Two Qualitative Questions - The Contingency Table

Often when we obtain qualitative data, we ask more than one question or test for more than one attribute. In this lesson, we will consider the case in which we obtain two types of qualitative data. We will decide on the best way to record the answers to two survey question. In statistics, two types of data means two dimensions and suggests that we record the data in a two dimensional array. In common terms, we will record the data in a table. The major issue is how we should lay out our table.

We will be recording the results on the inside of the table and when we are done we will have a frequency or relative frequency distribution. We would like to be able to count the answers to the questions by making a mark in the table and then counting the number of marks. We then replace the marks with the number and that will be our frequency. The crucial issue is that we want to keep the results for single sample element together. In our example, we will be doing marketing research. We will simply ask whether or not the person saw our advertisement and whether or not they bought our product. If a person sees the advertisement it is important to know whether that person bought our product. If we simply recorded the number of answers for the questions separately, we would be unable to determine what an individual did.

We want to create a table in which we can make a single mark that represents both answers to our questions. This way, the number of marks would be the same as the number of people or things in the sample. Then the frequencies would have essentially the same meaning that they have when we only ask one question. The really important point however, is that when one mark represents both answers, the associations between answers obtained from each sample element is preserved. If we sampled people, a person could point to his mark and we would know both of the answers that that person gave.

This may seem like an impossible task but it is actually easier to achieve than it sounds. The secret has to do with where we make our mark. I t takes two pieces of information to locate ourselves in a table, the row number and the column number. Of course, that is exactly the number of answers that we wish to record, so it should be possible.

We will look for a table to record the answers to the questions in the following example:

Example. We are going to record answers to the following questions: