Homework Sourse20 young pigs are assigned at random among 4 experimental gr
20 young pigs are assigned at random among 4 experimental groups. Each group is fed a different diet. (This design is a completely randomized design.) The data are the pig\'s weight in kg after being raised on these diets for 10 months. We wish to ask whether mean pig weights are the same for all 4 diets. (10pts)
Data from study of pigs’ weights.
Feed_1
Feed_2
Feed_3
Feed_4
60.8
68.3
102.6
87.9
57.1
67.7
102.2
84.7
65.0
74.0
100.5
83.2
58.7
66.3
97.5
85.8
61.8
69.9
98.9
90.3
Please identify the statistical test to be run and run the analysis.
Please report the results and provide a conclusion. Please report mean values for each of the groups in your conclusion.
Are post hoc tests necessary? Please explain.
| Data from study of pigs’ weights. | |||
| Feed_1 | Feed_2 | Feed_3 | Feed_4 |
| 60.8 | 68.3 | 102.6 | 87.9 |
| 57.1 | 67.7 | 102.2 | 84.7 |
| 65.0 | 74.0 | 100.5 | 83.2 |
| 58.7 | 66.3 | 97.5 | 85.8 |
| 61.8 | 69.9 | 98.9 | 90.3 |
Solution
Here we want to compare averages of 4 samples. Therefore, we should use one-way ANOVA. The excel output for one-way ANOVA is shown below.
Since p-value is extremely small, we reject the null hypothesis of equal means. At least one mean is significantly different from others. To find which group is significantly different from others, post hoc tests are necessary.
| Anova: Single Factor | ||||||
| SUMMARY | ||||||
| Groups | Count | Sum | Average | Variance | ||
| Feed_1 | 5 | 303.4 | 60.68 | 9.167 | ||
| Feed_2 | 5 | 346.2 | 69.24 | 8.748 | ||
| Feed_3 | 5 | 501.7 | 100.34 | 4.683 | ||
| Feed_4 | 5 | 431.9 | 86.38 | 7.737 | ||
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-value | F crit |
| Between Groups | 4703.188 | 3 | 1567.729 | 206.7222 | 5.28E-13 | 3.238872 |
| Within Groups | 121.34 | 16 | 7.58375 | |||
| Total | 4824.528 | 19 |
