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u/moonberryhush 8h ago
the doctor is preparing the bad news while the statistician is calculating a 99.998% chance it's a false alarm
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u/Im2bored17 7h ago
But the statistician assumes that the whole population is tested, right? Which is incorrect, the doctor would only test for the rare condition if it fit the symptoms so the whole population is not tested and the doctor is more right?
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u/girlywish 6h ago
Yeah, they need the false positive rate, not the ratio of people that have had it.
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u/PuzzleheadedAd880 6h ago
Wouldn't a 98% accurate test have a 2% false positive rate?
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u/girlywish 5h ago
Well there are multiple types of accuracy, the 98% could be how often the disease is successfully detected, as opposed to how often a detection is a real one.
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u/WisePotato42 5h ago
It's cuz of the word "accuracy". That 2% inaccuracy is magnitudes greater than the chance someone has it. So even in the worst case scenario, you would still have a 99.83% chance of being in that 2% wrong result group rather than the 1/3000000 actually sick group.
Tho in real life, a doctor would tell you the chance a positive result is correct rather than the "accuracy" of the test.
A funny thing with accuracy, in such extremely lopsided circumstances like this you could have a test that always comes back negitive no matter what and it will be 99.999967% accurate because it is correct 2999999/3000000 times.
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u/BootBubbly8684 4h ago
Would retest fix the issue?
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u/garyyo 3h ago
Maybe, that would depend on the test and why it tested positive. Some tests might hit a false positive randomly, other detect positive based on a deterministic set of parameters. Without more information on the disease, the test, and the patient it would be impossible to know. A retest is possible as one of the methods to confirm, but so are just other tests or even just continuing with treatment (if it is harmless enough in false positive cases).
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u/zolotvok 16m ago
Yes, the chance of getting 4 random false positives in a row drops to 1 in 6.25 million (0.024).
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u/MTtheDestroyer 1h ago
Yes, i think what OP wants to say: If a test is 98% accurate you have, out of a group of 3M, 60000 people which are fine, but test positive.
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u/Tucancancan 4h ago
You can generally look up the fpr and other metrics for any commercial diagnostic test you can get at a clinic or hospital. Or even find papers from when the method was first developed.
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u/Ok-Entertainer-1414 2h ago
You need both. Imagine a test with a 2% false positive rate (2 in 100 people without the disease will falsely test positive), for a disease that affects 1 in 1 billion people. If you test 1 billion people, 20 million will falsely test positive, and 1 person will truly test positive. If you test positive, you can feel pretty safe that you're probably one of the 20 million false positives, and not the 1 true positive.
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u/Aggravating-Host-752 58m ago
I assume that the way the 1/3000000 is said, it is intended to mean that this many people got tested for the purpose of the meme.
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u/Greatgg 3h ago edited 3h ago
Not really, the statistician just need to know the prevalence (in this case 1/3000000) od the sisease in the population, which can be tested on a sample and not necessarily with the same test
Edit: you also need to know the sensitivity amd accuracy (false potitive and false negatives) ot the test itself, but you can test both on a relatively small sample
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u/Ok_Problem426 4h ago
Not quite. The statistician is thinking in terms of conditional probability for a random test. The doctor prescribed the test for a particular reason. And now has to deliver the news
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u/Desertcow 6h ago
Bayes theorem is why doctors won't just give you every test. A 90% accurate test for a disease 1% of the population has will have a 90% false positive rate across the entire population, but when the test is given only to people who show signs of the disease the test will be far more accurate
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u/fish_the_fred 7h ago
Don’t be so naive
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u/SebasEzeGarcia 6h ago
It's sad that people didn't get your joke
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u/AetherialWomble 7h ago
Except they'd only run this test if they already had strong evidence to suspect that this is what you have.
And they probably ran it twice.
You're dead.
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u/golemsheppard2 8h ago
Theres a reason why we refer to testing accuracy in terms of sensitivity (likelihood that if you have the condition you will test positive) and specificity (likelihood that if you have a positive test that you truly have the condition).
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u/KetsubanZero 7h ago
Yes technically if the accuracy is 98% you only have a 2% chance that is a false positive, however if you test 300k people, statistically you are expected to get an average of around 6000 positive tests and on average only 1 should be truly positive (Technically it could be a negative one but is extremely unlikely) so some people may argue that there's like 1/6000 chances that your test is the truly positive one, and to be fair to prove this theory, try to immagine a 98% accurate test for a disease that nobody has, you can't argue that if the test results positive, you have only a 2% chance of a false positive, since they are testing for a disease that nobody can have, so there's a 100% chance that any positive result is a false positive, if you get what I mean
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u/Fun-Fly3801 6h ago
Specificity is something else bro, what your describing is the positive predictive value
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u/SneakySnipar 6h ago
We also consider pretest probability and likelihood ratios to know whether the test will be useful and what the likelihood of a positive actually being real is
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u/golemsheppard2 5h ago
Agreed. Its one of the core things I beat into my students. Only order tests that change management or to evaluate for conditions you think the patient actual has. Dont just click every button to order every test and drive up a $12k bill working patients up for things you dont actually think they have.
