2. Interpreting statistical software output for a two-factor ANOVA Shai and colleagues (2008) conducted a study in Israel comparing three diets: a low-carbohydrate diet, a low-fat diet, and a Mediterranean diet that consists of moderate fat and a high proportion of monounsaturated fats. They found various differences between the diets, but no striking differences particularly with respect to weight loss. These results led these researchers to conclude that the Mediterranean diet and the low-carbohydrate diets are effective and safe alternatives to a lowfat diet. They suggested that selecting a diet from among these might best be accomplished by considering the individual's lifestyle, preferences, and health needs. [Shai, I., Schwarzfuchs, D., Henkin, Y., Shahar, D. R., Witkow, S., Greenberg, I., . . . Stampfer, M. J. (2008). Weight loss with a lowcarbohydrate, Mediterranean, or lowfat diet. New England Journal ofMedicine, 359, 229241.] Suppose you are a bariatric researcher conducting a similar study among a random sample of moderately obese volunteers in the United States. Since you believe that women and men respond to diets differently, you recruit an equal number of male and female volunteers and randomly assign them to one of three diets. You are particularly interested in differences among the three diets between men and women with respect to the decrease in the average number of calories consumed per day over the first month. You use a statistical computing package, such as SPSS, to conduct a twofactor ANOVA. The table that follows shows the data in stacked format from the first five study participants. The column labeled \"GENDER" is the gender of the volunteer, where 1 = female and 2 = male. The column labeled \"CALORIES_DEC\" is each participant's decrease in calories consumed in calories. The column labeled \"DIET\" describes which diet the participant followed, where 1 = low-carbohydrate, 2 = low-fat, and 3 = Mediterranean. IDNUM GENDER CALORIES_DEC DIET 001 1 201 2 002 2 659 3 003 2 452 1 004 1 211 2 005 2 56 1 When setting up your analysis, you place the variable in the Dependent List box. You also place the variables CALORIES_DEC and GENDER in the Fixed Factor box IDNUM IDNUM and GENDER DIET DIET and GENDER CALORIES_DEC DIET and CALORIES_DEC Descriptives GENDER CALORIES_DEC GENDER DIET Mean Std Deviation N Female Low-carbohydrate 314.739 253.555 10 Low-fat 467.306 144.100 10 Mediterranean 453.046 200.772 10 Total 411.697 209.293 30 Male Low-carbohydrate 505.609 234.949 10 Low-fat 699.311 158.372 10 Mediterranean 652.538 259.789 10 Total 619.153 230.013 30 Total Low-carbohydrate 410.174 257.271 20 Low-fat 583.308 189.424 20 Mediterranean 552.792 248.064 20 Total 515.425 241.820 60Test of Between-Subjects Effects Source Sum of Squares df Mean Square F Sig Corrected Model 991,920 5 198,384 4.358 0.002 Intercept 15,939,766 1 15,939,766 350.149 0.000 GENDER 645,568.63 1 64,5569 14.181 0.000 DIET 341,645.36 2 170,823 3.752 0.030 GENDER*DIET 4,705.87 2 2,353 0.052 0.950 Error 2,458,230.04 54 45,523 Total 19,389,915 60 Corrected Total 3,450,150 59 The two prior tables consist of the output of the statistical computing package. Considering these results, select which of the following statements about the result are true. Assume that your chosen significance level is a = .05. (Note: Recall that p in the statements that follow indicates the p valuethat is, the probability of obtaining this result if the null hypothesis were true. These results are hypothetical.) What do the results of the two-factor analysis of variance indicate? Check all that apply. There is no significant effect for the interaction between gender and diet (F(2, 54) = 0.052, p = 0.950). There is a significant effect for the interaction between gender and diet (F(2, 54) = 350.149, p = 0.000). There is no significant main effect for diet (F(1, 54) = 14.181, p = 0.000). There is a significant main effect for diet (F(2, 54) = 3.752, p = 0.030)