Homework SourseQUESTION 2 a Why do we use the pooled variance in calculatio
QUESTION 2:
(a). Why do we use the pooled variance in calculations of independent samples t-statistics and ANOVAs? (5 points)
(b). How are t-tests related to F-tests?. In what ways are they similar, and how are they different? (5 points)
(c). The F-statistic is the ratio of Sb2 to Sw2, where Sb2 is the variability between the sample means and Sw2 is the variability within the samples. Why is the F-statistic constructed this way? And what does it tell us? (5 points)
(d). Consider the following two tables. For which of these two tables are you more likely to find a significant ANOVA results? and Why? (5 points)
Group 1
Group 2
Group 3
Xbar
10
13
12
SS
38
35
35
Group 4
Group 5
Group 6
Xbar
10
18
9
SS
38
35
35
(e). Complete the following ANOVA table by filling in the blanks marked X.
(5 points)
Source
df
SS
MS
F
Between
2
X
15
X
Within
X
36
X
Total
14
66
Please show complete work by hand, no minitab/ddxl
| Group 1 | Group 2 | Group 3 | |
| Xbar | 10 | 13 | 12 |
| SS | 38 | 35 | 35 |
Solution
(e) Complete the following ANOVA table
Source
df
SS
MS
F
Between
2
15*2=30
15
15/3=5
Within
14-2=12
36
36/12=3
Total
14
66
| Source | df | SS | MS | F |
| Between | 2 | 15*2=30 | 15 | 15/3=5 |
| Within | 14-2=12 | 36 | 36/12=3 | |
| Total | 14 | 66 |
