Question

can someone help me I have a question similar to this and I am completely lost. How do you determine the between vs within groups?

Three sets of three mice were randomly selected to be placed in a standard maze but with different color doors. The response is the time required to complete the maze as seen in the table below. Perform appropriate analysis to test whether there is an effect due to door coloring.

Color	Time			Yi.	ȳi.	ȳ..
Red	9	11	10	30	10	11.89
Green	20	21	17	58	19.33
Black	6	5	8	19	6.33

H₀:                                                                                                                   H_A:

ANOVA Table

Source	Df	SS	MS	F	p
Between groups
Within groups
Total

Answer 1

The summary statistics obtained from the given data are as below.

	No Music	Soft Rock	Classical
Total	30	58	19
n	3	3	3
Mean	10.00	19.33	6.33
Sum Of Squares	2	8.67	4.67

The Hypothesis:

H0: There is no difference between the means of the timings for the three colored doors.

Ha: The mean of at least one time is different from the others..

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The ANOVA table is as below. the p value is calculated for F = 52.97 for df1 = 2 and df2 = 6

The Fcritical is calculated at = 0.05 (default level) for df1 = 2 and df2 = 6

Source	DF	SS	Mean Square	F	Fcv	p
Between	2	269.55	134.78	52.97	5.143	0.0002
Within	6	15.27	2.54
Total	8	284.82

The Decision Rule:

If Ftest is > F critical, Then Reject H0.

Also if p-value is < , Then reject H0.

The Decision:

Since Ftest (52.97) is > F critical (5.143), We Reject H0.

Also since p-value (0.0002) is < (0.05, default), We Reject H0.

The Conclusion: There is sufficient evidence at the 95% level of significance to conclude that the mean of at least one time is different from the others.

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Calculations For the ANOVA Table:

Overall Mean = Average of Means = (10 + 19.33 + 6.33) / 3 = 11.89

SS treatment = SUM [n* ( - overall mean)²] = 3 * (10 - 11.89)² + 3 * (19.33 - 11.89)² + 3 * (6.33 - 11.89)² = 269.55

df1 = k - 1 = 3 - 1 = 2

MSTR = SS treatment/df1 = 269.55 / 2 = 134.78

SSWithin = SUM (Sum of Squares) = 2 + 8.67 + 4.67 = 15.27

df2 = N - k = 9 - 3 = 6

Therefore MS within = SSwithin/df2 = 15.27 / 6 = 2.54

F = MSTR/MSE = 134.78 / 2.54 = 52.97

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