Whos Afraid of ANOVA Dr Ron TibbenLembke Comparing

Who’s Afraid of ANOVA? Dr. Ron Tibben-Lembke

Comparing Batteries Brand Observation A B C 1 493 108 94 2 490 95 75 3 489 115 93 4 612 82 72

Comparing Batteries Brand Obs A B C 1 493 108 94 2 490 95 75 3 489 115 93 4 612 82 72 Average 521 100 83. 5 Count 4 4 4 =234. 833

Sum of Squares § Compute average for each group § For each data point, § (data value – group average)^2 § Sum these squared values

Sum of Squares Within Groups Brand Obs A B C 1 (493 -521)2 (108 -100)2 (94 -83. 5)2 2 (490 -521)2 (95 -100)2 3 (489 -521)2 (115 -100)2 (93 -83. 5)2 4 (612 -521)2 (82 -100)2 SS 11, 050 638 (75 -83. 5)2 (72 -83. 5)2 405 =12, 093

Sum of Squares-Total Brand Obs A B C 1 (493 -234. 83)2 (108 -234. 83)2 (94 -234. 83)2 2 (490 -234. 83)2 (95 -234. 83)2 (75 -234. 83)2 3 (489 -234. 83)2 (115 -234. 83)2 (93 -234. 83)2 4 (612 -234. 83)2 (82 -234. 83)2 (72 -234. 83)2 SS 338, 615 73, 358 92, 012 503, 985

So Far: § § § Total Sum of Squares: 503, 985. 67 Within Groups: 12, 093 Between Groups: 491892. 67

Computing F statistic § Total number of degrees of freedom = number of samples - 1 = 12 -1 = 11 § There are 3 groups, so ‘between groups’ Degrees of Freedom = 3 – 1 = 2 § Within Groups DF = 11 – 2 = 9

Computing F statistic Source of Var. Between Within Total SS 491, 892. 67 12, 093 503, 985. 67 df MS F 2 245, 946. 3 183. 04 9 1343. 67 11

Look up F critical Value

Significant? § § § Compare F statistic: 183. 04 F critical value: 4. 256 Yes! The difference is significant! § For alpha=0. 01, Fcrit = 8. 011 § P value = 5. 13 x 10 -8 § = 0. 0000000513 probability not significant