Table of Contents
What Is the IQV?
The Index of Qualitative Variation (IQV) measures the degree of diversity or variability in categorical (nominal) data. It ranges from 0 (no variation, all cases in one category) to 1 (maximum variation, cases equally distributed across all categories).
Unlike standard deviation which applies to numerical data, the IQV is specifically designed for categorical variables such as race, religion, political party, or product type. It quantifies how evenly distributed the observations are across the categories.
Formula
Where K is the number of categories, N is total frequency, f is frequency per category, and p = f/N is the proportion per category.
Interpretation
| IQV Range | Interpretation |
|---|---|
| 0.00 - 0.20 | Very low diversity |
| 0.20 - 0.40 | Low diversity |
| 0.40 - 0.60 | Moderate diversity |
| 0.60 - 0.80 | High diversity |
| 0.80 - 1.00 | Very high diversity |
Frequently Asked Questions
When is the IQV equal to 1?
The IQV equals 1 when all categories have equal frequencies, representing maximum possible variation. For example, if 4 categories each have 25 observations out of 100, the distribution is perfectly even.
Can IQV be used for ordinal data?
While IQV can technically be computed for ordinal data, it does not account for the ordering of categories. For ordinal data, other measures like the ordinal dispersion index may be more appropriate.
How does IQV differ from entropy?
Both measure diversity, but they use different formulations. Shannon entropy uses logarithms and can exceed 1. The IQV is normalized to always fall between 0 and 1, making it more intuitive to interpret as a percentage of maximum possible variation.