What are cross-tabulations?

This is a perfectly reasonable question. To illustrate what we mean by cross-tabulations in PEPiN Nerd Blog Post 3 , let’s have an example. We could compare Secure Employment with a variable we (sadly) did not measure, ‘Owns One Or More Pets’ in a two-by-two (2 x 2) cross-tabulation. It is a called a 2 x 2 cross-tabulation because it reflects the fact that each variable can only have two outcomes. Either you are or are not in secure employment, and either you are or are not an owner of one or more pets.

 Secure Employment? YES NO TOTAL Owns one or more pets YES Cell 1 Cell 2 = Cell 1+2 NO Cell 3 Cell 4 = Cell 3+4 TOTAL = Cell 1+3 = Cell 2 +4 = Cell 1+2+3+4

All cross-tabulations have rows and columns. Columns go up and down, like columns on a building. Rows go left and right, like rows in a stadium or movie-theatre.

Collectively, these rows and columns create a series of boxes. The boxes that contain numbers are called cells. In this example, there are nine cells, but we’ve named them in a weird way. You will see why in a moment. Cells can contain numbers that are counts, percentages or both.

A count is the number of persons ending up in a particular cell, whereas the percentage is that count converted to a percentage by dividing the count by the total number of responses.

In this example, Cell 1 includes all the people who have secure employment and who own one or more pets. Cells 2 includes all the people who do not have secure employment, but do own one or more pets. Cells 3 is the reverse of Cell 2, as it contains all the people who have secure employment but who own no pets. Cell 4 is the reverse of Cell 1, as it contains all the people who lack secure employment and pets.

The bottom and right-most cells of a cross-tabulation always contain the row, column or total totals (this last one is not a typo). These totals are taken by adding their corresponding row or column. The special case is the bottom-most, right-most cell, as it is the total of the row totals and column totals. This total of the totals should always equal the total number of persons who answered both questions.

So now you have had an accidental lecture on the construction of cross-tabulations. Why would we ever bother to use these funny looking tables?

Cross-tabulations are useful because they allow us to see if one outcome varies with another. If we think that lots of people with secure employment are likely to have pets, we would expect to see that in this table, especially given our random sampling procedure (to be discussed in another blog post). To use some examples for which we do have data: Do people with secure employment tend to have children? Do they tend to be partnered (common-law or otherwise)? Do they tend to have health problems? These kinds of questions can be answered using cross-tabulations of the PEPiN survey data.

Ultimately, this — constructing a variable to measure precarious employment and comparing it in a cross-tabulation with another variable — allows us to see if the things alleged to accompany precarious employment actually happen more to someone who is precariously employed in Niagara.