a. Means
Mean for Group 1( ) = (2 + 6) / 2 = 4
Mean for Group 2 ( ) = (5 + 7) / 2 = 6
Grand Mean for Y (
) = (2 + 6 + 5 + 7) / 4 = 5
b. SS Total Calculations
Case |
X |
Y |
|
|
1 |
1 |
2 |
2-5 = -3 |
(-3)2 = 9 |
2 |
1 |
6 |
6-5 = 1 |
(1)2 = 1 |
3 |
2 |
5 |
5-5 = 0 |
(0)2 = 0 |
4 |
2 |
7 |
7-5 = 2 |
(2)2 = 4 |
|
|
|
|
Σ = 14 |
d. See b above. Both values should be 14
f. SS Between Groups Calculations
Case |
X |
Y |
|
|
|
1 |
1 |
2 |
4 |
4-5 = -1 |
(-1)2 = 1 |
2 |
1 |
6 |
4 |
4-5 = -1 |
(-1)2 = 1 |
3 |
2 |
5 |
6 |
6-5 = 1 |
(1)2 = 1 |
4 |
2 |
7 |
6 |
6-5 = 1 |
(1)2 = 1 |
|
|
|
|
|
Σ = 4 |
g. See f above for SS. Should correspond to SS Regression.
h. Regression line intersects X = 1 at Y = 4.
Which Y' values from Exercise #1 does this correspond to? Y' = 4 for X = 1
Regression line intersects X = 2 at Y = 6.
Which Y' values from Exercise #1 does this correspond to? Y' = 6 for X = 1
i. SS Within Groups Calculations
Case |
X |
Y |
(Group Mean) |
|
|
1 |
1 |
2 |
4 |
2-4 = -2 |
(-2)2 = 4 |
2 |
1 |
6 |
4 |
6-4 = 2 |
(2)2 = 4 |
3 |
2 |
5 |
6 |
5-6 = -1 |
(-1)2 = 1 |
4 |
2 |
7 |
6 |
7-6 = 1 |
(1)2 = 1 |
|
|
|
|
|
Σ = 10 |
k. See i for SS. Corresponds to SS Error.
l. Calculation of F
F = [4 / 1] / [10 / 2]
= 4 / 5 = 0.8.
n. Calculation of Eta-Squared
4 / 14 = .286. Corresponds to r2.