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Conventions for Displaying Bivariate Tables

There are some easy-to-follow conventions for displaying tables like these. Table 21.4 is a complete table. The numbers at the margins—down the right-hand column and along the bottom row—are called, unsurprisingly, the marginals. The sum of the marginals down the right-hand side and the sum of the marginals across the bottom are identical, and the number in the lower-right-hand corner (36,054) is the total frequency of elements in the table.

I prefer to keep tables uncluttered and to show only the percentages in each cell and the n for each column. You get a better understanding of what’s going on from percentages than from raw numbers in a table like this, and the interested reader can always calculate the n for each cell.

In bivariate tables, no matter what size (2 X 2, 3 X 2, or larger tables), the convention is to put the dependent variables in the rows and the independent variable in the columns. Then there’s an easy rule to follow in reading a table: percentage down the columns and interpret across the rows. There are, of course, exceptions—they are, after all, conventions and not laws. When the independent variable has too many categories to fit on a narrow page, it makes sense to show the independent variables in the rows.

Percentaging down table 21.4, we see that 75.1% of white households with children had two parents in 2008, and 24.9% were headed by single parents. In black households with children, the percentages are 40.3% and 59.7%, respectively. Interpreting across, we see that 75.1% of white households with children had two parents in 2008 compared to 40.3% for black households. Among single-parent households, 24.9% were white and 59.7% were black. Interpreting the numbers in a cross-tab forces you to think about explanations. The probability of a child having two parents was much higher for white children in 2008 than it was for black children—about two-and-a-half times higher, in fact.

What’s going on? As I explained in chapter 2, association between two variables does not, by itself, imply cause—no matter how strong the association. The dependent variable in table 21.4 is obviously family type. Nobody’s skin color (which is, at bottom, what the so-called race variable is about in the United States) depends on whether they are a member of a two-parent or a one-parent family.

And clearly—and I mean absolutely, positively, no-fooling, clearly—being black did not cause anyone, not one single person, to be part of a single-parent household. Being a black man in the United States, however, means a high probability of attending poorly funded schools, and poor schooling produces severe disadvantage in the labor market. When men in the United States don’t provide financial support, poor women are likely to turn to welfare.

Historically, welfare systems have punished women who have a live-in husband by lowering the women’s allotments. Some women respond by maintaining single-parent households and some fraction of African American, single-parent families are caused by this sequence of events. There are, then, several intervening and antecedent variables that link being counted as black by the U.S. Census and being part of a single-parent household. (See figure 2.4 about intervening and antecedent variables.)

Some of the most interesting puzzles about human life involve understanding the role of intervening and antecedent variables—and figuring out which is which. Middle-aged men who drink at least six cups of coffee a day are more likely to have a heart attack than are men who don’t drink coffee at all. Men who drink a lot of coffee, however, consume more alcohol, more saturated fats, and more cholesterol than men who don’t drink coffee. The heavy coffee drinkers are less likely to exercise, more likely to smoke, and more likely to be impatient, aggravated people (the famous Type A personality). The jury is still out on how all these factors are related, but lots of researchers are trying to disentangle this problem (Ketterer and Maercklein 1991; Riksen et al. 2009).

Here’s another one. Interethnic marriage often increases when tribal peoples move from rural villages to cities. One effect of this is that unilineal systems are under pressure to become bilateral over time. Is it just the lack of prospective mates from one’s own ethnic group that causes this? Or is there something inherently unstable about unilineal kinship systems under urban conditions (see Clignet 1966; Feldman 1994)?

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