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Chapter 7. Hypothesis Testing > 7.1 Proof by Statistical Contradiction - Pg. 190

190 Chapter 7 You will see how to do these statistical tests and interpret the results. You will learn not only how to do tests correctly, but also how to recognize tests that are misleading. 7.1 Proof by Statistical Contradiction Statistical tests are based on empirical data--ideally a random sample. These tests can never be as definitive as a mathematical or logical proof because a random sample is, well, random and therefore subject to sampling error. One random sample will yield one set of data and another sample will yield different data. There is always a chance, however small, that a new sample reverses a conclusion based on an earlier sample. We cannot be absolutely certain of the average looseness coefficient of all players unless we look at all players. Most theories are vulnerable to reassessment because there never is a final tabulation of all possible data. New experiments and fresh observations continually provide new evidence-- data that generally reaffirm previous studies but occasionally create doubt or even reverse conclusions that were once thought firmly established. Theories are especially fragile in the humanities and social sciences because it is difficult to control for extraneous influences. In the 1930s, John Maynard Keynes theorized that there was a very simple relationship between household income and consumer spending. This theory was seemingly confirmed