🕷️ Crawler Inspector

URL Lookup

Direct Parameter Lookup

Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 145 (from laksa017)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa145.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://slate.com/technology/2022/01/rapid-testing-covid-math-false-negatives-sensitivity.html\')), getAhrefsUnparsedNoserviceFromURL(\'https://slate.com/technology/2022/01/rapid-testing-covid-math-false-negatives-sensitivity.html\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/slate.com\/technology\/2022\/01\/rapid-testing-covid-math-false-negatives-sensitivity.html","crawl_time":1774358114,"first_indexed_time":1642203077,"http_code":200,"src_unparsed":"com,slate!\/technology\/2022\/01\/rapid-testing-covid-math-false-negatives-sensitivity.html s443","src_root_hash":"14993094292168895945","history_drop_reason":null,"meta_title":"What are sensitivity and specificity and what do they mean for COVID rapid tests?","meta_descriptions":["Breaking down false positives and negatives."],"attrs_boilerpipe_text":"Science\nThe Math Behind False Positives and False Negatives\nWhat are sensitivity and specificity, anyway?\nJan 14, 2022\n6:21 PM\nPhoto illustration by Slate. Photo by Getty Images Plus.\nYou probably know at this point in the pandemic that if you test positive on a rapid test (and you’ve used the test correctly—you’ve got to swab pretty hard!) that the odds are overwhelming that you have COVID and are infectious. You have, no doubt, been warned that a negative result on a rapid test should be taken with a grain of salt, especially if you’ve been exposed to the virus or you have symptoms. And you might have heard two terms about tests thrown around: sensitivity and specificity, particularly if you’ve been trying to\nget a grip\non exactly how accurate rapid tests are.\nAs a mathematician, I think knowing a bit more about how sensitivity and specificity are calculated can help you better understand\nwhy\na positive result should be heeded—and a negative test should be read with some caution.\nFirst we’ll look at specificity. The Centers for Disease Control and Prevention\nexplains\nthat having rapid tests widely available is a public good because\nThe high specificity and rapid BinaxNOW antigen test turnaround time facilitate earlier isolation of infectious persons. Antigen tests can be an important tool in an overall community testing strategy to reduce transmission.\nWhat does specificity mean here? Specificity is calculated based on the number of false positive results a test will produce (and though the CDC references one brand in the quote above, the results are similar for all of them). The number of false positives that studies report seems to be\nessentially zero\n. Basically, there are never (or very, very, very rarely) any false positives. So why is a “high specificity” good? It is because it means you have very few false positives!\nTo calculate the specificity of a test, we need to know the “false positive rate.” To calculate the false positive rate, you put the number of false positives that have been identified in the top of a fraction, and put the number of people you tested who did not have COVID-19, including both the false positives and “true negatives,” in the bottom number: (number of false positives)\/(number of false positives + number of true negatives).\nThe number of false positives for a rapid test is known to be essentially zero. I hope you recall that any fraction with a zero on top is zero, regardless of the size of the denominator. Thus, the false positive rate for a kind of test with no false positives is also zero.\nIt would certainly be more intuitive if clinical studies and articles just told us the false positive rate. Instead, that rate is used to calculate specificity. This is a percentage that comes from the false positive rate by subtracting the false positive rate from 1 and then multiplying by 100. So a test with a false positive rate of 2 out of 10, or 20 percent, would have a specificity of 80 percent. A test like a rapid COVID test with a false positive rate of essentially zero has a specificity of 100 percent. To put that a little more simply, the specificity tells you how often you can trust a positive result. The answer with rapid tests is basically 100 percent of the time!\nLet’s turn now to sensitivity, and to negative results on a rapid test. (A useful mnemonic: The\nn\nin\nsensitivity\nmeans it’s about negative tests.) Unfortunately, a negative result on a rapid test is much less informative than a positive one. People say the current rapid tests have a (relatively) high false negative rate and are\nless sensitive\ntests.\nA false negative means that the test says you don’t have a disease when you actually do. Sensitivity comes from knowing the “false negative rate”\n(sometimes called th\ne\n“miss rate”\n)\n. The false negative rate is a fraction you calculate from the number of false negatives, divided by the number of people who were known to\nactually\nbe positive.\nFor example, suppose you test 1,000 people who are known to have the disease (through some other test), and your rapid test shows 200 people are negative. Your false negative rate for that rapid test is 200 out of 1,000, or 20 percent. Sensitivity is then calculated by subtracting this number from 1, so if you have a false negative rate of 20 percent, your sensitivity is 80 percent. That is, in this example, you can trust a negative test 80 percent of the time.\nEstimates for this sensitivity of rapid tests are all over the place for previous variants of COVID, and there is\ngood evidence\nthat the sensitivity results reported for earlier versions of COVID don’t apply to omicron anyway. So the sensitivity of rapid tests for omicron, right now, is up in the air. While a negative test provides\nsome\nreassurance that you aren’t infectious, we just don’t really know how\nmuch.\nUpdate, Jan. 25, 2022: While most of the original studies of rapid tests (in particular those used for FDA approval) showed essentially 100 percent specificity—whether you were symptomatic or asymptomatic—the picture is becoming more complicated with real-life data, as this\nrecently published erratum\nto one of the better papers on this question indicates. The good news is that if you are symptomatic and use a rapid test, specificity for most tests remains at essentially 100 percent. However, if you are asymptomatic, the specificity drops a bit, but is probably still in the very high 90s. Unfortunately, once you drop below 100 percent specificity, the prevalence of the disease affects how much you can trust a positive test, even for a variant as common as omicron. In a nutshell: Current information seems to indicate that at this time, if you are asymptomatic, a positive test has about a 1 in 10 chance of being wrong (i.e., you don’t really have COVID at all). This may be too low, but is probably a good way to bet.