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>In most fields, if there's less than a five percent chance that you'd get the two numbers by random chance, then you can reject chance—the results are consider
by coherentpony 13y ago
>In most fields, if there's less than a five percent chance that you'd get the two numbers by random chance, then you can reject chance—the results are considered significant. In statistical terms, this is called having a p value of less than 0.05.
No it isn't [1].
[1]: https://en.wikipedia.org/wiki/P-value https://en.wikipedia.org/wiki/P-value
- capnrefsmmat 13y agoThe Ars definition of a p value is not precisely worded but, I think, reasonably accurate. It doesn't include the bit about also including the probability of obtaining results more extreme than what you obtained. The best definition I know is > The P value is defined as the probability, under the assumption of no effect or no difference (the null hypothesis), of obtaining a result equal to or more extreme than what was actually observed. S. N. Goodman. Toward evidence-based medical statistics. 1: The P value fallacy. Annals of Internal Medicine, 130:995–1004, 1999. edit: oh dear, and then the Ars article says "Individual experiments may be wrong five percent of the time," but that's exactly what p values do not measure. Statistics is hard.
- coherentpony 13y agoYeah that definition is good. For the purposes of understanding the definition, another way of looking at it is basically a 'statistical proof by contradiction': 1. Assume null hypothesis is true 2. Compute test statistic 3. Ask the question, "What is the probability of obtaining that test statistic or one more extreme?" (this probability is the p-value) 4. Pick a threshold (usually 0.05 but this is totally arbitrary) 5. If p < threshold then conclude the null hypothesis is false and reject it. Reductio ad statistico absurdum.
- astrec 13y agoIndeed. And any statistician worth their salt doesn't reject chance, they fail to reject the null hypothesis.