Sensitivity and Specificity- Definition, Formula, Calculation, Relationship

  • When developing diagnostic tests or evaluating results, it is important to understand how reliable those tests and therefore the results obtained are.
  • By using samples of known disease status, values such as sensitivity and specificity can be calculated that allow its evaluation.
  • Therefore, when evaluating diagnostic tests, it is important to calculate the sensitivity and specificity for that test to determine its effectiveness.
Sensitivity and Specificity- Definition, Formula, Calculation, Relationship

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Sensitivity

  • The term sensitivity was introduced by Yerushalmy in the 1940s as a statistical index of diagnostic accuracy.
  • It is also called the true positive rate, the recall, or probability of detection.
  • It has been defined as the ability of a test to identify correctly all those who have the disease, which is “true-positive”.
  • A 90 percent sensitivity means that 90 percent of the diseased people screened by the test will give a “true-positive” result and the remaining 10 percent a “false-negative” result.
  • Thus, a highly sensitive test rarely overlooks an actual positive (for example, showing “nothing bad” despite something bad existing).

Calculating Sensitivity

  • The sensitivity of a diagnostic test is expressed as the probability (as a percentage) that a sample tests positive given that the patient has the disease.
  • The following equation is used to calculate a test’s sensitivity:

Sensitivity FormulaSpecificity

  • It is defined as the ability of a test to identify correctly those who do not have the disease, that is, “true-negatives”.
  • It is also called as the true negative rate.
  • A 90 percent specificity means that 90 percent of the non-diseased persons will give a “true-negative” result, 10 percent of non-diseased people screened by the test will be wrongly classified as “diseased” when they are not.
  • Thus, a highly specific test rarely registers a positive classification for anything that is not the target of testing.

Calculating Specificity

The specificity of a test is expressed as the probability (as a percentage) that a test returns a negative result given that that patient does not have the disease.

The following equation is used to calculate a test’s specificity:

Specificity FormulaRelationship between Sensitivity and Specificity

  • In medical tests, sensitivity is the extent to which actual positives are not overlooked (so false negatives are few), and specificity is the extent to which actual negatives are classified as such (so false positives are few). 
  • Although a screening test ideally is both highly sensitive and highly specific, we need to strike a balance between these characteristics, because most tests cannot do both.
  • We determine this balance by an arbitrary cut-off point between normal and abnormal.
  • If we want to increase sensitivity and to include all true positives, we are obliged to increase the number of false positives, which means decreasing specificity.
  • Reducing the strictness of the criteria for a positive test can increase sensitivity, but by doing this the test’s specificity is reduced.
  • Likewise, increasing the strictness of the criteria increases specificity but decreases sensitivity.

References

  1. Park, K. (n.d.). Park’s textbook of preventive and social medicine.
  2. Beaglehole, Robert, Bonita, Ruth, Kjellström, Tord & World Health Organization. (‎1993)‎. Basic epidemiology, Updated reprint. World Health Organization. 
  3. Gordis, L. (2014). Epidemiology (Fifth edition.). Philadelphia, PA: Elsevier Saunders.
  4. Hennekens CH, Buring JE. Epidemiology in Medicine, Lippincott Williams & Wilkins, 1987.
  5. https://www.technologynetworks.com/analysis/articles/sensitivity-vs-specificity-318222
  6. https://academic.oup.com/bjaed/article/8/6/221/406440

About Author

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Sagar Aryal, PhD

Dr. Sagar Aryal is a microbiologist, researcher, and science communicator from Nepal. He is also co-founder and Research Head of the Department of Natural Products at the Kathmandu Research Institute for Biological Sciences (KRIBS), where he leads research on natural product discovery and microbial biodiversity. Dr. Aryal earned his Ph.D. in Microbiology from Tribhuvan University, Kathmandu, Nepal, in 2025, supported by a DAAD Research Grant and a University Grants Commission (UGC) Nepal Ph.D. Fellowship. His research interests include Actinomycetes, Myxobacteria, microbial taxonomy, and natural products, particularly the discovery of bioactive compounds with potential pharmaceutical applications. He isolated and identified Nocardia nepalensis, a novel bacterial species from Nepal, contributing to understanding microbial diversity in the region. Dr. Aryal has published more than 16 research articles in international journals and contributed three book chapters to established academic publications. He has presented scientific research findings and developed international research collaborations through visits to more than 18 countries across Asia, Europe, North America, and Oceania. From 2023 to 2025, he served as the American Society for Microbiology (ASM) Young Ambassador to Nepal. Since December 2025, he has served as an Editorial Board Member of Scientific Reports, a Nature Portfolio journal. In recognition of his scientific contributions, Dr. Aryal received the NAST Science and Technology Youth Award 2025 from the Nepal Academy of Science and Technology. He previously received the Frs. Locke and Stiller Research Award (LSRA) for the 2017-2018 cycle from St. Xavier's College, Kathmandu, and a Nepal Academy of Science and Technology (NAST) Research Grant for 2017-2018. Alongside his scientific career, Dr. Aryal has more than 15 years of experience in blogging, content writing, and search engine optimization (SEO).