http://www.ck12.org Chapter 11. Analysis of Variance and the F-Distribution
Do gender and the length of an exercise program have an effect on the flexibility of students?
Solution:
From these data, we can calculate the following summary statistics:
TABLE11.8:
Length of
ProgramLength of
ProgramLength of
Program
1 Week 2 Weeks 3 Weeks Total
Gender Females (n) 8 8 8 24
Mean 24. 6 27. 4 41. 0 31. 0
St. Dev. 4. 24 3. 16 4. 34 8. 23
Males (n) 8 8 8 24
Mean 21. 9 27. 1 28. 3 25. 8
St. Dev. 4. 76 2. 90 3. 28 4. 56
Totals (n) 16 16 16 48
Mean 23. 2 27. 3 34. 6 28. 4
St. Dev. 4. 58 2. 93 7. 6 7. 10As we can see from the tables above, itappearsthat females have more flexibility than males and that the longer
programs are associated with greater flexibility. Also, we can take a look at the standard deviations within each cell
to get an idea of the variance within groups. This information is helpful, but it is necessary to calculate the test
statistic to determine the effects and the interaction of the two independent variables.
Technology Note - Excel
Here is the procedure for performing a Two-way ANOVA in Excel using this set of data.
- Copy and paste the above table into an empty Excel worksheet,withoutthe labels, “Length of program” and
“Gender.” Or use this table:
TABLE11.9:
1 week 2 weeks 3 weeks
Females 32 28 36
27 31 47
22 24 42
19 25 35
28 26 46
23 33 39
25 27 43
21 25 40
Males 18 27 24
22 31 27
20 27 33
25 25 25
16 25 26
19 32 30
24 26 32
31 24 29- Select Data Analysis from the Tools menu and choose “ANOVA: Single-factor” from the list that appears