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# Matthews Correlation Coefficient

EmilyB.Matthews Correlation Coefficient

The **Matthews Correlation Coefficient** calculator computes the Matthews Correlation Coefficient between observed and predicted binary classifications.

**INSTRUCTIONS:** Enter the following:

- (
**TP**) This is the number of true positives. - (
**FP**) This is the number of false positives. - (
**TN**) This is the number of true negatives. - (
**FN**) This is the number of false negatives.

**Matthews Correlation Coefficient (MCC):** The calculator returns the coefficient.

#### The Math / Science

The **Matthews Correlation Coefficient** is used in machine learning as a measure of the quality of binary (two-class) classifications. It takes into account true and false positives and negatives and is generally regarded as a balanced measure which can be used even if the classes are of very different sizes. The MCC is in essence a correlation coefficient between the observed and predicted binary classifications; it returns a value between -1 and +1. A coefficient of +1 represents a perfect prediction, 0 no better than random prediction and -1 indicates disagreement between prediction and observation.

The formula for the Matthews Correlation Coefficient is:

`"MCC"=(TP*TN-FP*FN)/sqrt((TP+FP)(TP+FN)(TN+FP)(TN+FN))`

where:

- MCC is the Matthews Correlation Coefficient
- TP = true positives
- FP = false positives
- TN = true negatives
- FN = false negatives

## References

Wikipedia (https://en.wikipedia.org/wiki/Matthews_correlation_coefficient)