Question

The following is a cross-tabulation of the variables gender and units (the number of units in which a student has enrolled) from a recent class survey. Number of Units Gender 1 2 3 4 5 female 4 11 60 191 3 male 2 10 28 86 1 Note that χ 2 tests require all expected frequencies to be at least 5. To ensure this you may need to combine columns in a way that makes sense in the context of a test for association. That is, you could combine columns 1 and 2, but not columns 1 and 4. Assuming the data come from randomly-selected Murdoch University students, test for an association between gender and unit load in the Murdoch University student population. If you find an association, describe it.

Answer 1

The following is a cross-tabulation of the variables gender and units (the number of units in which a student has enrolled) from a recent class survey. Number of Units Gender 1 2 3 4 5 female 4 11 60 191 3 male 2 10 28 86 1 Note that χ 2 tests require all expected frequencies to be at least 5. To ensure this you may need to combine columns in a way that makes sense in the context of a test for association. That is, you could combine columns 1 and 2, but not columns 1 and 4. Assuming the data come from randomly-selected Murdoch University students, test for an association between gender and unit load in the Murdoch University student population. If you find an association, describe it.

Given data:

Number of Units	1	2	3	4	5
female	4	11	60	191	3	269
male	2	10	28	86	1	127
	6	21	88	277	4	396

Expected Frequencies
Number of Units	1	2	3	4	5	Total
female	4.08	14.27	59.78	188.16	2.72	269
male	1.92	6.73	28.22	88.84	1.28	127
Total	6	21	88	277	4	396

Expected values in column 1 and column 5 are smaller than 5.

So we combine column 1 with 2 and column 5 with 4.

Chi-Square Test
Observed Frequencies
						Calculations
	1 and 2	3	4 and 5	Total		fo-fe
female	15	60	194	269		-3.3409	0.2222	3.1187
male	12	28	87	127		3.3409	-0.2222	-3.1187
Total	27	88	281	396
Expected Frequencies
	1 and 2	3	4 and 5	Total		(fo-fe)^2/fe
female	18.3409	59.7778	190.8813	269		0.6086	0.0008	0.0510
male	8.6591	28.2222	90.1187	127		1.2890	0.0017	0.1079
Total	27	88	281	396
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	3
Degrees of Freedom	2
Results
Critical Value	5.991
Chi-Square Test Statistic	2.0590
p-Value	0.3572
Do not reject the null hypothesis

Ho: There is no association between gender and unit load

H1: There is an association between gender and unit load

Calculated chi square = 2.059 is < critical chi square 5.991 at 0.05 level of significance.

Ho is not rejected.

We conclude that there is no association between gender and unit load.