Question

Consider the following table:

	SS	DF	MS	F
Among Treatments	1433.611433.61		477.87477.87	1.151.15
Error	?
Total	6008.076008.07	1414

Step 1 of 8:

Calculate the sum of squares of experimental error. Please round your answer to two decimal places.

Step 2 of 8:

Calculate the degrees of freedom among treatments.

Step 3 of 8:

Calculate the degrees of freedom of experimental error.

Step 4 of 8:

Calculate the mean square of the experimental error. Please round your answer to two decimal places.

Step 5 of 8:

What is the sum of squares of sample means about the grand mean? Please round your answer to two decimal places

Step 6 of 8:

What is the variation of the individual measurements about their respective means? Please round your answer to two decimal places.

Step 7 of 8:

What is the critical value of F at the 0.050.05 level? Please round your answer to four decimal places, if necessary.

Step 8 of 8:

Is F significant at 0.050.05?

Answer 1

Standard ANOVA table is given by

	SS	DF	MS	F
Among Treatments	Tr.S.S	Tr DF	Tr.M.S. = Tr.S.S/Tr DF	Tr.M.S./E.M.S.
Error	E.S.S.	E DF	E.M.S. = E.S.S./E DF
Total	Total S.S.	Total DF

	SS	DF	MS	F
Among Treatments	1433.61	?	477.87	1.15
Error	?	?	?
Total	6008.07	14

Step 1 of 8:

sum of squares of experimental error (ESS) = Total SS - Tr. SS = 6008.07 – 1433.61

sum of squares of experimental error (ESS) = 4574.46

Step 2 of 8:

The degrees of freedom among treatments (Tr. DF) = Tr. SS/ Tr. MS = 1433.61/477.87

The degrees of freedom among treatments (Tr. DF) = 3

Step 3 of 8:

The degrees of freedom of experimental error (E DF) = Total DF – Tr. DF = 14 - 3

The degrees of freedom of experimental error (E DF) = 11

Step 4 of 8:

The mean square of the experimental error= ESS/ E DF = 4574.46/11

The mean square of the experimental error= 415.86

Step 5 of 8:

The sum of squares of sample means about the grand mean is same as the sum of squares among treatments i.e. Tr. SS = 1433.61

Step 6 of 8:

The variation of the individual measurements about their respective means is same as the Error sum of squares i.e. ESS = 4574.46

Step 7 of 8:

The critical value of F at the 0.05 = F (0.05,3,11) = 3.5874

Step 8 of 8:

Here the critical value is greater than the calculated value of F in ANOVA table that means the F is not significant at 0.05

In other words, we can say F is not significant. Since Calculated F=1.15 is less than its critical value, 3.5874, F is not significant.

	SS	DF	MS	F	S/NS
Among Treatments	1433.61	3	477.87	1.15	S at 0.05
Error	4574.46	11	415.86
Total	6008.07	14