Categorical Data and Chi-Square Tests

Categorical Data and Chi-Square Tests

The chi-square test is one of the most commonly cited tests in the biomedical literature. Before discussing this statistic, we would like to digress briefly to consider how it fits into the “big picture” of statistical testing. Previously, we presented the concepts of measurement systems, levels of measurement, and the appropriate use of statistics for each type of measurement system.

To review, the four levels of measurement are nominal, ordinal, interval, and ra-tio. Nominal measures are classifications such as sex (male, female) or race (white, black, Asian). Ordinal measures refer to rankings, e.g., shoe size (narrow, medium, wide) or year in college (freshman, sophomore, junior, senior). Both interval and ratio measures have the property of equal measurement intervals. The measurement systems are different in that an interval scale does not have a true zero point, where-as a ratio scale has a meaningful zero point.

For example, the Fahrenheit temperature scale is an interval scale; IQ scores also denote interval measurement. You may see that any two adjacent points on an inter-val scale have the same distance between them as any other two adjacent points, i.e., the distance between IQ 60 and 61 is the same as the distance between 120 and 121—one unit. Note that the measurement scale for IQ does not have a true zero point; there is no such thing as a zero IQ. A ratio scale is also an interval scale but it has the property of a “true” zero point that means nothing. There are many exam-ples of ratio scales: blood cholesterol level, height, and weight are only a few. You can see that a cholesterol value of 0 would mean 0 cholesterol. However, a Fahren-heit temperature of 0 does not mean the absence of heat. In the Kelvin scale (a ratio scale), a temperature of 0 refers to the absence of heat (purely a theoretical concept that has never been attained).