A researcher records the following data for each of three groups.
Group A | Group B | Group C |
---|---|---|
5 | 12 | 13 |
12 | 6 | 11 |
11 | 12 | 4 |
15 | 4 | 12 |
7 | 16 | 10 |
What is the value of the F-statistic? (Round your answer
to two decimal places.)
F =
Explain your answer.
F is the indicated value because the group means are different. There is no variability between groups.
F is the indicated value because the groups means are different. There is substantial variability between groups.
F is the indicated value because the group means are the same. There is no variability between groups.
F is the indicated value because the group means are the same. There is substantial variability between groups.
The following table is obtained:
Group 1 | Group 2 | Group 3 | |
5 | 12 | 13 | |
12 | 6 | 11 | |
11 | 12 | 4 | |
15 | 4 | 12 | |
7 | 16 | 10 | |
Sum = | 50 | 50 | 50 |
Average = | 10 | 10 | 10 |
= | 564 | 596 | 550 |
St. Dev. = | 4 | 4.899 | 3.536 |
SS = | 64 | 96 | 50 |
n = | 5 | 5 | 5 |
The total sample size is N = 15. Therefore, the total degrees of freedom are:
dftotal=15−1=14
Also, the between-groups degrees of freedom are dfbetween=3−1=2, and the within-groups degrees of freedom are: dfwithin=dftotal−dfbetween=14−2=12
First, we need to compute the total sum of values and the grand mean. The following is obtained
Also, the sum of squared values is
Based on the above calculations, the total sum of squares is computed as follows
The within sum of squares is computed as shown in the calculation below:
Now that sum of squares are computed, we can proceed with computing the mean sum of squares:
Finally, with having already calculated the mean sum of squares, the F-statistic is computed as follows:
F is the indicated value because the group means are the same. There is no variability between groups.
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