Analysis of Variance
Item 1
Year in school and car accidents.
10th 11th 12th
2 13 4
9 17 8
3 14 2
1 9 1
7 1 4
SS df ms
Between ____ ___ ____
Within ____ ___ ____
Total ____ ___ ____
F =
Which grade has the most car accidents:
Item 2
House color and people’s stay (in years).
Blue Green Peach
8 11 4
7 9 8
3 7 9
1 18 2
9 12 4
SS df ms
Between ____ ___ ____
Within ____ ___ ____
Total ____ ___ ____
F =
Which color of house is lived in the longest (in years)?
Item 3
13 1 5
4 1 2
10 2 2
13 2 2
11 2 6
3 4 4
Between
Within
Total
Critical value of F =
Item 4
3 5 8
9 1 2
5 2 6
11 5 4
Between
Within
Total
Critical value of F = .
Which is candle lasts more days?
ANSWERS
Item 1
Year in school and car accidents.
10th 11th 12th
2 13 4
9 17 8
3 14 2
1 9 1
7 1 4
SS df ms
Between 150.53 2 75.27
Within 228.80 12 19.07
Total 379.33 14 27.10
F = 3.95
Which grade has the most car accidents: The critical value is 3.74, so F is significant. You can now do multiple t-tests to discover which means are significantly different from each other.
Item 2
House color and people’s stay (in years).
Blue Green Peach
8 11 4
7 9 8
3 7 9
1 18 2
9 12 4
SS df ms
Between 116.13 2 58.07
Within 151.60 12 12.63
Total 267.73 14 19.12
F = 4.60
Which color of house is lived in the longest (in years)? The critical value is 3.74, so F is significant. You can now do multiple t-tests to discover which means are significantly different from each other.
Item 3
Which is the best coffee (most cups ordered):
Blue-Label Green-Label Red-Label
13 1 5
4 1 2
10 2 2
13 2 2
11 2 6
3 4 4
Sum 54 12 21 87
Sum X2 584 30 89 703
N 6 6 6 18
SS 98 6 15.50 119.50
SS df ms
Between 163.00 2 81.50
Within 119.50 15 7.97
Total 282.50 17 16.62
F = 10.23
Critical value of F = 3.68. F is significant.
Which is the best coffee. You’ll have to do t-tests to find out. But looking at the numbers above, you can guess that Blue Label is most likely to be the big winner. But you’ll know more after you do the post tests.
Item 4
Which is candle lasts more days?
Non-Sented Low-Sented High-Sented
3 5 8
9 1 2
5 2 6
11 5 4
Sum 28 13 20 61
Sum X2 236 55 120 411
N 4 4 4 12
SS 40 12.75 20 72.75
SS df ms
Between 27.17 2 14.08
Within 72.75 9 8.08
Total 100.92 11 9.17
F = 1.74
Critical value of F = 4.26. F is not significant.
Which is candle lasts more days? No significant difference between them. Choose any.
