Confusion Matrix

Question

Let us say you are trying to predict the diabetic status of 200 patients as diabetic or not. 120 of these patients are actually diabetic and the rest are not. You apply an algorithm, which correctly identifies 80 of the diabetic patients and 60 of the non-diabetic patients. What is your:

1. Accuracy b. False Positive Rate c. False Negative Rate d. Sensitivity e. Specificity

f. Precision g. Recall h. F Score

 

Assume being Diabetic to be the positive class. Submit your answer in a word file.

Answer 1

P = 120

N = 200 - 120 = 80

TP = 80

FN = 120 - 80 = 40

TN = 60

FP = N - TN = 80 - 60 = 20

Accuracy = (TP + TN)/Total = (80 + 60)/200 = 140/200 = 7/10 = 70%

False Positive Rate = FP/N = 20/80 = 1/4 = 25%

False Negative Rate = FN/P = 40/120 = 1/3 = 33 1/3 %

Sensitivity = TP/P = 80/120 = 2/3 = 66 2/3%

Specificity = TN/N = 60/80 = 3/4 = 75%

Precision = TP/(TP+ FP) = 80/(80 + 20) = 80/100 = 4/5 = 80%

Recall = Sensitivity = 2/3 = 66 2/3%

F Score = TP/(TP + 1/2(FN + FP)) = 80/(80+1/2(40+20)) = 80/(80+30) = 8/11 = 72 8/11 %

Answer 2

the confusion matrix is:

80 20

40 60

accuracy = 140/200 = 70%

false positive rate = 20/80 = 25%

false negative rate = 40/120 = 1/3 = 33 + 1/3 %

sensitivity = recall = true positive rate = 80/120 = 2/3 = 66 + 2/3 %

specificity = true negative rate = 60/80 = 3/4 = 75%

precision = 80 / (80+20) = 80/100 = 80%

F1 score = 2 * 80 / (2 * 80 +20 + 40)

= 160/220

=16/22

= 8/11

= 72.72...%

all of these formula I found in the wikipedia article upon googling CONFUSION MATRIX