Two-Way Tables (Contingency Tables) Defined for AP Statistics

Practice problems for these concepts can be found at:

• Inference for Catergorial Data Multiple Choice Practice Problems for AP Statistics
• Inference for Catergorial Data Free Response Practice Problems for AP Statistics
• Inference for Catergorial Data Review Problems for AP Statistics
• Inference for Catergorial Data Rapid Review for AP Statistics

A two-way table, or contingency table, for categorical data is simply a rectangular array of cells. Each cell contains the frequencies for the joint values of the row and column variables. If the row variable has r values, then there will be r rows of data in the table. If the column variable has c values, then there will be c columns of data in the table. Thus, there are r × c cells in the table. (The dimension of the table is r × c). The marginal totals are the sums of the observations for each row and each column.

example: A class of 36 students is polled concerning political party preference. The results are presented in the following two-way table.

The values of the row variable (Gender) are "Male" and "Female." The values of the column variable (Political Party Preference) are "Democrat," "Republican," and "Independent." There are r = 2 rows and c = 3 columns. We refer to this as a 2 × 3 table (the number of rows always comes first). The row marginal totals are 20 and 16; the column marginal totals are 18, 15, and 3. Note that the sum of the row and column marginal totals must both add to the total number in the sample.

In the example above, we had one population of 36 students and two categorical variables (gender and party preference). In this type of situation, we are interested in whether or not the variables are independent in the population. That is, does knowledge of one variable provide you with information about the other variable? Another study might have drawn a simple random sample of 20 males from, say, the senior class and another simple random sample of 16 females. Now we have two populations rather than one, but only one categorical variable. Now we might ask if the proportions of Democrats, Republicans, and Independents in each population are the same. Either way we do it, we end up with the same contingency table given in the example. We will look at how these differences in design play out in the next couple of sections.

Practice problems for these concepts can be found at:

• Inference for Catergorial Data Multiple Choice Practice Problems for AP Statistics
• Inference for Catergorial Data Free Response Practice Problems for AP Statistics
• Inference for Catergorial Data Review Problems for AP Statistics
• Inference for Catergorial Data Rapid Review for AP Statistics