drowson Concentration, and the Interaction between Previous Use and Drowson Concentration, using α = 0.05. The appropriate test for these evaluations is the Two-Way Analysis of Variance. To have SPSS do the analysis using this test,

Click Analyze. Select General Linear Model. Click Univariate…. Select Row and Column. Click the ► button for the Fixed Factors: box. Click Time in the large box on the left. Click the ► button for the Dependent Variable: box. Click the Options button. Click Descriptive. Click Continue. Click OK.

This produces a drop-down menu. This also produces a menu. This produces the Univariate dialog box with Row highlighted. This highlights Row and Column. This moves Row and Column into the Fixed Factors: box. . This highlights Time. This moves Time into the Dependent List: box. This produces the Univariate: Options dialog box. This puts a P in the Descriptive box, telling SPSS to compute some descriptive statistics and include them in the output. This returns you to the Univariate dialog box. SPSS analyzes the Time data and outputs the results to the Viewer. The output is shown below in Figure 16.1.2.

Figure 1.2 Results of Two-Way ANOVA analysis.

SPSS outputs three tables, the Between-Subjects Factors table, the Descriptive Statistics table, and the Tests of Between-Subjects Effects table. The Tests of Between-Subjects Effects table gives us information about the main and interaction effects. This table shows that for the Row main effect, F_obt = 11.633 and has an obtained probability of .002. Since .002 < .05, you reject H₀. There is a significant row main effect. Since the row independent variable is “Previous Use”, this means that “Previous Use” has a significant main effect. This table also shows that for the Column main effect, F_obt = 17.822, with an obtained probability of .000. Since .000 < .05, you reject H₀. There is a significant column main effect. Since the column independent variable is “Drowson Concentration”, this means that Drowson Concentration has a significant main effect. Finally, the table shows that for the Row X Column interaction, F_obt = 8.607, with an obtained probability of .007.

Since .007 < .05, you reject H₀. There is a significant “Previous Use” X “Drowson Concentration” interaction.

p-value = 0.007 < 0.01 hence we reject at 0.01 level also