by **Azazeltje** » Thu Dec 06, 2018 11:01 pm

NeatNit wrote:Azazeltje wrote:I am so lost on the math here - is he saying that random chance would lead to correct guesses from Group A two-thirds of the time? Why is that not 50/50?

Random chance will often give you close to 50/50, but not exactly. He's saying that if they get it wrong more than 2/3 of the time, that's worse than even random guessing is statistically likely to get, but between 1/3 and 2/3 is kind of in the range of possible outcomes of random guessing.

Statistics is an entire branch of mathematics dedicated to figuring out what's a statistically likely result given a certain condition, and what isn't. Zach didn't seem to apply any statistical knowledge here, so he just fudged it.

Oh I think I misunderstood your answer - you're saying that even tho the odds are 50/50, actual outcomes are likely to be scattered in between the 1/3-2/3 range - so the cutoff is just 66% - higher passes, lower fails - that makes a certain kind of logical sense, but i don't think thats actually whats intended - because if the odds are 50/50 (which we seem to agree thats the prescriptive calculation) it would be rare for the actual outcomes to be SO far off that they come out at 1/3 or 2/3... in fact, shouldn't that question itself be something stats can shine a light on? how likely it would be for the outcome to be X number of standard deviations away from the prescriptive value?

I'm clearly not a mathematician, so if anyone knows anything, don't be shy

[quote="NeatNit"][quote="Azazeltje"]I am so lost on the math here - is he saying that random chance would lead to correct guesses from Group A two-thirds of the time? Why is that not 50/50?[/quote]

Random chance will often give you close to 50/50, but not exactly. He's saying that if they get it wrong more than 2/3 of the time, that's worse than even random guessing is statistically likely to get, but between 1/3 and 2/3 is kind of in the range of possible outcomes of random guessing.

Statistics is an entire branch of mathematics dedicated to figuring out what's a statistically likely result given a certain condition, and what isn't. Zach didn't seem to apply any statistical knowledge here, so he just fudged it.[/quote]

Oh I think I misunderstood your answer - you're saying that even tho the odds are 50/50, actual outcomes are likely to be scattered in between the 1/3-2/3 range - so the cutoff is just 66% - higher passes, lower fails - that makes a certain kind of logical sense, but i don't think thats actually whats intended - because if the odds are 50/50 (which we seem to agree thats the prescriptive calculation) it would be rare for the actual outcomes to be SO far off that they come out at 1/3 or 2/3... in fact, shouldn't that question itself be something stats can shine a light on? how likely it would be for the outcome to be X number of standard deviations away from the prescriptive value?

I'm clearly not a mathematician, so if anyone knows anything, don't be shy