# Goodness of Fit and Related Chi-Square Tests

Learning Objectives

After reading this section you should be able to:

- Create frequency distribution tables
- Compute percentiles for scores within a frequency distribution
- Apply the goodness of fit test — chi-square statistical procedure to evaluate nominal level data for one or more samples
- Compute the contingency table using a chi-square statistical procedure
- Describe and compute the chi-square statistical procedure for a 2 x 2 research design to test for difference in two variables measured at the nominal level
- Describe and compute the phi-coefficient in a 2 x 2 design to evaluate the association between two variables measured at the nominal level
- Describe and compute Fisher’s Exact test in a 2 x 2 design to determine the exact probability associated with the computation of the chi-square statistic

This textbook was developed to demonstrate biostatistical research applications that can use either web-based JavaScripted calculators —**aka the Webulators** or the Statistical Analysis System —**aka SAS coding** to resolve questions arising in healthcare research. In the following sections, we will work through the concepts of statistical applications using specific examples that demonstrate the robustness of **the Webulators** and **SAS coding**. The SAS applications are based on the SAS Studio Education Analytic Suite. The Webulators are located at https://health.ahs.upei.ca/webulators to resolve specific questions using online tools. The “webulators—the web-based calculators”, provide several useful resources that extend well beyond this textbook.