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STEPS FOR CONDUCTING A CONTINGENCY TABLE ANALYSIS

1. Set your null (two-classifications are independent) and alternative hypotheses (two-classifications are dependent)

2. Calculate expected cell counts and find the value of the Chi-squared test statistic

3. Check the model assumptions;

random sample from relevant population
all expected cell counts are at least 5

4. Use the p-value to decide on "rejecting the null hypothesis" or "failing to reject the null hypothesis"

5. If your decision is reject the null hypothesis, compare the observed and expected cell counts to see the association pattern.

ACTIVITY

A social scientist want to determine whether the marital status (divorced or not divorced) of U.S. men is independent of their religious affiliation (or lack thereof). A sample of 500 U.S. men is surveyed and the results are tabulated as shown in the following table:

		Religious Affiliation					TOTALS
		A	B	C	D	None	TOTALS
Marital Status	Divorced	39	19	12	28	18	116
Marital Status	Never Divorced	172	61	44	70	37	384
	TOTALS	211	80	56	98	55	500

Use the following steps and Statlets window given above, to carry out a chi-square test of independence on this data

Step 1. Enter the data:

Double click on "Col_1" and replace it with "Marital Status".

Double click on "Col_2" and replace it with "Religion A".

Double click on "Col_3" and replace it with "Religion B".

Double click on "Col_4" and replace it with "Religion C".

Double click on "Col_5" and replace it with "Religion D".

Enter the counts for each cell. (Note if you would like to see an example on how the data should be entered please click on the "Example" button on the Statlets window.

Step 2 & 3. Model checking:

Select the "Table" menu option and check whether or not any one of the expected cell counts is less than 5.

Step 4. Decision:

Select the "Chi-squared test" menu option. Report the value of the ch-squared test statistic and the associated p-value. Is there a statistical evidence to show that marital status and religious affiliation are dependent?

Step 5. Interpretation: Note that you need to do this step if you decide that the variables are dependent.

Select the "Table" menu option and compare observed and expected cell counts. Do you see a pattern?

Select the "Barchart" menu option and interpret. Do you see a pattern?

Select the "Mosaic chart" menu option and interpret. Do you see a pattern?

Select the "Skychart" menu option and interpret. Do you see a pattern?