This assignment refers to the following scenario and dataset. Dr. Bergenson is a health psychologist. He has obtained a large government grant to conduct research on the best ways to decrease adult obesity in the United States. He has a list of 2D interventions that might reduce obesity, but decides that it would be a better use of taxpayer money to narrow them down before doing his massive study. Isn't that thoughtful ofhim? You are a research assistant in his laboratory, and he has put you in charge of the analyses from the first pilot study comparing 3 of the interventions to a control group. You are to determine which intervention works best in this study, and if any should be retained for the larger-scale study. He recruits several obese volunteers, weighs them before the intervention, and then randomly assigns each to one of four groups: {a} keeping a food journal, (b) eating a cup of ice cream within 30 minutes of waking (the theory there is that one's appetite will be satiated for some time and one will eat less food overall over the rest of the day}, {c} fasting one day on and one day off, and (d) doing nothing out of the ordinary (the control group]. He makes sure that they are complying with the intervention, and then after 6 months, weighs them again. Here are the results: Participant Group Assigned Total Weight Loss (lbs) 1 1 Uoumal) 9 2 1 (Journal) 8 3 1 (Journal) 10 4 1 (Journal) 12 5 1 Uoumal) 3 B 2 [Ice Cream) 5 7 2 [Ice Cream) 2 8 2 [Ice Cream) 5 9 2 [Ice Cream) 4 10 2 [Ice Cream) 3 11 3 (Fasting) 3 12 3 {Fasting} 10 13 3 [Fasting]I 13 14 3 (Fasting) 12 15 3 (Fasting) 15 16 4 {Control} 8 17 4 {Control} 2 18 4 {Control} 6 19 4 [Control] 3 20 4 {Control} 11 Note. Negative numbers mean that this was weight gained (not lost]I over the trial. 1. Why should we analyze these data with an analysis of variance, instead of just doing a series of { tests? Step 1: The Omnibus 2. What is the purpose of the omnibus test in an ANOVA? In other words, what question does the omnibus test answer? 3. First, write the null and alternative hypotheses both in symbols, and then words. Ho. HA: our default hypothesis is... 4. Now comes the math. We begin the process of figuring out whether there is more variation among the groups than there is among all of the participants regardless of the groups, I've rearranged the data from the first table to make it simpler to use. Complete the table. Participants' Pounds Lost by Each Group Journal (X1) Ice Cream (X2) Fasting (X3) Control (X4) 9 3 8 8 -2 10 10 5 13 EWON 12 -4 12 3 15 Ex, = EX2 = EX3 = ExA = Ex? = Ex; = Ex; = Ex) = Extotal = Extotal = Here is the big equation we will be solving, step by step, for your reference: E -(x7) (Extotal) ni N F = Extotal Extotal)2] V E (Exi)2 (Extotal)2 ni N (N - 1) - (k -1) You may find it useful to complete this source table as you finish your calculations. The numbers in parentheses tell you which problem gives you that part of the table. Source SS df MS Between-groups (7.) 240.4 (10.) 3 (12.) 80.133 Within-groups (8.) 298.4 (11.) 16 (12.) Total (6.) 538 8 (9.) 19 18.65 5. Let us begin with the correction for the mean (CM). Compute CM. 12842 16,384 (Extotal)2 = 819.20 CM = 20 20 N 6. Now calculate the total sum of squares (SStotal). SStotal = Ex- total - CM 7. Now compute the sums of squares between the groups (SSbetween). (Ex1)2 (Ex2) 2 (Ex3) 2 SSbetween + + . (ExA) - CM n1 n2 n3 n4