1. What is the Index of Dispersion?

The Index of Dispersion (ID), also known as the variance-to-mean ratio, is a normalized measure of the dispersion of a probability distribution. It is used to identify whether observed data are more or less clustered than expected for a particular statistical model.

2. How Does the Calculator Work?

The calculator uses the Index of Dispersion formula:

Where:

• \( \text{Variance} \) — The variance of the dataset (σ²)
• \( \text{Mean} \) — The arithmetic mean of the dataset (μ)

Explanation: The Index of Dispersion compares the variance to the mean, providing insights into the distribution pattern of the data.

3. Importance of Index of Dispersion

Details: The Index of Dispersion is particularly useful in statistics for testing whether data follows a Poisson distribution (where ID ≈ 1), or shows overdispersion (ID > 1) or underdispersion (ID < 1).

4. Using the Calculator

Tips: Enter the variance and mean values. Both values must be positive numbers. The result is a dimensionless quantity that indicates the dispersion pattern.

5. Frequently Asked Questions (FAQ)

Q1: What does an ID value of 1 indicate?
A: An ID value of approximately 1 suggests that the data follows a Poisson distribution, where variance equals mean.

Q2: What is overdispersion?
A: Overdispersion occurs when ID > 1, indicating that the variance is greater than the mean, suggesting more variability than expected.

Q3: What is underdispersion?
A: Underdispersion occurs when ID < 1, indicating that the variance is less than the mean, suggesting less variability than expected.

Q4: In which fields is the Index of Dispersion commonly used?
A: It is widely used in ecology, epidemiology, quality control, and various scientific fields to analyze count data and distribution patterns.

Q5: Are there limitations to using the Index of Dispersion?
A: The Index of Dispersion can be sensitive to sample size and may not be appropriate for all types of data distributions. It works best with count data.