RESEARCH METHODS HANDBOOK

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Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

Chi-square Test of Independence
Comparing frequencies of nominal data for k-sample cases

Assumptions

Independent random sampling

Nominal/Ordinal level data

No more than 20% of the cells have an expected frequency less than 5

No empty cells

State the Hypothesis Null Hypothesis (Ho): The observed frequencies occur independently of the variables tested.

Alternative Hypothesis (Ha): The observed frequencies depend on the variables tested.

Set the Rejection Criteria Determine degrees of freedom df=(# of rows - 1)(# of columns - 1)

Establish the confidence level (.05, .01, etc.)

Use the chi-square distribution table to estimate the critical value

Compute the Test Statistic

Fo= observed frequency

Fe= expected frequency for each cell

Fe=(frequency for the row)(frequency for the column)/n

Decide Results of Null Hypothesis The frequencies exhibited are/are not independent of the variables tested. There is/is not a significant association in the population between the variables.

Example