# total of 4543 patients were tested. total of 300 patients had cancer. 250 patients tested positive for cancer, of which 84% had cancer. I dont know how to work out the number of true positives,...

total of 4543 patients were tested. total of 300 patients had cancer. 250 patients tested positive for cancer, of which 84% had cancer.

I dont know how to work out the number of true positives, false positives, true negatives, and false negatives, from this kind of data. I need it to calculate the specificity and sensitivity.

Please help

(I dont know if this would come under science or maths, its a bit of both really)

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### 1 Answer

Let's look at true positives first. They would be the patients who tested positive for cancer and actually did have cancer. 250 tested positive, but only 84% of them really had cancer. This amounts to 210 patients with true positive results.

Let's look at false positives next. These are the patients who test positive, but do not really have cancer. This will be the difference between the 250 positive and the 210 true positives, or 40 patients.

Next, let's look at the false negatives. These are patients with cancer who did not test positive. We know from the problem that 300 patients really have cancer. Only 210 were in the true positives. That leaves 90 that tested falsely as negative.

Finally we will look at the true negatives. There were a total of 4543 patients tested. Of these, 300 were tested as positives, that leaves 4243 as negative results. 90 of these were false negatives, which means the difference 4243-90, or 4153 were true negatives.