The in-class worksheet for this week is all about practicing statistical inference for categorical variables!
Recall we have learned the following procedures:
Chi-square goodness of fit
\(H_0: p_{1} = p_{1,0}, p_{2} = p_{2,0}, p_{3} = p_{3,0}, \dots, p_{k} = p_{k,0}\)
Example: Does the distribution of beak types for finches on the San Cristobal island match the distribution of beak types for finches on the Pinta island. On Pinta island \(56\%\) of the finches have the first beak types, \(30\%\) of the finches have the second beak types, \(7\%\) have the third type, and \(7\%\) have the fourth type.
Chi-square test of homogeneity
\(H_0: p_{1} = p_{2} = p_{3} = \cdots = p_{k}\)
Example: Are all the flavors of jelly beans evenly distributed in the packages sold at a supermarket?
Chi-square test of independence
\(H_0:\) Categorical variable \(X\) is independent of categorical variable \(Y\).
Example: Is whether or not a person aboard the Titanic survived independent of their class status?
Recognize whether or not a statistical question involves count data.
Determine which chi-square procedure is appropriate for different inference questions about count data.
Just because some data can be presented in tabular format doesn’t mean that it is count data!
Although the format of the null and alternative hypotheses are standard for each procedure, translating these statements about population parameters into a particular applied context takes careful thought.
Let’s take a minute to review our previous in-class worksheets.