The first major application of statistical theory concerns “goodness of fit.” This topic concerns creating hypothesis test relating an observed (data) distribution to a hypothesized (population) distribution. At some level these tests are all related to the Chi-Square test. However, that level is frequently far removed from our observations.

Objectives

By the end of this module, the student will

• understand Chi-Square tests
• create/apply a Chi-Square test to multnomial data
• create/apply a Chi-Square test to testing independence between two categorical variables
• perform parametric analysis, comparing an observed distribution to a theorized distribution

Readings

All readings are from our official textbook.

• Sections 7.1 to 7.4
• Guided Thought Questions

Example Scripts

The following R script provide some additional practice in statistical computing. Consider these to be required activities.

• Chi-Square test explorations
• More uses of the Chi-Square tests
• Goodness-of-Fit tests for distributions, Kolmogorov and Smirnov
• Other Goodness-of-Fit tests for distributions, I
• Other Goodness-of-Fit tests for distributions, II

Statistical Computing Activity

• SCA 5: Chi-Square Tests

Assignment

• Assignment 5: Kolmogorov and Smirnov