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

2. Comparing Batteries Brand ObservationABC 149310894 24909575 348911593 46128272

3. Brand ObsABC 149310894 24909575 348911593 46128272 Average52110083.5=234.833 Count444

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

5. Sum of Squares Within Groups Brand ObsABC 1 (493-521) 2 (108-100) 2 (94-83.5) 2 2 (490-521) 2 (95-100) 2 (75-83.5) 2 3 (489-521) 2 (115-100) 2 (93-83.5) 2 4 (612-521) 2 (82-100) 2 (72-83.5) 2 SS11,050638405=12,093

6. Sum of Squares-Total Brand ObsABC 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 SS338,61573,35892,012503,985

7. So Far:  Total Sum of Squares: 503,985.67  Within Groups:12,093  Between Groups:491892.67

8. 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

9. Computing F statistic Source of Var. SSdfMSF Between491,892.672245,946.3183.04 Within12,09391343.67 Total503,985.6711

10. Look up F critical Value

11. 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 = 5.13x10 -8  = 0.0000000513 probability not significant