Homework SourseAssume that an analysis of variance is conducted for a study
Assume that an analysis of variance is conducted for a study where there are N=50 observation and k=5 categories. Fill in the blanks. Please explain with details....please...
| Sums of Squares | Degree of freedom | Mean Square | F | |
| Between | _______________ | _______________ | 116.3 | ___ |
| Within | 2000 | _________________ | ___________ | |
| Total | _______________ | _________________ | ___________ |
Solution
N = 50
k = 5
Degrees of freedom between the groups = k - 1 = 5 - 1 = 4
Degrees of freedom (Total) = No. of observations - 1 = N - 1 = 50 - 1 = 49
Degrees of freedom between the groups + Degrees of freedom within the groups = Total Degrees of freedom
=> Degrees of freedom within the groups = 49 - 4 = 45
Mean Squares between the groups = SS(between)/Degrees of freedom between the groups
=> SS(between) = Mean Squares between the groups * Degrees of freedom between the groups
= 116.3 * 4 = 465.2
SS (within Groups) = 2000 (given)
SS Total = SS(between) + SS(within)
= 465.2 + 2000
= 2465.2
Mean Square (within) = SS(within)/Degrees of freedom(within)
= 2000/45
= 44.44
F = Mean Square (between) / Mean Square (within)
= 116.3 / 44.44
= 2.617
| Sums of Squares | Degree of freedom | Mean Square | F | |
| Between | 465.2 | 4 | 116.3 | 2.617 |
| Within | 2000 | 45 | 44.44 | |
| Total | 2465.2 | 49 |