\nHealth\nMath\nCoronavirus","attrs_markdown":"Advertisement\n\nAdvertisement\n\n[Skip to the content](https:\/\/slate.com\/technology\/2022\/01\/rapid-testing-covid-math-false-negatives-sensitivity.html#main)\n\n- [Slate Shop](https:\/\/shop.slate.com\/)\n- [Games](https:\/\/slate.com\/tag\/slate-games)\n- [Newsletters](https:\/\/slate.com\/newsletters)\n- [Sign In](https:\/\/slate.com\/sign-in)\n- Account\n  \n  [Account](https:\/\/slate.com\/account)   [Sign out](https:\/\/slate.com\/sign-out)\n\n- [News & Politics](https:\/\/slate.com\/news-and-politics)\n- [Culture](https:\/\/slate.com\/culture)\n- [Technology](https:\/\/slate.com\/technology)\n- [Business](https:\/\/slate.com\/business)\n- [Life](https:\/\/slate.com\/life)\n- [Advice](https:\/\/slate.com\/advice)\n- [Podcasts](https:\/\/slate.com\/podcasts)\n\nMenu\n\nMenu\n\n[News & Politics](https:\/\/slate.com\/news-and-politics) [Culture](https:\/\/slate.com\/culture) [Technology](https:\/\/slate.com\/technology) [Business](https:\/\/slate.com\/business) [Life](https:\/\/slate.com\/life) [Advice](https:\/\/slate.com\/advice) [Podcasts](https:\/\/slate.com\/podcasts)\n\n[Search](https:\/\/slate.com\/search)\n\nLight\n\nDark\n\nAuto\n\n[**Subscribe**](https:\/\/slate.com\/plus?utm_medium=link&utm_campaign=plus&utm_content=nav_bar&utm_source=nav)\n\n[Slate Shop](https:\/\/shop.slate.com\/) [Games](https:\/\/slate.com\/tag\/slate-games) [Newsletters](https:\/\/slate.com\/newsletters) [Sign in](https:\/\/slate.com\/sign-in) [Account](https:\/\/slate.com\/account) [Sign out](https:\/\/slate.com\/sign-out)\n\n[Account](https:\/\/slate.com\/account)\n\n[Responding to Increasingly Zany Situations](https:\/\/slate.com\/culture\/2026\/03\/jury-duty-show-season-2-company-retreat-prime.html)\n\nLight\n\nDark\n\nAuto\n\n[Science](https:\/\/slate.com\/technology\/science)\n\n# The Math Behind False Positives and False Negatives\n## What are sensitivity and specificity, anyway?\nBy   [Gary Cornell](https:\/\/slate.com\/author\/gary-cornell)\n\nJan 14, 20226:21 PM\n\n![A hand holding up a rapid coronavirus test](https:\/\/compote.slate.com\/images\/7c94e17e-21d4-48cf-ba9d-f9ec3919f150.jpeg?crop=1560%2C1040%2Cx0%2Cy0)\n\nPhoto illustration by Slate. Photo by Getty Images Plus.\n\n[Copy Link]()\n\n[Share](https:\/\/www.facebook.com\/sharer.php?u=https%3A%2F%2Fslate.com%2Ftechnology%2F2022%2F01%2Frapid-testing-covid-math-false-negatives-sensitivity.html%3Futm_medium%3Dsocial%26utm_campaign%3Dtraffic%26utm_source%3Darticle%26utm_content%3Dfacebook_share)\n\n[Share]()\n\n[Comment](https:\/\/slate.com\/comments\/technology\/2022\/01\/rapid-testing-covid-math-false-negatives-sensitivity.html)\n\n[Copy Link]()\n\n[Share](https:\/\/www.facebook.com\/sharer.php?u=https%3A%2F%2Fslate.com%2Ftechnology%2F2022%2F01%2Frapid-testing-covid-math-false-negatives-sensitivity.html%3Futm_medium%3Dsocial%26utm_campaign%3Dtraffic%26utm_source%3Darticle%26utm_content%3Dfacebook_share)\n\n[Share]()\n\n[Comment](https:\/\/slate.com\/comments\/technology\/2022\/01\/rapid-testing-covid-math-false-negatives-sensitivity.html)\n\nYou probably know at this point in the pandemic that if you test positive on a rapid test (and you’ve used the test correctly—you’ve got to swab pretty hard!) that the odds are overwhelming that you have COVID and are infectious. You have, no doubt, been warned that a negative result on a rapid test should be taken with a grain of salt, especially if you’ve been exposed to the virus or you have symptoms. And you might have heard two terms about tests thrown around: sensitivity and specificity, particularly if you’ve been trying to [get a grip](https:\/\/www.nytimes.com\/article\/at-home-covid-tests-accuracy.html) on exactly how accurate rapid tests are.\n\nAs a mathematician, I think knowing a bit more about how sensitivity and specificity are calculated can help you better understand *why* a positive result should be heeded—and a negative test should be read with some caution.\n\nFirst we’ll look at specificity. The Centers for Disease Control and Prevention [explains](https:\/\/www.cdc.gov\/mmwr\/volumes\/70\/wr\/mm7003e3.htm) that having rapid tests widely available is a public good because\n\n> The high specificity and rapid BinaxNOW antigen test turnaround time facilitate earlier isolation of infectious persons. Antigen tests can be an important tool in an overall community testing strategy to reduce transmission.\n\nWhat does specificity mean here? Specificity is calculated based on the number of false positive results a test will produce (and though the CDC references one brand in the quote above, the results are similar for all of them). The number of false positives that studies report seems to be [essentially zero](https:\/\/www.cdc.gov\/mmwr\/volumes\/70\/wr\/mm7003e3.htm). Basically, there are never (or very, very, very rarely) any false positives. So why is a “high specificity” good? It is because it means you have very few false positives\\!\n\nAdvertisement\n\nAdvertisement\n\nAdvertisement\n\nTo calculate the specificity of a test, we need to know the “false positive rate.” To calculate the false positive rate, you put the number of false positives that have been identified in the top of a fraction, and put the number of people you tested who did not have COVID-19, including both the false positives and “true negatives,” in the bottom number: (number of false positives)\/(number of false positives + number of true negatives).\n\nAdvertisement\n\nThe number of false positives for a rapid test is known to be essentially zero. I hope you recall that any fraction with a zero on top is zero, regardless of the size of the denominator. Thus, the false positive rate for a kind of test with no false positives is also zero.\n\nIt would certainly be more intuitive if clinical studies and articles just told us the false positive rate. Instead, that rate is used to calculate specificity. This is a percentage that comes from the false positive rate by subtracting the false positive rate from 1 and then multiplying by 100. So a test with a false positive rate of 2 out of 10, or 20 percent, would have a specificity of 80 percent. A test like a rapid COVID test with a false positive rate of essentially zero has a specificity of 100 percent. To put that a little more simply, the specificity tells you how often you can trust a positive result. The answer with rapid tests is basically 100 percent of the time\\!