Calculate coefficient of coincidence and interference from progeny totals, recombination rates, map distances, or crossover counts in genetics.

Use two adjacent intervals in known gene order. Rates and double-recombinant count must describe the same sample.

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Coefficient Of Coincidence Formula

For genetics, expected double recombinants under independence are N ร— rAB ร— rBC; COC = observed / expected and interference I = 1 โˆ’ COC. Rates are fractions, and each double recombinant contributes to both interval rates. An expectation of zero makes COC undefined. Map mode converts cM with Haldane or Kosambi, then uses an independence benchmark rather than a Kosambi-specific joint prediction. The separate category-count mode uses the unnormalized index of coincidence (IC) below:

IC = ฮฃ (fi ร— (fi - 1)) / (N ร— (N - 1))

Variables:

  • IC is the unnormalized category index of coincidence, not the genetic coefficient
  • fi is a nonnegative whole count for each separate category
  • N is the sum of all category counts and must be at least 2

To calculate this index of coincidence, for each category, multiply its count by that count 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?

Genetic COC compares observed double recombinants with an independent-interval expectation. COC below 1 gives positive interference; above 1 gives negative interference. The descriptive ratio does not establish statistical significance. The distinct cryptanalytic index IC is the probability that two observations drawn without replacement have the same category. A higher IC indicates a more concentrated category distribution, not necessarily correlation between variables.

How to Calculate Coefficient Of Coincidence?

The following steps calculate the category index of coincidence. For genetic COC, use the genetics modes above with known gene order and consistent progeny classes.

  1. First, determine the frequency of occurrence for each variable (fi).
  2. Next, calculate the sum of (fi * (fi – 1)).
  3. Next, determine the total number of observations or data points (N).
  4. Finally, calculate IC = ฮฃ (fi * (fi – 1)) / (N * (N – 1)).
  5. 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 category count (N): 5 + 3 + 2 + 4 = 14. The matching-pair numerator is 40, so IC = 40/(14 ร— 13) โ‰ˆ 0.21978022.