Solved – How to interpret Matthews correlation coefficient (MCC)

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The answer for the question Relation between the phi, Matthews and Pearson correlation coefficients? shows that the three coefficient methods are all equivalents.

I'm not from statistics, so it should be an easy question.

The Matthews paper (www.sciencedirect.com/science/article/pii/0005279575901099) describes the following: 

"A correlation of:
   C =  1 indicates perfect agreement,
   C =  0 is expected for a prediction no better than random, and
   C = -1 indicates total disagreement between prediction and observation"`.

According to Wikipedia (http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient), the Pearson correlation is described as:

giving a value between +1 and −1 inclusive, where:
   1 is total positive correlation, 
   0 is no correlation, and
  −1 is total negative correlation

The Pearson correlation coefficient interpretation is best understood as the following (according to http://faculty.quinnipiac.edu/libarts/polsci/Statistics.html):

If r =
   +.70 or higher Very strong positive relationship
   +.40 to +.69 Strong positive relationship
   +.30 to +.39 Moderate positive relationship
   +.20 to +.29 weak positive relationship
   +.01 to +.19 No or negligible relationship
   -.01 to -.19 No or negligible relationship
   -.20 to -.29 weak negative relationship
   -.30 to -.39 Moderate negative relationship
   -.40 to -.69 Strong negative relationship
   -.70 or higher Very strong negative relationship

Reading some papers, there is no degree of interpretation for MCC outcome range between -1 and 1. This coefficient is good for unbalanced datasets of negatives and positives, where the accuracy metric can't estimate well if the predictor is accurate in this case.

With unbalanced data sets, is the F-measure a good metric to compare with MCC to evaluate the predictor performance? For example: there are cases which F-measure = 94% and MCC = 0.58. What does it tell about the predictor?

May I adopt the same interpretation for Matthews correlation coefficient, or there is some different meaning on the interpretation? I believe that both coefficients are equivalent in the interpretation too.

Best Answer

This question was so simple and unfortunately no one could answer this question.

According to this paper: http://www.bioinfopublication.org/files/articles/2_1_1_JMLT.pdf, MCC is a contingency matrix method of calculating the Pearson product-moment correlation coefficient. Therefore, it has the same interpretation.

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