RESEARCH METHODS HANDBOOK

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Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

Chi-square Goodness of Fit Test
Comparing frequencies of nominal data for a one-sample case.

Assumptions

Independent random sampling

Nominal level data

State the Hypothesis Null Hypothesis (Ho): There is no significant difference between the categories of observed frequencies for the data collected.

Alternative Hypothesis (Ha): There is a significant difference between the categories of observed frequencies for the data collected.

Set the Rejection Criteria Determine degrees of freedom k - 1

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

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

Compute the Test Statistic

n = sample size

k = number of categories or cells

Fo = observed frequency

Fe = expected frequency (determined by the established probability of occurrence for each category/cell -- the unbiased probability for distribution of frequencies n/k)

Decide Results of Null Hypothesis The null hypothesis is rejected if the test statistic equals or exceeds the critical value. If the null hypothesis is rejected, this is an indication that the differences between the expected and observed frequencies are too great to be attributed to sampling fluctuations (error). There is a significant difference in the population between the frequencies observed in the various categories.

Example