Three different balanced arrangements of colored classification tokens. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
Different metrics retain different information
F1 combines precision and recall through their harmonic mean, or equivalently 2TP/(2TP+FP+FN). True negatives do not appear in that formula. Specificity measures TN/(TN+FP), the fraction of actual negatives correctly rejected. Matthews correlation coefficient uses all four confusion-matrix cells and can range from −1 to 1 when its denominator is defined. No single metric answers every deployment question.
Compare two reports with the same positive-side counts
Consider TP = 40, FP = 10 and FN = 10. With TN = 40, F1 is 0.8, specificity is 0.8 and MCC is 0.6. With TN = 940, F1 remains 0.8, specificity rises to about 0.989474 and MCC is about 0.789474. The positive prediction and positive actual counts stayed fixed, while the population of correctly rejected negatives changed.
Do not treat a score change as a threshold-only effect
In this example the evaluation population changed. A threshold comparison instead applies competing thresholds to a defined dataset or comparable population and records how all four cells move. Mixing a prevalence shift with a threshold shift can obscure the cause of a metric change. A high F1 can coexist with a costly number of false alerts, depending on the scale and consequences.
Report the counts that make a score interpretable
Use the Confusion Matrix Calculator to calculate the metric set without replacing zero-denominator ratios with invented values. Include the four input counts, class definition, threshold and population description. MCC is undefined if a required marginal count is zero; a perfect-looking headline percentage does not fix that. The orientation guide helps prevent swapped FP and FN inputs. For the separate effect of changing prevalence while holding sensitivity and specificity fixed, read why precision changes with prevalence.
Check the model behind your result
Use the Confusion Matrix Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26