P-value that had only 6 cups been presented (3 of each), a perfect classification would have only yielded a "p"-value of formula_38 which would not have met this level of significance. Fisher also underlined the interpretation of "p," as the long-run proportion of values at least as extreme as the data, assuming the null hypothesis is true. In later editions, Fisher explicitly contrasted the use of the "p"-value for statistical inference in science with the Neyman–Pearson method, which he terms "Acceptance Procedures". Fisher emphasizes that while fixed levels such as 5%, 2%, and 1% are convenient, the exact "p"-value can be
Generalized p-value the problem is not trivial with conventional "p"-values, the task can be easily accomplished based on the generalized test variable where formula_9 is the observed value of formula_3 and formula_11 is the observed value of formula_12. Note that the distribution of formula_13 and its observed value are both free of nuisance parameters. Therefore, a test of a hypothesis with a one-sided alternative such as formula_14 can be based on the generalized "p"-value formula_15, a quantity that can be easily evaluated via Monte Carlo simulation or using the non-central t-distribution. Generalized p-value In statistics, a generalized "p"-value is an extended version