Question

You say you want to calculate some F statistics? Well, you've come to the right place. Use the following data for Questions 6-10. There are four people per cel. The total sum of squares is 1968, and the within group sum of squares is 1080. The dependent variable is test score. The independent variables are state and major. If for any test, the degrees of freedom aren't on the table, use the closet value the table has. CA ND CN 10 Bio History 14 20 8 Eng. 963 6-7. (two questions-twenty points) Is there a main effect of Major? Please calculate the F-statistic, state the critical value, and come to a conclusion about the null hypothesis, and state what this means with regards to the experiment. (a05) 8-9 (two questions -twenty points) Is there a simple effect of State at English? Please calculate the F-statistic, state the critical value, and come to a conclusion about the null hypothesis, and state what this means with regards to the experiment. (a.05), 10. Re-draw the 3x3 table above showing what the cell means would be if the main effects were removed-the differences between the cell means will thus indicate the interaction (like we did in class).

Answer 1

6-7:

	CA	ND	CN
Bio	10	4	7
History	14	20	8
Eng	9	6	3

SS(Major) = 12 [ (7-9)^2 + (14-9)^2 + (6-9)^2 ] = 456

F = (456/2) / (1080/27) = 5.7

Number of people in each cell is 4.

So, d.f. of each cell i.e. within the group of people per cell is 4 - 1 = 3.

Total number of cells is 9. Hence, d.f. within the group is 3 × 9 = 27. Hence, the reason.

F-critical value = 2.96. which is less than calculated F-value.

Hence p-value = 0.00185. The p-value is significant at 0.05 significance level.

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