Question

You assume that students are more likely to miss a standardized test scheduled in April than December. You ask 11 professors from 11 different schools who all teach a full year course to keep track of the number of students who are ill during the testing period for each term. The table shows you how many students missed a test for each testing period for the 11 different schools:

class	Dec	April	+ -	RANK-Dec	RANK-April	D	D2
1	4	7	-	3	4	-1	1
2	3	8	-	2	5	-3	9
3	11	12	-	9	9	0	0
4	13	16	-	10	11	-1	1
5	8	6	+	7	2.5	4.5	20.25
6	5	9	-	5	6	-1	1
7	7	10	-	6	7	-1	1
8	5	6	-	4	2.5	1.5	2.25
9	2	2	T	1	1	0	0
10	9	11	-	8	8	0	0
11	14	15	-	11	10	1	1
SUM	81	102		66	66	0	36.5
St Dev	4.03	4.13		3.32	3.31	1.91	6.16

What are the rules of this analysis? What would you calculate for your value? What is your decision? What is your conclusion?

Answer 1

The independent variable is the professors who all teach a full-year course.

The dependent variable is the number of students who are ill during the exam.

If the original difference < 0 then the rank is multiplied by -1; if the difference is positive the rank stays positive. For the Wilcoxon signed-rank test we can ignore cases where the difference is zero.

		variables:	April - Dec
		50.5	sum of positive ranks
		4.5	sum of negative ranks
		10	n
		27.500	expected value
		9.811	standard deviation
		2.344	z
		.0095	p-value (one-tailed, upper)
	No.	Data	Rank
	1	3	7
	2	5	10
	3	1	2
	4	3	7
	5	-2	4.5
	6	4	9
	7	3	7
	8	1	2
	9	2	4.5
	10	1	2

The test statistic is 2.344.

The p-value is 0.0095.

Since the p-value (0.0095) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that students miss more exams in April than December.