Topcis

1. Chi-Square Tests for Goodness of Fit
   • A chi-square test for goodness of fit tests $H_0$ that a categorical variable has a specified distribution in the population of intrest
   • The test compares the observed count in each category with what we would expect if $H_0$ was true (expected count). The expected counts are found by $np$
   • The chi-square statistic is found by $\sum \frac{(\textrm{observed}-\textrm{expected})^2}{\textrm{expected}}$
   • The conditions for as follows:
     • Random: The data comes from a random sample or experiment
       • 10%: If you are sampling without replacement, check that $10N \ge n$
     • Large Counts: Expected couns are all at least 5
   • The sampling distribution of the statistic $X^2$ can be modeled by a chi-square distribution
     • Large values of $X^2$ are in favor of $H_a$.
     • The P-value is the area to the right of $X^2$
     • $df = \textrm{number of categories} - 1$
2. Inference for Two-Way Tables
   • A chi-square test for homogeneity tests to see if there is a difference between the same categorical variables for two different populations. A chi-square test for independence tests to see if there is an association between two categorical variable for the same population.
     • Each test is performed the same with the only difference being how you state $H_0$ and $H_a$
     • The conditions are the same as test for goodness of fit
   • The expected count equals $\frac{\textrm{row total} \cdot \textrm{column total}}{\textrm{table total}}$
   • The degrees of freedom equals $df=(\textrm{number of rows} - 1)(\textrm{number of columns} - 1)$

Formulas

Terms