Homework Sourse1220 For the following data assuming a betweengroups design
12.20: For the following data, assuming a between-groups design, determine:
Group 1: 11, 17, 22, 15
Group 2: 21, 15, 16
Group 3: 7, 8, 3, 10, 6, 4
Group 4: 13, 6, 17, 27, 20
a. dfbetween
b. dfwithin
c. dftotal
d. The critical value, assuming a p value of 0.05
e. The mean for each group and the grand mean
f. The total sum of squares
g. The within –groups sum of squares
h. The between- groups sum of squares
i. The rest of the ANOVA source table for these data
j. Tukey HSD values
Solution
ANOVA in excel gives the following results.
Based on the table the answers are,
a. dfbetween = 3
b. dfwithin = 14
c. dftotal = 17
d. critical value = 3.34
e.
Grand Mean = 13.22
f.
Sum of Squarestotal = 791.11
g.
Sum of Squareswithin groups = 361.95
h.
Sum of Squaresbetween groups= 429.16
i.
Use the table given above.
j.
qcritical = 4.111
| Anova: Single Factor | ||||||
| SUMMARY | ||||||
| Groups | Count | Sum | Average | Variance | ||
| Group 1 | 4 | 65 | 16.25 | 20.92 | ||
| Group 2 | 3 | 52 | 17.33 | 10.33 | ||
| Group 3 | 6 | 38 | 6.33 | 6.67 | ||
| Group 4 | 5 | 83 | 16.60 | 61.30 | ||
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-value | F crit |
| Between Groups | 429.16 | 3 | 143.05 | 5.53 | 0.01 | 3.34 |
| Within Groups | 361.95 | 14 | 25.85 | |||
| Total | 791.11 | 17 |
