Define the case
Pick a preset above or enter the 2×2 below. Non-negative integers; pre-test probability between 0% and 100%.
Results
Values are shown with 95% confidence intervals where applicable.
Explore
Change one thing at a time: prevalence, a second test, a decision threshold or a continuous cutoff. Every tool keeps the same probability axis.
Inter-rater agreement (Cohen's κ)
Two raters classify the same items as positive / negative. Enter the four counts to get Cohen's κ with 95% asymptotic CI adjusted for estimated rater marginals and a Landis–Koch qualitative label. Useful for imaging or pathology cases where the "test" is a human judgement.
Learn
The calculation is only the start. These notes explain what the numbers mean, what can bias them, and where to read further.
Interpretation guide
Sensitivity and specificity
Quantify the test's ability to correctly identify people with and without the condition. Useful for understanding the intrinsic performance of the test. Learn more at Wikipedia.
Predictive values
Depend on prevalence (pre-test probability). Use them to estimate the probability that a person has or does not have the disease after a positive or negative result. See Wikipedia for further reading.
Likelihood ratios
Relate the probability of a result in diseased vs. non-diseased individuals and can be applied directly in Bayes' formula to update the probability of disease. Further reference at Wikipedia.
Post-test probabilities
Result from applying the LR to pre-test odds. They are crucial for clinical decisions such as initiating treatment or ordering additional tests. See also Wikipedia.
STARD essentials
Numbers from a 2×2 only mean what the underlying study allows them to mean. The STARD 2015 checklist has 30 items; six of them dominate the interpretation of sens / spec / PPV / NPV.
1. Reference standard — what counted as "truth"?
If the gold standard is imperfect (e.g. expert consensus instead of biopsy), sensitivity and specificity are biased. Worse: if the reference standard incorporates the index test result, agreement is inflated (incorporation bias). Ask which standard was used and whether the index test fed into it.
2. Spectrum of patients — who got tested?
Performance estimated in obvious cases ("sick" vs healthy volunteers) almost always overestimates real-world accuracy. Check whether enrolment was consecutive or random, and whether it spanned the clinical spectrum you'll apply the test to (mild, atypical, comorbid).
3. Verification — was the reference standard applied to everyone?
Partial verification bias arises when positive-index-test patients are more likely to receive the gold standard than negative ones — inflates sensitivity, deflates specificity. Look for differential or post-hoc verification protocols.
4. Blinding — were readers independent?
If the person interpreting the index test also knew the reference result (or vice versa), expect review bias: estimates drift toward perfect agreement. Imaging and pathology studies should explicitly report blinding between readers and from clinical context.
5. Indeterminate results — where did the "?"s go?
If indeterminate, missing, or excluded results were silently dropped, the 2×2 misrepresents real practice. Ask how many results fell outside the binary scheme and how they were handled (re-tested, excluded, counted as negative…).
6. Subgroups — does one number describe everyone?
Sensitivity / specificity often vary by age, severity, prior testing, or setting. A single 2×2 hides those differences. Check whether the authors pre-specified clinically meaningful subgroups and reported them separately.
Resources and references
Supporting literature
- Akobeng AK. Understanding diagnostic tests 1-3: sensitivity, specificity, and predictive values. Acta Paediatr. 2007;96(3):338-341. DOI: 10.1111/j.1651-2227.2006.00180.x
- McGee S. Simplifying likelihood ratios. J Gen Intern Med. 2002;17(8):646-649. DOI: 10.1046/j.1525-1497.2002.10750.x
- Fagan TJ. Nomogram for Bayes theorem. N Engl J Med. 1975;293(5):257. DOI: 10.1056/NEJM197507312930513
Online resources
- The Centre for Evidence-Based Medicine (CEBM): EBM Tools and Resources
- StatPearls: Sensitivity and Specificity
- Deeks JJ, Altman DG. Diagnostic tests 4: likelihood ratios. BMJ. 2004;329(7458):168-169. Open access
Complementary calculators
- MDCalc: Medical calculators
- ClinCalc: Diagnostic Test Calculator
About DIAGCALC
Interactive calculator for exploring diagnostic test performance measures and applying Bayesian reasoning in clinical practice.
Key measures
Sensitivity, specificity, PPV, NPV, and likelihood ratios with 95% CI.
Post-test probability
Convert pre-test probability into positive and negative post-test probability.
Guided interpretation
Results explained to support self-directed learning.
History
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