Class examples

Wax 1 Wax 2 Wax 3 Anova: Single Factor 27 33 29 30 28 28 SUMMARY 29 31 30 Groups Count 28 30 32 Wax 1 5 31 30 31 Wax 2 5 Wax 3 5 ANOVA Source of Variation SS Between Groups 5.19999999999999 Within Groups 33.2 Total 38.4 They are not different since the P-Value is high random noise: Within Groups 33.2 Wax 1 Wax 2 Wax 3 Wax 4 Anova: Single Factor 27 33 29 1 30 28 28 2 SUMMARY 29 31 30 1 Groups 28 30 32 2 Wax 1 31 30 31 5 Wax 2 Wax 3 Wax 4 ANOVA Source of Variation Between Groups Within Groups Total units of differences due to noies:

Sum Average Variance 145 29 2.5 152 30.4 3.3 150 30 2.5 df MS F P-value F crit 2 2.6 0.939759 0.417678 3.885294 12 2.766667 14 Count Sum Average Variance 5 145 29 2.5 5 152 30.4 3.3 5 150 30 2.5 5 11 2.2 2.7 SS df MS F P-value F crit 2861.8 3 953.9333 346.8848 9.164E-15 3.238872 44 16 2.75 2905.8 19 2905.8 2861.8 Between Groups

Sum Average Variance 275 55 26 340 68 26.5 285 57 24.5 df MS F P-value F crit 2 245 9.545455 0.003306 3.885294 12 25.66667 14

Plant 1 Buffalo Plant 2 Pittsburgh Bonus structure 1 48 57 Bonus structure 2 54 63 Bonus structure 3 53 59 Bonus structure 4 77 71 Bonus structure 5 64 66 Bonus structure 6 59 64 SUMMARY Count Sum Bonus structure 1 3 156 Bonus structure 2 3 180 Bonus structure 3 3 170 Bonus structure 4 3 212 Bonus structure 5 3 191 Bonus structure 6 3 177 Plant 1 Buffalo 6 355 Plant 2 Pittsburgh 6 380 Plant 3 Detroit 6 351 ANOVA Source of Variation SS df 608 5 82.3333333333335 2 Error 181.666666666667 10 Total 872 17 Anova: Two-Factor Without Replication Rows (bonus Stracture) Columns (Plants)

Buffalo Buffalo Pittsburgh Pittsburgh Detroit Detroit Not Raise Eligible Not Raise Eligible 48 48 57 57 51 51 54 54 63 63 63 63 53 53 59 59 58 58 Raise Eligible Raise Eligible 77 77 71 71 64 64 64 64 66 66 61 61 59 59 64 64 54 54 Anova: Two-Factor With Replication SUMMARY Buffalo Pittsburgh Detroit Not Raise Eligible Count 3 3 3 Sum 155 179 172 Average 51.66666666667 59.6666666666667 57.33333333333 Variance 10.33333333333 9.33333333333333 36.33333333333 Raise Eligible Count 3 3 3 Sum 200 201 179 Average 66.66666666667 67 59.66666666667 Variance 86.33333333333 13 26.33333333333 Total Count 6 6 6 Sum 355 380 351 Average 59.16666666667 63.3333333333333 58.5 Variance 106.1666666667 25.0666666666667 26.7 ANOVA Source of Variation SS df MS 304.2222222222 1 304.2222222222 82.33333333333 2 41.16666666667 122.1111111111 2 61.05555555556 Sample (Raise eligability) Columns (Plants) Interaction (Raise eligability * plant)

Within 363.3333333333 12 30.27777777778 Total 872 17

20 21 22 22 23 24 30 31 32 33 34 35 50 51 52 51 52 53 Anova: Two-Factor With Replication SUMMARY Plant 1 Buffalo Plant 2 Pittsburgh Plant 3 Detroit Total Low bonus structure Count 2 2 2 6 Sum 42 44 46 132 Average 21 22 23 22 Variance 2 2 2 2 ium bonus structure Count 2 2 2 6 Sum 63 65 67 195 Average 31.5 32.5 33.5 32.5 Variance 4.5 4.5 4.5 3.5 high bonus structure Count 2 2 2 6 Sum 101 103 105 309 Plant 1 Buffalo Plant 2 Pittsburgh Plant 3 Detroit Low bonus structure medium bonus structure high bonus structure

EX 2 med

P-value F crit 3.205949917E-10 4.2564947290938 0.1308199855582 4.2564947290938 1 3.6330885114191

Variance 8 12.5 18 95.9 Total Count 6 6 6 Sum 189 252 315 Average 31.5 42 52.5 Variance 91.1 93.2 95.9 ANOVA Source of Variation SS df MS F Sample 1323 2 661.5 76.326923076923 Columns 1323 2 661.5 76.326923076923 Interaction 0 4 0 0 Within 78 9 8.6666666666667 Total 2724 17

P-value F crit 2.267013484E-06 4.2564947290938 2.267013484E-06 4.2564947290938 1 3.6330885114191

2.0833333333332 1 2.083333 0.042662 Within 390.666666666667 8 48.83333 Total 1348.91666666667 11 there is a significant difference between dogs and cats, but no differnces between the programs Interaction (different effect of treatment on animal type)

Dogs Dogs Cats Cats Anova: Two-Facto SUMMARY Dogs Count Sum Average Variance Cats Count Sum Average Variance Total Count Sum Average Variance ANOVA P-value F crit Source of Variation 0.002226 5.317655 Sample 0.841523 5.317655 Columns