\n\nAdvertisement\n\nAdvertisement\n\nLet’s turn now to sensitivity, and to negative results on a rapid test. (A useful mnemonic: The *n* in *sensitivity* means it’s about negative tests.) Unfortunately, a negative result on a rapid test is much less informative than a positive one. People say the current rapid tests have a (relatively) high false negative rate and are *less sensitive* tests.\n\nAdvertisement\n\nA false negative means that the test says you don’t have a disease when you actually do. Sensitivity comes from knowing the “false negative rate”(sometimes called th*e* “miss rate”*)*. The false negative rate is a fraction you calculate from the number of false negatives, divided by the number of people who were known to *actually* be positive.\n\nFor example, suppose you test 1,000 people who are known to have the disease (through some other test), and your rapid test shows 200 people are negative. Your false negative rate for that rapid test is 200 out of 1,000, or 20 percent. Sensitivity is then calculated by subtracting this number from 1, so if you have a false negative rate of 20 percent, your sensitivity is 80 percent. That is, in this example, you can trust a negative test 80 percent of the time.\n\nAdvertisement\n\nAdvertisement\n\nAdvertisement\n\nEstimates for this sensitivity of rapid tests are all over the place for previous variants of COVID, and there is [good evidence](https:\/\/www.fda.gov\/medical-devices\/coronavirus-covid-19-and-medical-devices\/sars-cov-2-viral-mutations-impact-covid-19-tests) that the sensitivity results reported for earlier versions of COVID don’t apply to omicron anyway. So the sensitivity of rapid tests for omicron, right now, is up in the air. While a negative test provides *some* reassurance that you aren’t infectious, we just don’t really know how much.\n\n# Popular in  [Technology](https:\/\/slate.com\/technology)\n1. [Why YouTuber Hank Green Turned Down More Money to Make a Bigger Difference](https:\/\/slate.com\/technology\/2026\/03\/hank-green-crash-course-youtube-ai-education.html)\n\n*Update, Jan. 25, 2022: While most of the original studies of rapid tests (in particular those used for FDA approval) showed essentially 100 percent specificity—whether you were symptomatic or asymptomatic—the picture is becoming more complicated with real-life data, as this* [*recently published erratum*](https:\/\/www.cdc.gov\/mmwr\/volumes\/70\/wr\/mm7004a6.htm?s_cid=mm7004a6_w) *to one of the better papers on this question indicates. The good news is that if you are symptomatic and use a rapid test, specificity for most tests remains at essentially 100 percent. However, if you are asymptomatic, the specificity drops a bit, but is probably still in the very high 90s. Unfortunately, once you drop below 100 percent specificity, the prevalence of the disease affects how much you can trust a positive test, even for a variant as common as omicron. In a nutshell: Current information seems to indicate that at this time, if you are asymptomatic, a positive test has about a 1 in 10 chance of being wrong (i.e., you don’t really have COVID at all). This may be too low, but is probably a good way to bet.*\n\n[Copy Link]()\n\n[Share](https:\/\/www.facebook.com\/sharer.php?u=https%3A%2F%2Fslate.com%2Ftechnology%2F2022%2F01%2Frapid-testing-covid-math-false-negatives-sensitivity.html%3Futm_medium%3Dsocial%26utm_campaign%3Dtraffic%26utm_source%3Darticle%26utm_content%3Dfacebook_share)\n\n[Share]()\n\n[Comment](https:\/\/slate.com\/comments\/technology\/2022\/01\/rapid-testing-covid-math-false-negatives-sensitivity.html)\n\n- [Health](https:\/\/slate.com\/tag\/health)\n- [Math](https:\/\/slate.com\/tag\/math)\n- [Coronavirus](https:\/\/slate.com\/tag\/coronavirus)\n\nAdvertisement\n***\n\nAdvertisement\n\n#### About\n- [About Us](https:\/\/slate.com\/about)\n- [Work With Us](https:\/\/jobs.lever.co\/slate)\n- [Contact](https:\/\/slate.com\/contact)\n- [Pitch Guidelines](https:\/\/slate.com\/pitch)\n- [Send Us Tips](https:\/\/slate.com\/tips)\n- [Corrections](https:\/\/slate.com\/briefing\/corrections)\n- [Commenting](https:\/\/slate.com\/commenting)\n- [Reprints](http:\/\/www.slatereprints.com\/)\n\n#### Subscriptions\n- [Subscribe](https:\/\/slate.com\/plus)\n- [Group Subscriptions](https:\/\/slate.com\/academic-group-subscriptions)\n- [Sign In](https:\/\/slate.com\/sign-in)\n- [Account](https:\/\/slate.com\/account)\n- [Subscription FAQs](https:\/\/slate.com\/plus\/faq)\n- [Podcast FAQs](https:\/\/slate.com\/podcastfaqs)\n- [Newsletters](https:\/\/slate.com\/newsletters)\n- [Customer Support](https:\/\/slatehelp.freshdesk.com\/support\/solutions)\n\n#### Advertising\n- [AdChoices](https:\/\/optout.aboutads.info\/)\n- [![California Consumer Privacy Act (CCPA) Opt-Out Icon](https:\/\/dot.cdnslate.com\/static\/media\/components\/onetrust-update\/ccpa-icons\/privacyoptions29x14.f2f5996.png) Cookie Preferences](https:\/\/slate.com\/do-not-sell)\n\nSlate is published by The Slate Group, a Graham Holdings Company.\n\n#### Follow Us\n[Facebook](https:\/\/www.facebook.com\/Slate\/)\n\n[X](https:\/\/twitter.com\/slate)\n\n[Bluesky](https:\/\/bsky.app\/profile\/slate.com)\n\n[Instagram](https:\/\/www.instagram.com\/slate\/)\n\n[YouTube](https:\/\/www.youtube.com\/slate)\n\n[RSS Feed](https:\/\/slate.com\/rss)\n\n- [User Agreement](https:\/\/slate.com\/terms)\n- [Privacy Policy](https:\/\/slate.com\/privacy)\n\nAll contents © 2026 The Slate Group LLC. All rights reserved.\n\n# We need to talk about your adblocker\nSlate relies on advertising to support our journalism. If you value our work, please disable your ad blocker. If you want to block ads but still support Slate, consider subscribing.\n\n[Enable Ads on Slate](https:\/\/slate.com\/news-and-politics\/2017\/04\/how-to-disable-your-ad-blocker-on-slate.html) [Subscribe](https:\/\/slate.com\/plus?via=ad_blocker_modal&tpcc=slate-ui--ad_blocker_modal)\n\nAlready a member? [Sign in here](https:\/\/slate.com\/sign-in)\n\n# This article is only for Slate Plus members.\nJoin today to keep reading. You'll also get access to all of Slate's independent journalism, unparalleled advice, and daily games. Cancel anytime.\n\n[Join Slate Plus](https:\/\/slate.com\/plus?via=ad_blocker_hardwall&tpcc=slate-ui--ad_blocker_hardwall)\n\nAlready a member? [Sign in here](https:\/\/slate.com\/sign-in)","attrs_readable_markdown":"[Science](https:\/\/slate.com\/technology\/science)\n\n## The Math Behind False Positives and False Negatives\n## What are sensitivity and specificity, anyway?