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 heads and is a two-tailed test. Suppose the researcher observes heads for each flip, yielding a test statistic of "n" and a "p"-value of 2/2. If the coin was flipped only 5 times, the "p"-value would be 2/32 = 0.0625, which is not significant at the 0.05 level. But if the coin was flipped 10 times, the "p"-value would be 2/1024 ≈ 0.002, which is significant at the 0.05 level. In both cases the data suggest that the null hypothesis is false (that is, the coin is not fair somehow), but changing the sample size changes the "p"-value. In