Question

Identify two important operating standards that are routinely measured in your organization. These measures must meet the criteria for qualitative, nominal measures. Observations must be cross-classified into a contingency table. Obtain a sample that will produce at least five observations into each group of the cross-classification.

Purpose:  To demonstrate the application of non-parametric tests in your organization.

Example:  A standard measure that fits these requirements is the human resource department’s employee tracking system. The director of human resources of my company wants to do a study to determine if there is a relationship between the management status and gender of the employees. She creates a contingency table that has Male or Female categories for the rows, and Manager or non-manager categories for the columns. Then she counts the number of female managers, female non-managers, male managers, and male non-managers and enters the numbers in the table. This is the observed value table. Then she conducts the hypothesis test.

a)      Perform the cross-classification of the two nominal variables into a contingency table.

b)       Test the hypothesis that there is no relationship between the two variables.

c)       Discuss the result and interpretation of your hypothesis test

Answer 1

As observed there are 30 males of which 16 are managers and 20 females of which 13 are managers

Then the 2x2 contingency table is given as

Status/Gender	Male	Female	Total
Manager	16	13	29
Non manager	14	7	21
Total	30	20	50

The expected frequency is Row total * Column total / Grand total

Status/Gender	Male	Female
Manager	17.4	11.6
Non manager	12.6	8.4

B)Null Hypothesis ,H₀: There is no relation between gender and management status

Alternative Hypothesis,H_a: There is relationship between gender and management status

Test Statistic is

Oi	Ei	(Oi-Ei)	(Oi-Ei)2	(Oi-Ei)2/Ei
16	17.4	-1.4	1.96	.11
13	11.6	1.4	1.96	.17
14	12.6	1.4	1.96	.16
7	8.4	-1.4	1.96	.23

The value of test statistic is .67

Degree of freedom is (r-1)(c-1)= 1

Critical value is 3.841

Since the calculated value is less than critical value , we accept the null hypothesis and conclude that there is no relationship between gender and management status