1. What is the Simpson Gini Index?

The Simpson Gini Index (also known as the Gini-Simpson index) is a measure of diversity that represents the probability that two randomly selected items belong to different categories. It ranges from 0 (no diversity) to 1 (maximum diversity).

2. How Does the Calculator Work?

The calculator uses the Simpson Gini Index formula:

Where:

• \( p_i \) — Proportion of items in category i
• \( \sum p_i^2 \) — Sum of squared proportions

Explanation: The index subtracts the sum of squared proportions from 1, measuring the probability that two randomly chosen items belong to different categories.

3. Importance of Gini Index Calculation

Details: The Simpson Gini Index is widely used in ecology, economics, sociology, and information science to measure diversity, inequality, and concentration across various populations and distributions.

4. Using the Calculator

Tips: Enter proportions as comma-separated values between 0 and 1. The sum of all proportions must equal 1.0. For example: "0.2,0.3,0.5" for three categories.

5. Frequently Asked Questions (FAQ)

Q1: What does a Gini index of 0 mean?
A: A value of 0 indicates no diversity - all items belong to the same category.

Q2: What does a Gini index of 1 mean?
A: A value of 1 indicates maximum diversity - items are evenly distributed across all categories.

Q3: How is this different from the economic Gini coefficient?
A: While related, the Simpson Gini Index measures diversity in categorical data, while the economic Gini coefficient measures income or wealth inequality.

Q4: What are typical applications of this index?
A: Used in biodiversity studies, market concentration analysis, linguistic diversity, and measuring species evenness in ecological systems.

Q5: Can I use percentages instead of proportions?
A: Yes, but convert percentages to proportions first (divide by 100) and ensure they sum to 1.0.