1. What is Variation Ratio?

Definition: The variation ratio (VR) is a measure of statistical dispersion in nominal distributions, showing how much a distribution varies from the modal category.

Purpose: It helps researchers understand the diversity or concentration of categorical data.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( VR \) — Variation ratio (dimensionless, between 0 and 1)
• \( f_m \) — Frequency of the modal category (proportion between 0 and 1)

Explanation: The formula subtracts the modal frequency from 1, showing what proportion of cases don't fall into the modal category.

3. Interpretation of Results

Details:

• VR = 0: All cases are in the modal category (no variation)
• VR = 1: No cases are in the modal category (maximum variation)
• VR between 0 and 1: Indicates degree of dispersion

4. Using the Calculator

Tips: Enter the frequency of the modal category as a decimal between 0 and 1 (e.g., 0.75 for 75%).

5. Frequently Asked Questions (FAQ)

Q1: What's a good variation ratio value?
A: There's no "good" value - it depends on your research context. Higher values indicate more diversity in responses.

Q2: How do I find the modal frequency?
A: Divide the count of the most frequent category by the total number of observations.

Q3: When should I use variation ratio?
A: Use it when analyzing nominal data where other dispersion measures (like standard deviation) aren't applicable.

Q4: Can VR be greater than 1?
A: No, since f_m is a proportion, VR is always between 0 and 1.

Q5: What's the difference between VR and variance?
A: VR is for categorical data, while variance is for interval/ratio data.