The formula to calculate the Coefficient of Coincidence (COC) is:
\[ COC = \frac{\sum (f_{i} (f_{i} - 1))}{N (N - 1)} \]
Where:
Let's say the frequencies are 5, 3, and 2, and the total number of observations (N) is 10. Using the formula:
\[ COC = \frac{(5 \times 4) + (3 \times 2) + (2 \times 1)}{10 \times 9} = \frac{20 + 6 + 2}{90} = \frac{28}{90} = 0.3111 \]
So, the Coefficient of Coincidence (COC) is 0.3111.
Definition: The coefficient of coincidence is a measure of the actual frequency of double crossovers compared to the expected frequency.
Formula: \( COC = \frac{Observed\ Double\ Crossovers}{Expected\ Double\ Crossovers} \)
Example: \( COC = \frac{5}{8} \)
Definition: Interference is the degree to which one crossover event inhibits another nearby crossover event.
Formula: \( Interference = 1 - COC \)
Example: \( Interference = 1 - 0.625 \)
Definition: The index of coincidence is a measure used in cryptography to determine the similarity between two strings of text.
Formula: \( IC = \frac{\sum_{i=1}^{n} f_i (f_i - 1)}{N (N - 1)} \)
Example: \( IC = \frac{(5 \times 4) + (3 \times 2)}{10 \times 9} \)
