“A SCALE or INDEX is a composite measure combining several variables [or items] into a single unified measure of a concept” (Meier, Brudney, and Bohte, 2011, p. 144). Scale/index variables are useful for several reasons:
- They can make analyzing a concept less complicated by reducing the number of variables
- They allow for more detailed analysis by
- providing a more reliable and comprehensive measure of the underlying concept than any single item could provide on its own
- transforming nominal level data into interval/ratio level data through summation (as the “scale” term indicates)
- They provide a clearer interpretation of the data by summarizing the information from multiple items into single scores, making it easier to communicate findings
If two or more variables are measured along the same scale (for instance, binary dummy variables), the values for these variables for each observation can simply be adding together to create a SUMMATIVE SCALE/INDEX variable. If we have three such variables, the resulting summative scale/index variable will range from 0 to 3, use real numbers, have equal intervals between categories, and have an absolute zero point. These characteristics describe a ratio-level variable. You could also divide the range of the summative scale/index variable by the number of variables (for this example, 3/3) to transform it to a MEAN SCALE/INDEX variable that captures the average of across all three variables, using the original scale (for this example, ranging from 0 to 1).
If the variables you want to use when constructing a scale/index variable are measured along different scales, you would first standardize your variables so they are measured using the same scale (specifically, both following a standard normal distribution). Then, the standardized values (i.e., z-scores) for these variables for each observation can simply be adding together to create a summative scale/index variable with the characteristics of a ratio-level variable.