Reframing, if you picked 5 apples out of a bag of 1 million, I would suggest you need more sampling because your analysis doesn’t have enough power to correctly reject the hypothesis
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Replying to @CravenRave @hurricaneross and
You don't understand probability. The probability of picking 5 rotten apples out of a bag of 1 million and when those are the only 5 rotten ones is near zero. If half are rotten the probability is still only about .03. It becomes 50/50 when 87% of the apples are rotten.
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Replying to @CovfefeAnon @hurricaneross and
No, it actually doesn’t unless you are going on the binary belief that it’s either all bad or all good or you don’t understand significance. The likelyhood of all 5 being bad is low, but no statistician would be comfortable drawing that conclusion that it’s the prevailing norm.
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Replying to @CravenRave @hurricaneross and
Those are the probabilities from *your example*. Look up binomial distribution. (Proof that you don't get probability is that it doesn't matter how many apples are in the bag - the only numbers that matter are the probability of each being rotten and the number you pull out)
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Replying to @CovfefeAnon @hurricaneross and
My example wasn’t there was only 5 bad apples. In a bag of apples that large there’s going to be some non-zero number of bad apples in all probability above 5. Also you should probably use more Bayesian ideas here; there’s an incentive to find bad apples.
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Replying to @CravenRave @hurricaneross and
You set out an *extremely* simple probability example that's solvable using the binomial distribution and it ... illustrated exactly the point you thought you were refuting There's no "incentive to find bad apples" either - the opposite actually - those are the best apples found
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Replying to @CovfefeAnon @hurricaneross and
Bad apples spoil the bunch comes to mind. Media is encouraged to sensationalize news especially crime stories. You aren’t using the real world in this instance.
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Replying to @CravenRave @CovfefeAnon and
If you’ve collected a bag of apples, you would want to remove the bad apples from good apples. Also again your ignoring the small sample hypothesis test results
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Replying to @CravenRave @hurricaneross and
You treat "sample size" like a magic incantation because you don't understand what it is supposed to qualify and when. Probability allows for some very powerful conclusions when *seemingly* improbable things happen often.
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Replying to @CovfefeAnon @hurricaneross and
Wrong sample size bias When the wrong sample size is used in a study: small sample sizes often lead to chance findings, while large sample sizes are often statistically significant but not clinically relevant.
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You don't get it. Take *your example* - you can draw exactly the conclusions I stated above - very simple calculations to show each of them. With random 5 draws you can make a very good guess about a distribution. In reality we have way more than 5 draws.
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