DATA i group j person j 1 j 2 j 3 j 4 j 5 Weight Loss pounds for 20 subjects Low Cal Low Fat Low CarbControl 2 2 1 0 3 2 4 3 5 1 3 5 4 2 3 8 9 6 7 3 15 5 3 17 5 3 4 6 5 1 2 STEP 1 Group Stats Ti Group total ni Group sample size Yi Bar Group mean Groups T Grand Total N Total sample size Y bar Grand Mean STEP 2 Calculate SS Total 33 5 6 6 4 71 20 3 55 1 4 2 4 0 6 0 4 3 6 0 Yij Y bar j 1 j 2 j 3 j 4 j 5 Sum over people Low Cal Low Fat Low CarbControl 0 8 0 8 2 2 1 2 1 8 SSTotal 0 4 1 6 0 6 1 4 0 4 0 1 1 0 2 2 0 0 0 STEP 3 Calculate SS within groups Yi Yi Bar 2 Low cal Low fat Low carb Control 0 64 0 64 4 84 1 44 3 24 1 96 5 76 0 36 0 16 12 96 0 16 2 56 0 36 1 96 0 16 1 1 0 4 4 j 1 j 2 j 3 j 4 j 5 Sum over people 21 2 10 5 2 10 8 SSWithin 47 2 STEP 4 Calculate SS Between groups ai Yi Bar Y Bar 2 Low cal Low fat Low carb Control 46 5125 27 6125 0 1125 1 5125 75 75 Sum over groups STEP 5 ANOVA Table SS 75 75 47 2 Source df Between Groups SSB 3 Within Groups SSW 16 MS 25 25 2 95 Total SStot 19 122 95 F 8 5593 p value 0 001278 use the F DIST RT function PROBLEM A researcher wanted to know what type of diet is best for weight reduction She conducted a research study where 5 participants were recruited in four different diet types Low Cal Low carb Low fat and control no specific diet At the end of the study weight change was assessed Weight at start weight at end You have been asked to analyze the presented data to decide whether there is a significant difference in mean weight loss among the 4 different diet programs