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> 1. p-values are intrinsically none-too-intuitive P-values are quite intuitive. They are the ratio of observations made which agree with the null hypothesis t
by jsprogrammer 11y ago
> 1. p-values are intrinsically none-too-intuitive
P-values are quite intuitive. They are the ratio of observations made which agree with the null hypothesis to the total number of observations made.
Edit: If you are going to downmod, at least point out the error you perceive.
- nickpsecurity 11y agoThat was as intuitive as the seemless connection between the Magic Bullet Theory and Ballistics.
- jsprogrammer 11y agoIt comes directly from the calculation of p-values through probability theory.
- omginternets 11y agoI'm reminded of a joke about how Haskell empowers you to apply the infinite power of abstract mathematics using the intuitive simplicity of abstract mathematics. I think the resistance you're encountering stems from the fact that you're appealing to formality rather than intuition.
- senekerim 11y agoAlso from the fact that he doesn't know what he's talking about.
- jsprogrammer 11y agoYou talking about me?
- jsprogrammer 11y agoCounting positive observations vs. total observations is a formality rather than intuition? The formality is the axioms of probability. The intuition is that you make a theory and measure how many predictions it gets right.
- omginternets 11y agoIt's all relative, as they say.
- deleted 11y ago[deleted]
- evanpw 11y agoIt doesn't make sense to say in a binary sense that an observation agrees or disagrees with the null hypothesis, there are only probabilities. The p-value is the probability of seeing a set of values as extreme as your actual observations, assuming that the null hypothesis is true.
- jsprogrammer 11y ago>It doesn't make sense to say... That depends on your hypothesis. >The p-value is the probability of seeing a set of values That is a circular definition. What is, "probability"? P-values are not prescriptive statements about future observations, but are descriptions of actual observations.
- evanpw 11y agoAs TeMPOraL points out, you seem to be defining probability in general. The p-value is a very specific concept in statistics, not an abbreviation for "probability value" (https://en.wikipedia.org/wiki/P-value https://en.wikipedia.org/wiki/P-value).
- jsprogrammer 11y agoYour link defines p-value as a probability. >More specifically, the p-value is defined as the probability of... Edit: A good exercise would be to start with the axioms[0] of probability theory and then derive the p-value for a simple experiment, using only those axioms (and your measured values). [0] https://en.wikipedia.org/wiki/Probability_axioms https://en.wikipedia.org/wiki/Probability_axioms
- deleted 11y ago[deleted]
- evanpw 11y agoExample: The null hypothesis is that X has a standard normal distribution, and you have one observation, with value 0.7. Since you only have one observation, your definition of p-value can only give the values 0 or 1, depending on whether you consider 0.7 to agree or disagree with the null hypothesis. The actual answer is 0.2419637 (or double that, depending on whether you do a one-tailed or two-tailed test), the probability of drawing a value >= 0.7 from a standard normal distribution (you can get this value by computing an integral on the density function of the standard normal).
- kgwgk 11y ago> P-values are quite intuitive. Do you agree now that if the null hypothesis is true the p-value is uniformly distributed between 0 and 1? Or do you still think that "if that were true, p-value would be entirely useless"? In any case, you were completely wrong about p-values a few months ago; maybe they are not so intuitive after all. https://news.ycombinator.com/item?id=10156510 https://news.ycombinator.com/item?id=10156510
- jsprogrammer 11y agoWhere was I wrong? >Do you agree now that if the null hypothesis is true the p-value is uniformly distributed between 0 and 1? If the null hypothesis is true, the p-value will converge to 1. (This makes complete intuitive sense as well, if you hypothesis is true, every observation you make should/will agree with it, making the ratio of agreeable_observations:total_observations = 1.) You haven't shown anything where a true null hypothesis uniformly generates p-values between 0 and 1. Perhaps for a single observation you can only get a 0 or 1 value, and, perhaps for a over/under the average test (where every experiment will give 0 or 1) your sequence of p-values for each observation would be uniformly distributed, but p-values are generally computed as a normalized sum over many observations, in which case the value should converge to 1 if the null hypothesis is true. One unintuitive aspect is that you might expect p-value to converge to 0 if the null hypothesis is false, however p-value is undefined when the null hypothesis is false.
- kgwgk 11y agoOk, I see you still have your very own definition of "p-value". I just thought it was useful to make clear to the audience that your "p-values" are not the same "p-values" being discussed here. Edit: Probably you don't care, but for the record: "Since the value of x that defines the left tail or right tail event is a random variable, this makes the p-value a function of x and a random variable in itself defined uniformly over [0,1] interval, assuming x is continuous." [ https://en.wikipedia.org/wiki/P-value https://en.wikipedia.org/wiki/P-value ] "In statistics, when a p-value is used as a test statistic for a simple null hypothesis, and the distribution of the test statistic is continuous, then the p-value is uniformly distributed between 0 and 1 if the null hypothesis is true." [ https://en.wikipedia.org/wiki/Uniform_distribution_(continuous) https://en.wikipedia.org/wiki/Uniform_distribution_(continuo... ]