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Let Ω = R (real line), F = the set of Lebesque-measurable subsets of R, and P(E) = the integral over E of the density function of the standard normal. This is a
by evanpw 11y ago
Let Ω = R (real line), F = the set of Lebesque-measurable subsets of R, and P(E) = the integral over E of the density function of the standard normal. This is a probability space in the Kolmogorov sense, and my previous example carries through perfectly well in this framework. You observe x = 0.7, and compute the probability of the event X >= 0.7 as an integral. There are no ratios, and you don't need to label the observation as agreeing or disagreeing with the null hypothesis.
- jsprogrammer 11y agoSee my response here: https://news.ycombinator.com/item?id=10630389 https://news.ycombinator.com/item?id=10630389 You are doing it wrong. A p-value based on a single observation is meaningless. P-values are much more useful when they are continuously computed on a running experiment with sequential observations. See the work at the LHC for an example.