Enter the frequency of occurrence for each variable and the total number of observations into the calculator to determine the Coefficient of Coincidence.

## Coefficient Of Coincidence Formula

The following formula is used to calculate the Coefficient of Coincidence (COC).

COC = Σ (fi * (fi - 1)) / (N * (N - 1))

Variables:

- COC is the Coefficient of Coincidence
- fi is the frequency of occurrence of each variable
- N is the total number of observations or data points

To calculate the Coefficient of Coincidence, for each variable, multiply the frequency of occurrence by the frequency of occurrence minus one. Sum up these products for all variables. Then, multiply the total number of observations by the total number of observations minus one. Finally, divide the sum of the products by the product of the total number of observations.

## What is a Coefficient Of Coincidence?

A Coefficient of Coincidence (COC) is a statistical measure used in cryptanalysis that helps in determining the likelihood of two random variables coinciding. It is often used in the analysis of cipher texts to identify patterns and break codes. The COC is calculated by comparing the frequency of occurrence of different variables in a given data set. A higher COC indicates a higher probability of coincidence, suggesting a stronger correlation between the variables.

## How to Calculate Coefficient Of Coincidence?

The following steps outline how to calculate the Coefficient of Coincidence (COC).

- First, determine the frequency of occurrence for each variable (fi).
- Next, calculate the sum of (fi * (fi – 1)).
- Next, determine the total number of observations or data points (N).
- Finally, calculate the Coefficient of Coincidence (COC) using the formula COC = Σ (fi * (fi – 1)) / (N * (N – 1)).
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem:**

Use the following variables as an example problem to test your knowledge.

Frequency of occurrence of each variable (fi): 5, 3, 2, 4

Total number of observations or data points (N): 10