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 formula_16 (left-tail event) or the "smaller" of formula_17 and formula_15 (double-tailed event). Thus, the "p"-value is given by The smaller the "p"-value, the higher the significance because it tells the investigator that the hypothesis under consideration may not adequately explain the observation. The null hypothesis formula_4 is rejected if any of these probabilities is less than or equal to a small, fixed but arbitrarily pre-defined threshold value formula_23, which is referred to as the level of significance. Unlike the "p"-value, the formula_23 level is not derived from any observational data and does not depend on the underlying hypothesis; the value