\nJan 14, 20226:21 PM\n\n![A hand holding up a rapid coronavirus test](https:\/\/compote.slate.com\/images\/7c94e17e-21d4-48cf-ba9d-f9ec3919f150.jpeg?crop=1560%2C1040%2Cx0%2Cy0)\n\nPhoto illustration by Slate. Photo by Getty Images Plus.\n\nYou probably know at this point in the pandemic that if you test positive on a rapid test (and you’ve used the test correctly—you’ve got to swab pretty hard!) that the odds are overwhelming that you have COVID and are infectious. You have, no doubt, been warned that a negative result on a rapid test should be taken with a grain of salt, especially if you’ve been exposed to the virus or you have symptoms. And you might have heard two terms about tests thrown around: sensitivity and specificity, particularly if you’ve been trying to [get a grip](https:\/\/www.nytimes.com\/article\/at-home-covid-tests-accuracy.html) on exactly how accurate rapid tests are.\n\nAs a mathematician, I think knowing a bit more about how sensitivity and specificity are calculated can help you better understand *why* a positive result should be heeded—and a negative test should be read with some caution.\n\nFirst we’ll look at specificity. The Centers for Disease Control and Prevention [explains](https:\/\/www.cdc.gov\/mmwr\/volumes\/70\/wr\/mm7003e3.htm) that having rapid tests widely available is a public good because\n\n> The high specificity and rapid BinaxNOW antigen test turnaround time facilitate earlier isolation of infectious persons. Antigen tests can be an important tool in an overall community testing strategy to reduce transmission.\n\nWhat does specificity mean here? Specificity is calculated based on the number of false positive results a test will produce (and though the CDC references one brand in the quote above, the results are similar for all of them). The number of false positives that studies report seems to be [essentially zero](https:\/\/www.cdc.gov\/mmwr\/volumes\/70\/wr\/mm7003e3.htm). Basically, there are never (or very, very, very rarely) any false positives. So why is a “high specificity” good? It is because it means you have very few false positives\\!\n\nTo calculate the specificity of a test, we need to know the “false positive rate.” To calculate the false positive rate, you put the number of false positives that have been identified in the top of a fraction, and put the number of people you tested who did not have COVID-19, including both the false positives and “true negatives,” in the bottom number: (number of false positives)\/(number of false positives + number of true negatives).\n\nThe number of false positives for a rapid test is known to be essentially zero. I hope you recall that any fraction with a zero on top is zero, regardless of the size of the denominator. Thus, the false positive rate for a kind of test with no false positives is also zero.\n\nIt would certainly be more intuitive if clinical studies and articles just told us the false positive rate. Instead, that rate is used to calculate specificity. This is a percentage that comes from the false positive rate by subtracting the false positive rate from 1 and then multiplying by 100. So a test with a false positive rate of 2 out of 10, or 20 percent, would have a specificity of 80 percent. A test like a rapid COVID test with a false positive rate of essentially zero has a specificity of 100 percent. To put that a little more simply, the specificity tells you how often you can trust a positive result. The answer with rapid tests is basically 100 percent of the time\\!\n\nLet’s turn now to sensitivity, and to negative results on a rapid test. (A useful mnemonic: The *n* in *sensitivity* means it’s about negative tests.) Unfortunately, a negative result on a rapid test is much less informative than a positive one. People say the current rapid tests have a (relatively) high false negative rate and are *less sensitive* tests.\n\nA false negative means that the test says you don’t have a disease when you actually do. Sensitivity comes from knowing the “false negative rate”(sometimes called th*e* “miss rate”*)*. The false negative rate is a fraction you calculate from the number of false negatives, divided by the number of people who were known to *actually* be positive.\n\nFor example, suppose you test 1,000 people who are known to have the disease (through some other test), and your rapid test shows 200 people are negative. Your false negative rate for that rapid test is 200 out of 1,000, or 20 percent. Sensitivity is then calculated by subtracting this number from 1, so if you have a false negative rate of 20 percent, your sensitivity is 80 percent. That is, in this example, you can trust a negative test 80 percent of the time.\n\nEstimates for this sensitivity of rapid tests are all over the place for previous variants of COVID, and there is [good evidence](https:\/\/www.fda.gov\/medical-devices\/coronavirus-covid-19-and-medical-devices\/sars-cov-2-viral-mutations-impact-covid-19-tests) that the sensitivity results reported for earlier versions of COVID don’t apply to omicron anyway. So the sensitivity of rapid tests for omicron, right now, is up in the air. While a negative test provides *some* reassurance that you aren’t infectious, we just don’t really know how much.\n\n*Update, Jan. 25, 2022: While most of the original studies of rapid tests (in particular those used for FDA approval) showed essentially 100 percent specificity—whether you were symptomatic or asymptomatic—the picture is becoming more complicated with real-life data, as this* [*recently published erratum*](https:\/\/www.cdc.gov\/mmwr\/volumes\/70\/wr\/mm7004a6.htm?s_cid=mm7004a6_w) *to one of the better papers on this question indicates. The good news is that if you are symptomatic and use a rapid test, specificity for most tests remains at essentially 100 percent. However, if you are asymptomatic, the specificity drops a bit, but is probably still in the very high 90s. Unfortunately, once you drop below 100 percent specificity, the prevalence of the disease affects how much you can trust a positive test, even for a variant as common as omicron. In a nutshell: Current information seems to indicate that at this time, if you are asymptomatic, a positive test has about a 1 in 10 chance of being wrong (i.e., you don’t really have COVID at all). This may be too low, but is probably a good way to bet.*\n\n- [Health](https:\/\/slate.com\/tag\/health)\n- [Math](https:\/\/slate.com\/tag\/math)\n- [Coronavirus](https:\/\/slate.com\/tag\/coronavirus)","meta_canonical":null}

