This is why I hate statistics

genna

genna

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Covid related fun with statistics. Or how to make my head hurt.

*FDA approves 90% accurate positive and 95% negative antibody tests.

*Current estimates on how many people in US have had the virus range from 5% to 15% of population

So what does that actually mean? Taking 5% number, that means that if 100 random people are tested, 15 will have positive result. 5 have actually had the virus and 10 are false positive. Or roughly 33% of positive results are actually positive

Fun!

Taking 15% number would translate to 64% of positive results being actually positive

Basically, we need to get more people infected for these tests to be meaningful at all.

This is right up there with Monty Hall problem. Well, almost
 
Testing is only as good as the error rates. This applies to ALL MEDICAL DIAGNOSTICS....
 
genna said:
Covid related fun with statistics. Or how to make my head hurt.

*FDA approves 90% accurate positive and 95% negative antibody tests.

*Current estimates on how many people in US have had the virus range from 5% to 15% of population

So what does that actually mean? Taking 5% number, that means that if 100 random people are tested, 15 will have positive result. 5 have actually had the virus and 10 are false positive. Or roughly 33% of positive results are actually positive

Fun!

Taking 15% number would translate to 64% of positive results being actually positive

Basically, we need to get more people infected for these tests to be meaningful at all.

This is right up there with Monty Hall problem. Well, almost
Click to expand...

I am not certain that "90% accurate positive" necessarily means that 10% will be false positives. Of the remaining 10%, its quite possible that 9% fall in the indeterminate category, and only 1% is a false positive. Not positive does not always mean negative.
 
I got my only "C" in 'Probs and Stats' because I was convinced that when asked what the probability of an event was, I said either it will or it won't so the answer is always 50-50.
 
sarangan said:
I am not certain that "90% accurate positive" necessarily means that 10% will be false positives. Of the remaining 10%, its quite possible that 9% fall in the indeterminate category, and only 1% is a false positive. Not positive does not always mean negative.
Click to expand...

I can't answer that. My OP -- and I have no reasons to believe otherwise -- assumes that there are only 2 possible outcomes of the test: Y or N. If there is an F(failed), then the calculus is different.

The concept here is a base rate fallacy. Something that is very counter-intuitive but legit. At the risk of derailing my own thread, this also has a very interesting effect on DUI random road-blocks
 
genna said:
Covid related fun with statistics. Or how to make my head hurt.

*FDA approves 90% accurate positive and 95% negative antibody tests.

*Current estimates on how many people in US have had the virus range from 5% to 15% of population

So what does that actually mean? Taking 5% number, that means that if 100 random people are tested, 15 will have positive result. 5 have actually had the virus and 10 are false positive. Or roughly 33% of positive results are actually positive

Fun!

Taking 15% number would translate to 64% of positive results being actually positive

Basically, we need to get more people infected for these tests to be meaningful at all.

This is right up there with Monty Hall problem. Well, almost
Click to expand...
Not quite right. A group of 100 random people probably will not have the exact number calculated. But on average, many groups of 100 will average out as that number per group.

There's a saying "lies, damn lies, and then there are statistics".
 
wsuffa said:
Not quite right. A group of 100 random people probably will not have the exact number calculated. But on average, many groups of 100 will average out as that number per group.

There's a saying "lies, damn lies, and then there are statistics".
Click to expand...

so 10000 or 1000000. 100 was just a number i picked. You can use 320,000,000 (US population).
 
I nearly failed statistics in college. I don't know how people manage to deal with the subject.
 
I avoided stats in college like the plague. And then I had to understand probabilistic risk assessments and monte carlo analysis as part of litigating cases and in one instance guiding witnesses through a Congressional Hearing. After listening to several prominent Congressman fail to grasp what a 10 to the minus 7 probable risk of a tornado impact to a nuclear facility meant despite having it explained so that even a 3rd grader could get it, I realized this stuff doesn’t mean much to the average person.
 
“Statistics are like bikinis. What they reveal is interesting. What they conceal is vital!”

- Professor Aaron Levenstein

My favorite statistics story involves a person who had data in Excel, and tried out all the different curve-matching algorithms Excel had until he found one that gave him the result he wanted.

Someone else tried the same curve-match algorithm on their local high temperatures over a monthly period, and it predicted the temperature dropping to -60 degrees a week after the end of the data....

Ron Wanttaja
 
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