# Specificity

Specificity is the probability of a negative result in healthy patients b/b+d. The specificity of a test reflects on the ability of a test to identify true negatives.

\begin{align} \text{specificity} & = \frac{\text{number of true negatives}}{\text{number of true negatives} + \text{number of false positives}} \\ \\ & = \text{probability of a negative test given that the patient is well} \end{align}

For example, if he had a mammography screening for breast cancer with 100% specificity, it would mean that all women without breast cancer that underwent screening tested negative. We have a group of 4 women - Lucy, Jane, Cathie and Lenka. has breast cancer. Lucy has breast cancer. All women undergo the screening mammography. It detects Lucy and Jane as positive. Lucy is really positive. Jane is a false positive. Cathie and Lenka are actually negative. Nobody is falsely negative. When you enter the values into the formula above, we find that the test showed about 67% specificity (specificity = 0.67). One woman with no tumor was identified as positive (we have one woman falsely positive).

 Test Disease + Healthy- Total + a b a+b - c d c+d Total a+c b+d n