Bivariate analysis

Bivariate analysis

Simple Statistics, Part C: Bivariate analysis

As might be expected, bivariate analysis is simply the statistical analysis of data on two variables at the same time. The prefix bi refers to two, as in bicycle. Examples of this kind of analysis would include the earlier hypothetical study of the differences in GPA between males and females. (G.P.A. is one variable, sex is the other.) If data were gathered on educational achievement and earned income, the researcher would have data on two different variables and could see if people with more education tended to earn higher incomes or not. (Education is one variable, income is the second.)

Much of the time, bivariate data is presented to the reader in table form such that the values of one variable are the columns of the table (the vertical lines) and the values of the other variable are the rows (the horizontal lines). Table 8.1 shows hypothetical (fake) data on the variables education level completed (the columns) and annual earned income (the rows).


  High School Graduate College Graduate Master’s Degree
Low Income 75% 25% 10%
Middle Income 20% 60% 50%
High Income 5% 15% 40%

Table 8.1. Annual earned income by education level completed


If one looks at the column labeled High School Grad., it is seen that only 5% of those whose highest educational achievement was to graduate from high school were earning what was described as a High Income. On the other hand, those graduating from college and those with master’s degrees placed 15% and 40%, respectively, into the High Income bracket. Thus, it could be concluded that there is something about getting a college degree, and especially a master’s degree, that increases the chance that one will earn a high income. This table, then, would be called a bivariate table because it presents the data on two different variables at the same time.


Bivariate tables (sometimes called contingency tables) provide answers to questions such as “Has the percentage of adult Americans who are willing to vote for a woman president increased since 1972?” or, more generally, to questions such as “Is there a difference between sample members that fall into one category of an independent variable and their counter parts in other categories in their experience of another characteristic?”


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