ANOVA Computations.
WITHIN SUBJECTS DESIGNS
Sue Krose wanted to
determine if sweet coffee had an influence on how steady a surgeon’s had was
when performing an operation. Sue
realized that the amount of caffeine in the coffee might have an impact on the
results so she designed a study in which people got low, medium, or strong
coffee. The dependent variable was a measure of steadiness. A higher score on this measure means the
person’s hand was less steady. Sue recruited five surgeons to
participate in her study. Each
participated in all three treatment levels.
The following table is a summary of her results. Plot the results in the following table,
complete the summary table, compute F, and answer the questions. (n.b. This is a within
subject study.)
|
|
Low Caffeine |
Medium Caffeine |
Strong Caffeine |
|
|
0 |
0 |
6 |
|
|
1 |
3 |
5 |
|
|
0 |
1 |
5 |
|
|
4 |
5 |
9 |
|
|
0 |
1 |
5 |
|
Sum |
5 |
10 |
30 |
|
Mean |
1 |
2 |
6 |
|
Table
1. ANOVA summary table. |
||||
|
Source |
SS |
df |
MS |
F |
|
Between treatments |
70 |
(****) |
(****) |
(****) |
|
Within
treatments Between subjects Error |
40 36 4 |
12
8 |
(****) |
|
|
Total |
110 |
(****) |
|
|
|
**** You should
be able to get these without help |
||||
a.
Is
the F significant?
F2,8 = 70, p <.01 (critical value = 8.65)
b.
What
do you conclude about the difference between treatments?
The amount of caffeine in the coffee had a
major influence on hand steadiness.
c.
If
the F is significant, what is the effect size?
η2
= .64. Sixty-four percent of the
variability in hand steadiness is accounted for by knowing how much caffeine
the surgeon had. Moral of the story, if
you have surgery make sure your surgeon drinks juice.