True Positive, True Negative, False Positive, and False Negative

Laboratory test results are usually a numerical value, but these values are often converted into a binary system. For example, urine hCG Pregnancy Test test may give you values ranging from 0 to 30 mlU/mL, but the numerical continuum of values can be condensed in two main categories (positive and negative). We do this by setting a Cut-off Point. All measurements above this cut-off value are categorized as “positive” and all values below are “negative.” If you change that cut-off point the positive vs. negative classifications (as well as TP, FP, TN, & FN) change. In everyday life, positive things are good and negative things are bad. But remember in most laboratory tests, a positive result means the patient has a disease.

A True result is a lab result that matches the truth or our best estimate of the truth based on the results of the best available test (called the Gold Standard Test). So a true result would be a positive HIV test in a person we know to clinically have HIV. A False measurement is obviously when the result does not match the truth. “Good” tests have mostly true measurements and few false measurements.

• True Positive (TP) = A diseased person who is correctly identified as having a disease by the test
• False Positive (FP) = A healthy person that is incorrectly identified as having the disease by the test
• True Negative (TN) = A healthy person who is correctly identified as healthy by the test
• False Negative (FN) = A diseased person who is incorrectly identified healthy by the test

Here is another way to think about these definitions:

• All with Disease =TP + FN
• All without Disease = TN + FP
• All that Tested Positive = TP + FP
• All that Tested Negative = TN + FN

Two-by-Two Tables

Questions involving TP, FP, TN, and FN will usually have a two-by-two table. Sometimes they will give you the actual table and other times they will give you all of the data for the table in sentence form and you have to make the table for yourself. You may have learned to refer to the boxes in a two-by-two table as A, B, C & D. I am going to strongly recommend you not do this. First off, those letter labels have no meaning. It is therefore more likely for you to get confused and make a dumb mistake. Additionally, the top left box in a two-by-two table may not always represent true positive. Sometimes, test writers will mix up the order of the columns and/or rows. I suggest using TP, TN, FP, and FN instead.

Sometimes they will give you an extra row and column that has totals. Don’t let that throw you off. It is still a two-by-two table even though there are 3 columns and 3 rows. They just try to save you a step of calculation by giving you the row and column totals.

Now that you have finished this video on 2 by 2 tables you should check out the next video in the Biostatistics & Epidemiology section which covers Sensitivity, Specificity & Confirmatory Tests