Likelihood Ratio
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
LR = P(D|H)/P(D|¬H)
About this calculator
The Likelihood Ratio (LR) calculator helps assess the strength of evidence (D) in favor of a hypothesis (H) compared to its negation (¬H). LR is calculated by dividing the probability of observing the data under the hypothesis by the probability of observing the same data when the hypothesis is false. In Bayesian statistics, this ratio is critical for updating prior probabilities to posterior probabilities based on new evidence.
It is particularly useful in medical testing, where LR of a test result helps determine the probability of a disease after an examination. For example, a high LR indicates the data is more common with the hypothesis, strengthening its credibility. Conversely, a low LR suggests the data is more likely without the hypothesis, weakening it.
To use the calculator, input the values of P(D|H) and P(D|¬H). The result will show how much more likely the data is under the hypothesis versus its negation. Note that LR alone does not confirm a hypothesis but indicates the direction and magnitude of belief updates.
Cautions: Ensure the probability values entered are consistent with the problem's context. Errors in P(D|H) or P(D|¬H) can lead to misinterpretations. Additionally, LR does not replace qualitative analysis of evidence; it only quantifies statistical relevance.
Frequently asked questions
What's the difference between LR and Bayes' theorem?
LR is a component of Bayes' theorem. While LR measures conditional probability ratios, Bayes' theorem uses these ratios to update prior probabilities into posterior probabilities.
How to interpret an LR greater than 1?
An LR greater than 1 indicates the data is more likely under hypothesis H than ¬H, strengthening H's credibility.
When to use LR in medical tests?
Use LR to calculate disease probability after a test, considering the test's sensitivity and specificity.
Can LR be less than 1?
Yes. An LR less than 1 suggests data is more likely without the hypothesis, reducing its belief.
How does LR affect prior probabilities?
LR multiplies the ratio of prior probability to its negation, adjusting it to form posterior probability.