Final answer:
A chi-square test requires observed frequency data, which are compared to expected frequencies based on the null hypothesis. Categories in the test must have an expected frequency of at least five to ensure valid results.
Step-by-step explanation:
To conduct a chi-square test, there are specific types of data necessary. The three major applications of the chi-square distribution are:
- The goodness-of-fit test, which determines if data fit a particular distribution.
- The test of independence, which determines if events are independent.
- The test for homogeneity, which determines whether two populations come from the same distribution, even if this distribution is unknown.
For all these tests, the data needed are the observed frequencies in each category. These observed values are then compared to expected values. The expected values are calculated based on the null hypothesis being tested. For instance, the null hypothesis for the goodness-of-fit test states that the data come from the assumed distribution, while the test for homogeneity hypothesis states that the populations of the data sets come from the same distribution.
Each cell or category in a chi-square test must have an expected frequency of at least five. This condition is important to fulfill the requirements of the test and to ensure the validity of the results.