Variation Ratio
The typical value for a nominal variable is the mode, but besides knowing about the most typical value, another important piece of information is about how much variation there was. This is were measures of variability (or dispersion) come in. Although measures of dispersion are not often reported for nominal variables, there exists I think more different measures of dispersion for nominal variables than any other measurement level. A quick look on Wikipedia shows almost 40 different measures for a single nominal variable.
It will be too much to go over all the different measures and they are not often reported. If you are interested, then an article from Kader and Perry (2007) can be a nice start, it is available here.
The easiest method is most likely the Variation Ratio (VR) (Freeman, 1965). This is simply the proportion that does not belong to the modal category (Zedeck, 2014, p.406). So in the example in Table 1, we can see that 50.1% falls into the modal category of Married, and hence 49.9% does not. The Variation Ratio is therefor 49.9% (or 0.499).
Click here to see how to determine the Variation Ratio
with Excel
Excel file from video: DI - Variation Ratio.xlsm.
with Python
Jupyter Notebookfrom video: DI - Variation Ratio.ipynb.
Data used in video: GSS2012a.csv.
with SPSS
Unfortunately it is not possible (to my knowledge) to let SPSS determine the Variation Ratio. Luckily the calculation is not too difficult. I'd suggest to create a frequency table with SPSS and then use the online calculator or Excel to determine the Variation Ratio.
Online calculator
Enter the requested information below:
Manually (formula and example)
Formula
\(VR =1-\frac{n_{max}\times F_{max}}{n}\)
Symbols used
VR = Variation Ratio
nmax = the number of times the maximum frequency occurs
Fmax = the maximum frequency
n = the total sample size (i.e. the sum of all frequencies.
Example
From Table 1 the highest frequency is 972, so Fmax = 972, which only occurs once, so nmax = 1. The total frequency is 1941, so n = 1941. We can fill this out in the formula to obtain:
\(VR=1-\frac{n_{max}\times F_{max}}{n} =1-\frac{1\times972}{1941} =\frac{1941}{1941}-\frac{972}{1941} =\frac{969}{1941}\)
\(=\frac{3\times323}{3\times647} =\frac{323}{647} \approx0.4992\)
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