# 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.
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