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 is biased towards heads or tails. By the first test statistic, the data yield a high "p"-value, suggesting that the number of heads observed is not unlikely. By the second test statistic, the data yield a low "p"-value, suggesting that the pattern of flips observed is very, very unlikely. There is no "alternative hypothesis" (so only rejection of the null hypothesis is possible) and such data could have many causes. The data may instead be forged, or the coin may be flipped by a magician who intentionally alternated outcomes. This example demonstrates that the "p"-value depends completely on the test