3. Robots.txt Check

Query:

Response:

4. Spam/Ban Check

Query:

Response:

5. Seen Status Check

ℹ️ Skipped - page is already crawled

📄

INDEXABLE

✅

CRAWLED

20 days ago

🤖

ROBOTS ALLOWED

Page Info Filters

Filter	Status	Condition	Details
HTTP status	PASS	`download_http_code = 200`	HTTP 200
Age cutoff	PASS	`download_stamp > now() - 6 MONTH`	0.7 months ago
History drop	PASS	`isNull(history_drop_reason)`	No drop reason
Spam/ban	PASS	`fh_dont_index != 1 AND ml_spam_score = 0`	ml_spam_score=0
Canonical	PASS	`meta_canonical IS NULL OR = '' OR = src_unparsed`	Not set

Page Details

Property	Value
URL	https://slate.com/technology/2022/01/rapid-testing-covid-math-false-negatives-sensitivity.html
Last Crawled	2026-03-24 13:15:14 (20 days ago)
First Indexed	2022-01-14 23:31:17 (4 years ago)
HTTP Status Code	200
Meta Title	What are sensitivity and specificity and what do they mean for COVID rapid tests?
Meta Description	Breaking down false positives and negatives.
Meta Canonical	null
Boilerpipe Text	Science The Math Behind False Positives and False Negatives What are sensitivity and specificity, anyway? Jan 14, 2022 6:21 PM Photo illustration by Slate. Photo by Getty Images Plus. You probably know at this point in the pandemic that if you test positive on a rapid test (and you’ve used the test correctly—you’ve got to swab pretty hard!) that the odds are overwhelming that you have COVID and are infectious. You have, no doubt, been warned that a negative result on a rapid test should be taken with a grain of salt, especially if you’ve been exposed to the virus or you have symptoms. And you might have heard two terms about tests thrown around: sensitivity and specificity, particularly if you’ve been trying to get a grip on exactly how accurate rapid tests are. As a mathematician, I think knowing a bit more about how sensitivity and specificity are calculated can help you better understand why a positive result should be heeded—and a negative test should be read with some caution. First we’ll look at specificity. The Centers for Disease Control and Prevention explains that having rapid tests widely available is a public good because The high specificity and rapid BinaxNOW antigen test turnaround time facilitate earlier isolation of infectious persons. Antigen tests can be an important tool in an overall community testing strategy to reduce transmission. What does specificity mean here? Specificity is calculated based on the number of false positive results a test will produce (and though the CDC references one brand in the quote above, the results are similar for all of them). The number of false positives that studies report seems to be essentially zero . Basically, there are never (or very, very, very rarely) any false positives. So why is a “high specificity” good? It is because it means you have very few false positives! To calculate the specificity of a test, we need to know the “false positive rate.” To calculate the false positive rate, you put the number of false positives that have been identified in the top of a fraction, and put the number of people you tested who did not have COVID-19, including both the false positives and “true negatives,” in the bottom number: (number of false positives)/(number of false positives + number of true negatives). The number of false positives for a rapid test is known to be essentially zero. I hope you recall that any fraction with a zero on top is zero, regardless of the size of the denominator. Thus, the false positive rate for a kind of test with no false positives is also zero. It would certainly be more intuitive if clinical studies and articles just told us the false positive rate. Instead, that rate is used to calculate specificity. This is a percentage that comes from the false positive rate by subtracting the false positive rate from 1 and then multiplying by 100. So a test with a false positive rate of 2 out of 10, or 20 percent, would have a specificity of 80 percent. A test like a rapid COVID test with a false positive rate of essentially zero has a specificity of 100 percent. To put that a little more simply, the specificity tells you how often you can trust a positive result. The answer with rapid tests is basically 100 percent of the time! Let’s turn now to sensitivity, and to negative results on a rapid test. (A useful mnemonic: The n in sensitivity means it’s about negative tests.) Unfortunately, a negative result on a rapid test is much less informative than a positive one. People say the current rapid tests have a (relatively) high false negative rate and are less sensitive tests. A false negative means that the test says you don’t have a disease when you actually do. Sensitivity comes from knowing the “false negative rate” (sometimes called th e “miss rate” ) . The false negative rate is a fraction you calculate from the number of false negatives, divided by the number of people who were known to actually be positive. For example, suppose you test 1,000 people who are known to have the disease (through some other test), and your rapid test shows 200 people are negative. Your false negative rate for that rapid test is 200 out of 1,000, or 20 percent. Sensitivity is then calculated by subtracting this number from 1, so if you have a false negative rate of 20 percent, your sensitivity is 80 percent. That is, in this example, you can trust a negative test 80 percent of the time. Estimates for this sensitivity of rapid tests are all over the place for previous variants of COVID, and there is good evidence that the sensitivity results reported for earlier versions of COVID don’t apply to omicron anyway. So the sensitivity of rapid tests for omicron, right now, is up in the air. While a negative test provides some reassurance that you aren’t infectious, we just don’t really know how much. Update, Jan. 25, 2022: While most of the original studies of rapid tests (in particular those used for FDA approval) showed essentially 100 percent specificity—whether you were symptomatic or asymptomatic—the picture is becoming more complicated with real-life data, as this recently published erratum to one of the better papers on this question indicates. The good news is that if you are symptomatic and use a rapid test, specificity for most tests remains at essentially 100 percent. However, if you are asymptomatic, the specificity drops a bit, but is probably still in the very high 90s. Unfortunately, once you drop below 100 percent specificity, the prevalence of the disease affects how much you can trust a positive test, even for a variant as common as omicron. In a nutshell: Current information seems to indicate that at this time, if you are asymptomatic, a positive test has about a 1 in 10 chance of being wrong (i.e., you don’t really have COVID at all). This may be too low, but is probably a good way to bet. Health Math Coronavirus
