In this chapter, students learn about the levels of measurement that social scientists engage in when collecting data. The most common system for conceptualizing quantitative data was developed by Stevens, who defined four levels of data, which are (in ascending order of complexity) nominal, ordinal, interval, and ratio-level data. Nominal data consist of mutually exclusive and exhaustive categories, which are then given an arbitrary number. Ordinal data have all of the qualities of nominal data, but the numbers in ordinal data also indicate rank order. Interval data are characterized by all the traits of nominal and ordinal data, but the spacing between numbers is equal across the entire length of the scale. Finally, ratio data are characterized by the presence of an absolute zero. Higher levels of data contain more information, although it is always possible to convert from one level of data to a lower level. It is not possible to convert data to a higher level than it was collected at. It is important to recognize the level of data because there are certain mathematical procedures that require certain levels of data. Social scientists who ignore the level of their data risk producing meaningless results or distorted statistics.

When the dependent variable consists of nominal data, it is necessary to conduct a χ2 test, of which there are two types in this chapter: the one-variable χ2 test and the two-variable χ2 test. The former procedure tests the null hypothesis that each group formed by the independent variable is equal to a hypothesized proportion. The two-variable χ2 test has the null hypothesis that the two variables are uncorrelated. Both procedures use the same eight steps as all NHSTs.

The effect sizes for χ2 tests are the odds ratio (for both χ2 tests) and the relative risk (for the two-variable χ2 test). When these effect sizes equal to 1.0, the outcome of interest is equally likely for both groups. When these effect sizes are greater than 1.0, the outcome of interest is more likely for the non-baseline group. When these values are less than 1.0, the outcome of interest is more likely for the baseline group. However, odds ratio and relative risk values are not interchangeable. When there are more than two groups or two outcomes, calculating an effect size requires either (1) calculating more than one odds ratio, or (2) combining groups together.