A confusion matrix is a tabular representation of Actual vs Predicted values.
As you can see, the confusion matrix avoids “confusion” by measuring the actual and predicted values in a tabular format. In table above, Positive class = 1 and Negative class = 0. Following are the metrics we can derive from a confusion matrix:
Accuracy – It determines the overall predicted accuracy of the model. It is calculated as Accuracy = (True Positives + True Negatives)/(True Positives + True Negatives + False Positives + False Negatives)
True Positive Rate (TPR) – It indicates how many positive values, out of all the positive values, have been correctly predicted. The formula to calculate the true positive rate is (TP/TP + FN). Also, TPR = 1 – False Negative Rate. It is also known as Sensitivity or Recall.
False Positive Rate (FPR) – It indicates how many negative values, out of all the negative values, have been incorrectly predicted. The formula to calculate the false positive rate is (FP/FP + TN). Also, FPR = 1 – True Negative Rate.
True Negative Rate (TNR) – It indicates how many negative values, out of all the negative values, have been correctly predicted. The formula to calculate the true negative rate is (TN/TN + FP). It is also known as Specificity.
False Negative Rate (FNR) – It indicates how many positive values, out of all the positive values, have been incorrectly predicted. The formula to calculate false negative rate is (FN/FN + TP).
Precision: It indicates how many values, out of all the predicted positive values, are actually positive. It is formulated as:(TP / TP + FP).
F Score: F score is the harmonic mean of precision and recall. It lies between 0 and 1. Higher the value, better the model. It is formulated as 2((precision*recall) / (precision+recall)).
We can create the confusion matrix for our data.
Confusion Matrix and Statistics
Prediction 0 1
0 48 32
1 59 161
Accuracy : 0.6967
95% CI : (0.6412, 0.7482)
No Information Rate : 0.6433
P-Value [Acc > NIR] : 0.02975
Kappa : 0.2996
Mcnemar's Test P-Value : 0.00642
Sensitivity : 0.4486
Specificity : 0.8342
Pos Pred Value : 0.6000
Neg Pred Value : 0.7318
Prevalence : 0.3567
Detection Rate : 0.1600
Detection Prevalence : 0.2667
Balanced Accuracy : 0.6414
'Positive' Class : 0