Markdown	Advertisement Advertisement [Skip to the content](https://slate.com/technology/2022/01/rapid-testing-covid-math-false-negatives-sensitivity.html#main) - [Slate Shop](https://shop.slate.com/) - [Games](https://slate.com/tag/slate-games) - [Newsletters](https://slate.com/newsletters) - [Sign In](https://slate.com/sign-in) - Account [Account](https://slate.com/account) [Sign out](https://slate.com/sign-out) - [News & Politics](https://slate.com/news-and-politics) - [Culture](https://slate.com/culture) - [Technology](https://slate.com/technology) - [Business](https://slate.com/business) - [Life](https://slate.com/life) - [Advice](https://slate.com/advice) - [Podcasts](https://slate.com/podcasts) Menu Menu [News & Politics](https://slate.com/news-and-politics) [Culture](https://slate.com/culture) [Technology](https://slate.com/technology) [Business](https://slate.com/business) [Life](https://slate.com/life) [Advice](https://slate.com/advice) [Podcasts](https://slate.com/podcasts) [Search](https://slate.com/search) Light Dark Auto [Subscribe](https://slate.com/plus?utm_medium=link&utm_campaign=plus&utm_content=nav_bar&utm_source=nav) [Slate Shop](https://shop.slate.com/) [Games](https://slate.com/tag/slate-games) [Newsletters](https://slate.com/newsletters) [Sign in](https://slate.com/sign-in) [Account](https://slate.com/account) [Sign out](https://slate.com/sign-out) [Account](https://slate.com/account) [Responding to Increasingly Zany Situations](https://slate.com/culture/2026/03/jury-duty-show-season-2-company-retreat-prime.html) Light Dark Auto [Science](https://slate.com/technology/science) # The Math Behind False Positives and False Negatives ## What are sensitivity and specificity, anyway? By [Gary Cornell](https://slate.com/author/gary-cornell) Jan 14, 20226:21 PM ![A hand holding up a rapid coronavirus test](https://compote.slate.com/images/7c94e17e-21d4-48cf-ba9d-f9ec3919f150.jpeg?crop=1560%2C1040%2Cx0%2Cy0) Photo illustration by Slate. Photo by Getty Images Plus. [Copy Link]() [Share](https://www.facebook.com/sharer.php?u=https%3A%2F%2Fslate.com%2Ftechnology%2F2022%2F01%2Frapid-testing-covid-math-false-negatives-sensitivity.html%3Futm_medium%3Dsocial%26utm_campaign%3Dtraffic%26utm_source%3Darticle%26utm_content%3Dfacebook_share) [Share]() [Comment](https://slate.com/comments/technology/2022/01/rapid-testing-covid-math-false-negatives-sensitivity.html) [Copy Link]() [Share](https://www.facebook.com/sharer.php?u=https%3A%2F%2Fslate.com%2Ftechnology%2F2022%2F01%2Frapid-testing-covid-math-false-negatives-sensitivity.html%3Futm_medium%3Dsocial%26utm_campaign%3Dtraffic%26utm_source%3Darticle%26utm_content%3Dfacebook_share) [Share]() [Comment](https://slate.com/comments/technology/2022/01/rapid-testing-covid-math-false-negatives-sensitivity.html) You probably know at this point in the pandemic that if you test positive on a rapid test (and you’ve used the test correctly—you’ve got to swab pretty hard!) that the odds are overwhelming that you have COVID and are infectious. You have, no doubt, been warned that a negative result on a rapid test should be taken with a grain of salt, especially if you’ve been exposed to the virus or you have symptoms. And you might have heard two terms about tests thrown around: sensitivity and specificity, particularly if you’ve been trying to [get a grip](https://www.nytimes.com/article/at-home-covid-tests-accuracy.html) on exactly how accurate rapid tests are. As a mathematician, I think knowing a bit more about how sensitivity and specificity are calculated can help you better understand why a positive result should be heeded—and a negative test should be read with some caution. First we’ll look at specificity. The Centers for Disease Control and Prevention [explains](https://www.cdc.gov/mmwr/volumes/70/wr/mm7003e3.htm) that having rapid tests widely available is a public good because > The high specificity and rapid BinaxNOW antigen test turnaround time facilitate earlier isolation of infectious persons. Antigen tests can be an important tool in an overall community testing strategy to reduce transmission. What does specificity mean here? Specificity is calculated based on the number of false positive results a test will produce (and though the CDC references one brand in the quote above, the results are similar for all of them). The number of false positives that studies report seems to be [essentially zero](https://www.cdc.gov/mmwr/volumes/70/wr/mm7003e3.htm). Basically, there are never (or very, very, very rarely) any false positives. So why is a “high specificity” good? It is because it means you have very few false positives\! Advertisement Advertisement Advertisement To calculate the specificity of a test, we need to know the “false positive rate.” To calculate the false positive rate, you put the number of false positives that have been identified in the top of a fraction, and put the number of people you tested who did not have COVID-19, including both the false positives and “true negatives,” in the bottom number: (number of false positives)/(number of false positives + number of true negatives). Advertisement The number of false positives for a rapid test is known to be essentially zero. I hope you recall that any fraction with a zero on top is zero, regardless of the size of the denominator. Thus, the false positive rate for a kind of test with no false positives is also zero. It would certainly be more intuitive if clinical studies and articles just told us the false positive rate. Instead, that rate is used to calculate specificity. This is a percentage that comes from the false positive rate by subtracting the false positive rate from 1 and then multiplying by 100. So a test with a false positive rate of 2 out of 10, or 20 percent, would have a specificity of 80 percent. A test like a rapid COVID test with a false positive rate of essentially zero has a specificity of 100 percent. To put that a little more simply, the specificity tells