Question

Four sections of the same statistics course are taught by four teachers. Using the data given below and a level of significance of 5%

(a) Are the average grades of the four classes significantly different?

(b) Use the Duncan test to help decide which classes differed in mean grade.

Class 1	78	83	65	74	91	83	-	-
Class 2	92	81	87	76	94	85	90	-
Class 3	63	71	65	68	83	-	-	-
Class 4	94	87	89	92	90	89	85	93

Answer 1

a)

ANOVA
Grade
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	1397.565	3	465.855	10.759	.000
Within Groups	952.589	22	43.300
Total	2350.154	25

Ans: The estimated p-value of F-statistic is 0.000. Hence, we can conclude that at least a pair of the average grades of the four classes is significantly different at 0.05 level of significance.

b)

Ans: From the above table of Duncan, we can conclude that the class 3 has statistically significant from class 1,2 and 3 at 0.05 level of significance from subset 1. From subset 2, the class 2 is statistically significant from 1 and 4, and class 2 have statistically significant from class 1 and 4. Similarly, from subset 3, class 2 has statistically significant from class 3 and 1, and class 4 has statistically significant from class 3 and 1.