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Comment by Dylan16807 | Hacker News Reader

I'm reasonably sure the false negative rate is 1%, because the least misleading definition of "99% accurate" means it fails 1% of the time at random.

A 1% false negative rate has a negligible impact on the math. 50% isn't perfect down to the decimal point, but it's very close.

After the first round you have 99.99 false positives and .99 true positives.

After the second round, if independent, you have .9999 false positives and .9801 true positives.

And in fact the lower bound, if you had no false negatives, is slightly below 50%. .9999 vs 1.

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Their definition of accuracy is 1-false_positive_rate. They were quite explicit about that.

No, they didn't say that was the definition in their one post.

Their math shows that those are the same number, and they didn't elaborate on definitions.

The least misleading definition of accuracy is that accuracy = 1-false_positive_rate = 1-false_negative_rate. So unless told otherwise, I will use that definition.

Yes they did. They say it twice. I have italicised both places where they say it.

"Let's say there is a terrible disease that 0.01% (1 in 10,000) of the population is infected with, and we develop a test that is 99% accurate. You go to the doctor and get a test. Oh no, it's positive. What are the chances that it's a false positive?

Intuition would tell you 1% since the test is 99% accurate. Intuition, as it often is, is wrong. Take a sample size of 'x', we'll use 10,000. How many people will be infected? 1. How many false positives will there be? 1% * 10,000 = 100"

Then they conclude by saying:

  "So there will be 100 false positives, and 1 real positive."

The fact there is one real positive necessarily implies they are assuming the false negative rate is exactly 0, given that the disease prevalence is in 0.01 percent of the population.

> The fact there is one real positive necessarily implies they are assuming the false negative rate is exactly 0, given that the disease prevalence is in 0.01 percent of the population.

Or that they rounded .99 people to 1 person.

And given that they did round the false positives, I don't see why that's a strange idea.

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