you how often you can trust a positive result. The answer with rapid tests is basically 100 percent of the time\! Advertisement Advertisement Let’s turn now to sensitivity, and to negative results on a rapid test. (A useful mnemonic: The n in sensitivity means it’s about negative tests.) Unfortunately, a negative result on a rapid test is much less informative than a positive one. People say the current rapid tests have a (relatively) high false negative rate and are less sensitive tests. Advertisement A false negative means that the test says you don’t have a disease when you actually do. Sensitivity comes from knowing the “false negative rate”(sometimes called the “miss rate”). The false negative rate is a fraction you calculate from the number of false negatives, divided by the number of people who were known to actually be positive. For example, suppose you test 1,000 people who are known to have the disease (through some other test), and your rapid test shows 200 people are negative. Your false negative rate for that rapid test is 200 out of 1,000, or 20 percent. Sensitivity is then calculated by subtracting this number from 1, so if you have a false negative rate of 20 percent, your sensitivity is 80 percent. That is, in this example, you can trust a negative test 80 percent of the time. Advertisement Advertisement Advertisement Estimates for this sensitivity of rapid tests are all over the place for previous variants of COVID, and there is [good evidence](https://www.fda.gov/medical-devices/coronavirus-covid-19-and-medical-devices/sars-cov-2-viral-mutations-impact-covid-19-tests) that the sensitivity results reported for earlier versions of COVID don’t apply to omicron anyway. So the sensitivity of rapid tests for omicron, right now, is up in the air. While a negative test provides some reassurance that you aren’t infectious, we just don’t really know how much. # Popular in [Technology](https://slate.com/technology) 1. [Why YouTuber Hank Green Turned Down More Money to Make a Bigger Difference](https://slate.com/technology/2026/03/hank-green-crash-course-youtube-ai-education.html) Update, Jan. 25, 2022: While most of the original studies of rapid tests (in particular those used for FDA approval) showed essentially 100 percent specificity—whether you were symptomatic or asymptomatic—the picture is becoming more complicated with real-life data, as this [recently published erratum](https://www.cdc.gov/mmwr/volumes/70/wr/mm7004a6.htm?s_cid=mm7004a6_w) to one of the better papers on this question indicates. The good news is that if you are symptomatic and use a rapid test, specificity for most tests remains at essentially 100 percent. However, if you are asymptomatic, the specificity drops a bit, but is probably still in the very high 90s. Unfortunately, once you drop below 100 percent specificity, the prevalence of the disease affects how much you can trust a positive test, even for a variant as common as omicron. In a nutshell: Current information seems to indicate that at this time, if you are asymptomatic, a positive test has about a 1 in 10 chance of being wrong (i.e., you don’t really have COVID at all). This may be too low, but is probably a good way to bet. [Copy Link]() [Share](https://www.facebook.com/sharer.php?u=https%3A%2F%2Fslate.com%2Ftechnology%2F2022%2F01%2Frapid-testing-covid-math-false-negatives-sensitivity.html%3Futm_medium%3Dsocial%26utm_campaign%3Dtraffic%26utm_source%3Darticle%26utm_content%3Dfacebook_share) [Share]() [Comment](https://slate.com/comments/technology/2022/01/rapid-testing-covid-math-false-negatives-sensitivity.html) - [Health](https://slate.com/tag/health) - [Math](https://slate.com/tag/math) - [Coronavirus](https://slate.com/tag/coronavirus) Advertisement *** Advertisement #### About - [About Us](https://slate.com/about) - [Work With Us](https://jobs.lever.co/slate) - [Contact](https://slate.com/contact) - [Pitch Guidelines](https://slate.com/pitch) - [Send Us Tips](https://slate.com/tips) - [Corrections](https://slate.com/briefing/corrections) - [Commenting](https://slate.com/commenting) - [Reprints](http://www.slatereprints.com/) #### Subscriptions - [Subscribe](https://slate.com/plus) - [Group Subscriptions](https://slate.com/academic-group-subscriptions) - [Sign In](https://slate.com/sign-in) - [Account](https://slate.com/account) - [Subscription FAQs](https://slate.com/plus/faq) - [Podcast FAQs](https://slate.com/podcastfaqs) - [Newsletters](https://slate.com/newsletters) - [Customer Support](https://slatehelp.freshdesk.com/support/solutions) #### Advertising - [AdChoices](https://optout.aboutads.info/) - [![California Consumer Privacy Act (CCPA) Opt-Out Icon](https://dot.cdnslate.com/static/media/components/onetrust-update/ccpa-icons/privacyoptions29x14.f2f5996.png) Cookie Preferences](https://slate.com/do-not-sell) Slate is published by The Slate Group, a Graham Holdings Company. #### Follow Us [Facebook](https://www.facebook.com/Slate/) [X](https://twitter.com/slate) [Bluesky](https://bsky.app/profile/slate.com) [Instagram](https://www.instagram.com/slate/) [YouTube](https://www.youtube.com/slate) [RSS Feed](https://slate.com/rss) - [User Agreement](https://slate.com/terms) - [Privacy Policy](https://slate.com/privacy) All contents © 2026 The Slate Group LLC. All rights reserved. # We need to talk about your adblocker Slate relies on advertising to support our journalism. If you value our work, please disable your ad blocker. If you want to block ads but still support Slate, consider subscribing. [Enable Ads on Slate](https://slate.com/news-and-politics/2017/04/how-to-disable-your-ad-blocker-on-slate.html) [Subscribe](https://slate.com/plus?via=ad_blocker_modal&tpcc=slate-ui--ad_blocker_modal) Already a member? [Sign in here](https://slate.com/sign-in) # This article is only for Slate Plus members. Join today to keep reading. You'll also get access to all of Slate's independent journalism, unparalleled advice, and daily games. Cancel anytime. [Join Slate Plus](https://slate.com/plus?via=ad_blocker_hardwall&tpcc=slate-ui--ad_blocker_hardwall) Already a member? [Sign in here](https://slate.com/sign-in)
