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
P-value of formula_23 is instead set by the researcher before examining the data. The setting of formula_23 is arbitrary. By convention, formula_23 is commonly set to 0.05, 0.01, 0.005, or 0.001. Since the value of formula_7 that defines the left tail or right tail event is a random variable, this makes the "p"-value a function of formula_7 and a random variable in itself; under the null hypothesis, the "p"-value is defined uniformly over formula_30 interval, assuming formula_7 is continuous. Thus, the "p"-value is not fixed. This implies that "p"-value cannot be given a frequency counting interpretation since the probability has to