A researcher begins with a sample of 60 subjects and randomly assigns 12 to each of 5 treatment conditions. Based on his reading of other studies in the area, the researcher predicts that group 3 will obtain a significantly different mean from group 1, and that group 4 will obtain a significantly higher mean than group 1.
a)Given the following data (note that some subjects have dropped out) are the researcher's predictions supported with á .01?
1 2 3 4 5
n = 8 10 10 12 12
X-bar = 43.5 45.2 61.8 77.3 66.7
Si = 5.6 6.3 5.4 8.7 7.5
b)After collecting and inspecting the data, the researcher decides to perform three more tests. Specifically, he wishes to see whether X-bar3 is significantly different from X-bar2; whether X-bar5 is significantly different from X-bar2; and whether X-bar4 is significantly greater than X-bar2. Perform whichever statistical analyses are necessary and, if appropriate, use the procedure that allows each comparison to be tested with á .01.
Answer:
a) 3 vs. 1, t = 5.53, Reject Ho
4 vs. 1, t = 10.608, Reject Ho
b) F = 43.696, Reject Ho
3 vs. 2, q = 7.583, Reject Ho
5 vs. 2, q = 9.822, Reject Ho
4 vs. 2, no test valid
If you do an ANOVA test on your data, there are different ways to approach this.
You will need to determine mean squares between and within to find the F-ratio.
Using the data you listed, I found the F-ratio = 43.696 using the following method.
Mean squares within:
[7(5.6)^2 + 9(6.3)^2 + 9(5.4)^2 + 11(8.7)^2 + 11(7.5)^2]/[(8 + 10 + 10 + 12 + 12) - 5] = (2290.51)/(47) = 48.734
Mean squares between:
8(43.5) + 10(45.2) + 10(61.8) + 12(77.3) + 12(66.7) = 3146 -->first step
8(43.5)^2 + 10(45.2)^2 + 10(61.8)^2 + 12(77.3)^2 + 12(66.7)^2 = 198850.96 -->second step
[198850.96 - (3146)^2/52]/(5 - 1) = 2129.49 -->final step (Note: 52 = total number of subjects; 5 = total number of groups)
To find F-ratio:
(2129.49)/(48.734) = 43.696
To compare two means, you may want to use multiple comparison procedures to answer your other questions. (Note: the term "within" may be listed as "error" in some texts.)
I hope this will help.
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