The Shannon Diversity Index is a way to measure the diversity of species in a community.
To calculate this index for a given community, simply enter a list of observed frequencies for up to 10 species in the boxes below, then click the “Calculate” button:
| Species | Frequency |
|---|---|
| Species #1 | |
| Species #2 | |
| Species #3 | |
| Species #4 | |
| Species #5 | |
| Species #6 | |
| Species #7 | |
| Species #8 | |
| Species #9 | |
| Species #10 |
Shannon Diversity Index (H): 1.081384
Shannon Equitability Index (EH): 0.984318
Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike. My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.
УВажаемые разработчики, спасибо большое. НО почему индекс Шенона на вВашем калькуляторе можно посчитать для сообществ с числом видов не более 10. ? Может я что-то не понял?
С уважением, Александр Антонов
Thank You!
I need some note on Shannon Diversity Index (H):
Hello…Please let us know your question so that we may better guide you.
I want to use the Shannon diversity index for income diversification analysis, kindly can you assist me in this regard as I have doubt about its applicability and how to go about. Thank you very much in advance.
Absolutely — I’d be glad to help you apply the **Shannon Diversity Index (SDI)** to **income diversification analysis**. Let’s break this down:
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### 🔍 **1. What Is the Shannon Diversity Index (SDI)?**
The **Shannon Diversity Index**, originating from information theory and ecology, measures **entropy** or **uncertainty** in a system. It’s commonly used to quantify **diversity** in species, but it’s also widely adapted in economics for **income source diversification**.
The formula is:
$$
H = -\sum_{i=1}^{n} p_i \cdot \ln(p_i)
$$
Where:
* $n$ = number of income sources
* $p_i$ = proportion of total income from source $i$
* $\ln$ = natural logarithm
—
### ✅ **2. Applicability to Income Diversification**
**Why use it?**
* It captures both **richness** (number of income sources) and **evenness** (how income is distributed among them).
* A **higher value** of SDI implies a **more diversified** income structure.
* It can be applied at household, community, or regional levels.
**Examples of income sources**:
* Salary
* Farming
* Business
* Remittance
* Aid
* Investment returns
—
### 🧮 **3. How to Compute It (Step-by-Step)**
Suppose a household has the following income:
| Income Source | Amount (\$) |
| ————- | ———– |
| Farming | 5,000 |
| Remittance | 2,000 |
| Business | 3,000 |
| Total | 10,000 |
**Step 1:** Compute the proportion of income from each source:
* $p_{\text{farming}} = 5000 / 10000 = 0.5$
* $p_{\text{remittance}} = 2000 / 10000 = 0.2$
* $p_{\text{business}} = 3000 / 10000 = 0.3$
**Step 2:** Plug into the formula:
$$
H = -(0.5 \ln 0.5 + 0.2 \ln 0.2 + 0.3 \ln 0.3)
$$
$$
H \approx -(-0.3466 – 0.3219 – 0.3612) = 1.0297
$$
**Interpretation:**
* Max value of H = $\ln(n)$, where all sources are equally represented
* This value (\~1.03) indicates moderate diversification
—
### 📊 **4. Interpreting SDI in Income Analysis**
| **Value of H** | **Interpretation** |
| ————– | —————————— |
| Close to 0 | One dominant income source |
| Medium | Uneven but multi-source income |
| Close to ln(n) | Perfectly even diversification |
—
### 🧠 **5. Things to Keep in Mind**
* Make sure all income values are **non-zero and positive**.
* Normalize by **total income** before computing proportions.
* If income from some sources is zero, **exclude them** from the calculation or set $p_i = 0$, which contributes nothing to the index.
—