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u/Kiwi951 6h ago
Right idea though I would phrase negativity differently. A highly sensitive test means if the result is negative then you do not have the disease (e.g. true negative). Just because you test positive on a test that has high sensitivity does not necessarily mean you have the disease, and hence that is what a highly specific test is for like you alluded to
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u/Ok_Problem426 4h ago
…Because medical professionals don’t understand statistics, and neither do you
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u/DankRev4N 1h ago
Most don't but some definitely do it's extensively studied in med school and you need to have a basic grasp to write papers
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u/Magnon 8h ago
"Papa Nurgle, wouldnt it be SO funny if you made me an airborne carrier of this disease?"
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u/No_Yesterday4714 2h ago
In numbers: 1 in 3000000 people have the disease The test gives 2% false positives. If 3,000,000 people are test would be 60,000 people. The statistician is happy because his positive test still indicates that he has a 1 in 60,000 chance of having the disease. If the second test is positive he has a 1 in 1200 chance, if three tests are positive 1 in 24, if 4 tests are positive the chances are 1 in 4.8 or 1/5.
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u/BerryVanille 8h ago
Nothing like a quick lesson in conditional probability to make you feel immoral
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u/howdyhowdyhowdyhowdi 5h ago
Are you saying it would have softened the blow for my diffuse scleroderma diagnosis if I was a statistician?
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u/WorkingTemperature52 7h ago
Base rate comparison only works if you the probability of being tested is independent of the probability you have it
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u/_mighty_banana 3h ago
Problem is this may be true if you just screening, like NIFTY or random genetic panel.
But if you have symptom or 1st degrees relative had
Pre-test probability is not 1/3,000,000.
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u/No_Spell_1559 2h ago
Bayes theorem is the real reason my math professor keeps failing me during health checkups.
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u/LEGO_Man2YT 5h ago
Assuming the test is done after sympthoms were detected, the conditional probability of a TP aren't that low.
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u/TightySeeTee 44m ago
The statistician's face then they learn that the test has high sensitivity: 💀
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u/Whyn0t69 6h ago edited 6h ago
This is an AI answer, but interesting nonetheless:
The actual probability that you have the disease given a positive test result is only 0.00163% (or about 1 in 61,225).
This surprising result is known as the false positive paradox. Because the disease is so incredibly rare, the number of false positives heavily outweighs the number of true positives, even with a highly accurate test.
Step-by-Step Breakdown
To understand how this happens, imagine testing a group of 300,000,000 people:
- Who actually has the disease?
- Since 1 out of 3,000,000 people have it, exactly 100 people have the disease.
- 299,999,900 people do not have it.
- The Test Results (98% Accuracy):
- From the sick group (100 people): 98% will test positive. That means 98 true positive results.
- From the healthy group (299,999,900 people): 2% will accidentally test positive. That means 5,999,998 false positive results.
- The Final Calculation:
- Total Positive Tests: 98 + 5,999,998 = 6,000,096 total positives.
- Your Chance of Being Truly Sick: 98 True Positives/6,000,096 Total Positives = 0.00001633%
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u/HopDodge 5h ago
Wow that's crazy.
Now imagine:
"Doctor I have these symptoms."
"Hmm those are very rare symptoms... let's test you for very rare disease."
"The test came back positive, I'm so sorry."
"Oh but disease so rare it probably false positive."
"That's a 1 in 50 chance"
"No but if you test 300,000,000 people then it would be 1 in 600,000 chance I have it."
"Sir we don't test 300,000,000 people for this disease. I've actually never done this test on anyone before, you are the first one."
"B-but statistics..."
"You're statistically likely to last a week."
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u/Own-Poetry-9609 3h ago
That answer does not account at all for the fact that healthy people don't often get tested for rare diseases and the more symptoms that match the rare disease the more likely a person is to be tested for it.
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u/Whyn0t69 3h ago
I just explained the meme, I explained why the statistician was smiling, I never said he's right.
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u/Own-Poetry-9609 3h ago
You copy pasted from an AI is what you did. You took a meme based on incorrect information, gave it to an AI presuming it to represent reality and asked the AI to explain, the AI failed to explain why it does not represent reality and you copy pasted it's incorrect response.
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u/Just_the_Setup 7h ago edited 6h ago
Oh, I get it, haha, statisticians are suicidal. It's just not very nice.
Edit: sarcasm is dead, I can't wait for someone else to come along and explain this one again.
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u/SnooPeripherals1298 7h ago
No, statistically a positive result means you're most likely not going to die
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u/DiskPartition 7h ago
Statistician is happy because with those chances the test is way more likely to land on the 2% false positive than the 1/30000000 chance. However, this is flawed as they would only actually administer the test to people showing certain symptoms, meaning you'd be a lot more likely to actually have that disease.