Readable Markdown	[Science](https://slate.com/technology/science) ## The Math Behind False Positives and False Negatives ## What are sensitivity and specificity, anyway? Jan 14, 20226:21 PM ![A hand holding up a rapid coronavirus test](https://compote.slate.com/images/7c94e17e-21d4-48cf-ba9d-f9ec3919f150.jpeg?crop=1560%2C1040%2Cx0%2Cy0) Photo illustration by Slate. Photo by Getty Images Plus. You probably know at this point in the pandemic that if you test positive on a rapid test (and you’ve used the test correctly—you’ve got to swab pretty hard!) that the odds are overwhelming that you have COVID and are infectious. You have, no doubt, been warned that a negative result on a rapid test should be taken with a grain of salt, especially if you’ve been exposed to the virus or you have symptoms. And you might have heard two terms about tests thrown around: sensitivity and specificity, particularly if you’ve been trying to [get a grip](https://www.nytimes.com/article/at-home-covid-tests-accuracy.html) on exactly how accurate rapid tests are. As a mathematician, I think knowing a bit more about how sensitivity and specificity are calculated can help you better understand why a positive result should be heeded—and a negative test should be read with some caution. First we’ll look at specificity. The Centers for Disease Control and Prevention [explains](https://www.cdc.gov/mmwr/volumes/70/wr/mm7003e3.htm) that having rapid tests widely available is a public good because > The high specificity and rapid BinaxNOW antigen test turnaround time facilitate earlier isolation of infectious persons. Antigen tests can be an important tool in an overall community testing strategy to reduce transmission. What does specificity mean here? Specificity is calculated based on the number of false positive results a test will produce (and though the CDC references one brand in the quote above, the results are similar for all of them). The number of false positives that studies report seems to be [essentially zero](https://www.cdc.gov/mmwr/volumes/70/wr/mm7003e3.htm). Basically, there are never (or very, very, very rarely) any false positives. So why is a “high specificity” good? It is because it means you have very few false positives\! To calculate the specificity of a test, we need to know the “false positive rate.” To calculate the false positive rate, you put the number of false positives that have been identified in the top of a fraction, and put the number of people you tested who did not have COVID-19, including both the false positives and “true negatives,” in the bottom number: (number of false positives)/(number of false positives + number of true negatives). The number of false positives for a rapid test is known to be essentially zero. I hope you recall that any fraction with a zero on top is zero, regardless of the size of the denominator. Thus, the false positive rate for a kind of test with no false positives is also zero. It would certainly be more intuitive if clinical studies and articles just told us the false positive rate. Instead, that rate is used to calculate specificity. This is a percentage that comes from the false positive rate by subtracting the false positive rate from 1 and then multiplying by 100. So a test with a false positive rate of 2 out of 10, or 20 percent, would have a specificity of 80 percent. A test like a rapid COVID test with a false positive rate of essentially zero has a specificity of 100 percent. To put that a little more simply, the specificity tells you how often you can trust a positive result. The answer with rapid tests is basically 100 percent of the time\! Let’s turn now to sensitivity, and to negative results on a rapid test. (A useful mnemonic: The n in sensitivity means it’s about negative tests.) Unfortunately, a negative result on a rapid test is much less informative than a positive one. People say the current rapid tests have a (relatively) high false negative rate and are less sensitive tests. A false negative means that the test says you don’t have a disease when you actually do. Sensitivity comes from knowing the “false negative rate”(sometimes called the “miss rate”). The false negative rate is a fraction you calculate from the number of false negatives, divided by the number of people who were known to actually be positive. For example, suppose you test 1,000 people who are known to have the disease (through some other test), and your rapid test shows 200 people are negative. Your false negative rate for that rapid test is 200 out of 1,000, or 20 percent. Sensitivity is then calculated by subtracting this number from 1, so if you have a false negative rate of 20 percent, your sensitivity is 80 percent. That is, in this example, you can trust a negative test 80 percent of the time. Estimates for this sensitivity of rapid tests are all over the place for previous variants of COVID, and there is [good evidence](https://www.fda.gov/medical-devices/coronavirus-covid-19-and-medical-devices/sars-cov-2-viral-mutations-impact-covid-19-tests) that the sensitivity results reported for earlier versions of COVID don’t apply to omicron anyway. So the sensitivity of rapid tests for omicron, right now, is up in the air. While a negative test provides some reassurance that you aren’t infectious, we just don’t really know how much. Update, Jan. 25, 2022: While most of the original studies of rapid tests (in particular those used for FDA approval) showed essentially 100 percent specificity—whether you were symptomatic or asymptomatic—the picture is becoming more complicated with real-life data, as this [recently published erratum](https://www.cdc.gov/mmwr/volumes/70/wr/mm7004a6.htm?s_cid=mm7004a6_w) to one of the better papers on this question indicates. The good news is that if you are symptomatic and use a rapid test, specificity for most tests remains at essentially 100 percent. However, if you are asymptomatic, the specificity drops a bit, but is probably still in the very high 90s. Unfortunately, once you drop below 100 percent specificity, the prevalence of the disease affects how much you can trust a positive test, even for a variant as common as omicron. In a nutshell: Current information seems to indicate that at this time, if you are asymptomatic, a positive test has about a 1 in 10 chance of being wrong (i.e., you don’t really have COVID at all). This may be too low, but is probably a good way to bet. - [Health](https://slate.com/tag/health) - [Math](https://slate.com/tag/math) - [Coronavirus](https://slate.com/tag/coronavirus)
Shard	145 (laksa)
Root Hash	14993094292168895945
Unparsed URL	com,slate!/technology/2022/01/rapid-testing-covid-math-false-negatives-sensitivity.html s443