# A sensitive test does not make every positive result certain

A test is described as highly sensitive. A positive result follows, and it is tempting to read the performance claim as the probability that the person has the condition. That substitutes one question for another. Sensitivity, specificity and positive predictive value describe different groups.

The [National Cancer Institute's sensitivity definition](https://www.cancer.gov/publications/dictionaries/cancer-terms/def/sensitivity) concerns the proportion of people with a condition who test positive. Its [specificity definition](https://www.cancer.gov/publications/dictionaries/cancer-terms/def/specificity) concerns the proportion without the condition who test negative. [Positive predictive value](https://www.cancer.gov/publications/dictionaries/cancer-terms/def/positive-predictive-value) asks a different question: among those with positive results, how many actually have the condition?

Those definitions are useful beyond cancer testing, but their numbers still belong to particular tests, populations and purposes. A general performance adjective does not supply an individual's diagnosis.

## Work through a completely invented population

Imagine a fictional test and 100 fictional people. This is an editorial arithmetic exercise, not a study, a real disease estimate or evidence about a commercial product. Suppose 20 people have the condition and 80 do not. Assume the invented test has 75 per cent sensitivity and 90 per cent specificity in this group.

Among the 20 with the condition, 75 per cent is 15. Those 15 test positive, while five test negative. Among the 80 without the condition, 90 per cent is 72. Those 72 test negative, while eight test positive.

There are therefore 23 positive results altogether: 15 true positives plus eight false positives. The fraction of positive results that are true positives is 15 divided by 23, approximately 65 per cent. That is the positive predictive value in this invented example. It is not 75 per cent, because the sensitivity calculation used a different denominator.

There are also five false negatives. The example does not describe a test that catches every case, and a negative result is not made infallible by concentrating only on specificity. Each performance measure needs its own question and its own denominator.

## Why the group being tested matters

The proportion of people with the condition affects how many false positives appear relative to true positives. A test used in a group where the condition is uncommon can produce a different positive predictive value from the same test used in a group where it is more common.

For another explicitly invented calculation, take 1,000 people and a different fictional test with 90 per cent sensitivity and 90 per cent specificity. If 100 people have the condition, there are 90 true positives and 90 false positives among the remaining 900. Half of the 180 positive results are true positives.

Now keep those assumed performance percentages but suppose only ten of the 1,000 have the condition. There are nine true positives and 99 false positives among the remaining 990. Nine of the 108 positive results are true positives, about eight per cent. These are teaching assumptions, not measured performance in real populations.

In actual practice, test performance itself may also vary with the population and setting. The exercise holds it fixed only to isolate the arithmetic. It should not be used to predict what a named test will do without appropriate evidence.

## Read the performance claim's denominator

When a page says “accuracy”, ask what it means. Does it report sensitivity, specificity, predictive value or something else? Does it identify the group tested and the comparison used to establish who had the condition? A percentage without that context is not enough to interpret a result.

An editorial question for a healthcare conversation is: “What does a positive result mean in the setting where this test was used, and what confirmation or other assessment is needed?” This does not presume a false positive. It asks how the result contributes to the actual investigation.

Do not dismiss a result because false positives exist, or assume symptoms can be ignored because false negatives are uncommon. Follow the requesting service's plan and any urgent instructions. The mathematics explains uncertainty; it does not provide permission to decide which category you occupy.

Your practical next step is to translate one performance percentage into a sentence beginning with the group it describes. That small habit prevents a sensitivity claim from becoming an unsupported personal probability.

[The DomDNA quiz](https://domdna.com/quiz) is separate lifestyle education, with no DNA analysis, diagnostic testing or personal predictive-value calculation.

Draft • Research checked 4 October 2026 • AI-assisted DomDNA editorial content. No independent clinical review or publication is claimed. General education, not individual medical advice.