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Astronomy, Brewing, the Probable Error, and the .05 Criterion of Statistical Significance One of the articles on your reading list is: Cowles, M., & Davis, C. (1982). On the origins of the .05 level of statistical significance. American Psychologist, 37, 553-558. Here are three key paragraphs from that article William Gosset (who wrote under the pen name of "Student") began his employment with the Guinness Brewery in Dublin in 1899. Scientific methods were just starting to be applied to the brewing industry. Among Gosset's tasks was the supervision of what were essentially quality control experiments. The necessity of using small samples, meant that his results were, at best, only approximations to the probability values derived from the normal curve. Therefore the circumstances of his work led Gosset to formulate the small-sample distribution that is called the t distribution. With respect to the determination of a level of significance, Student's (1908) article, in which he published his derivation of the t test, stated that "three times the probable error in the normal curve, for most purposes, would be considered significant" (p. 13). A few years later, another important article was published under the joint authorship of an agronomist and an astronomer (Wood & Stratton, 1910). This paper was essentially to provide direction in the use of probability in interpreting experimental results. These authors endorse the use of PE as a measure: "The astronomer . . . has devised a method of estimating the accuracy of his averages . . . the agriculturist cannot do better than follow his example" (p. 425). They recommend "taking 30 to 1 as the lowest odds which can be accepted as giving practical certainty that a difference is significant" (p. 433). Such odds applied to the normal probability curve correspond to a difference from the mean of 3.2 PE (for practical purposes this was probably rounded to 3 PE). You already know that if you go out one PE in each direction from the mean of a normal distribution you mark off the middle 50% of the distribution. You also know that if you go out about 2/3 of a standard deviation in each direction from the mean you mark off the middle 50% of a normal distribution. Accordingly, one PE is equivalent to about 2/3 of a PE, and 3 PE is equivalent to about 2 standard deviations. If you go out about two standard deviations from the mean in a normal distribution, you have marked off about the middle 95%, leaving about 5% in the tails, the “rejection region” for the traditional .05 criterion of statistical significance. Another reason we might feel comfortable with the .05 criterion is that we have five fingers on each hand. My reasoning here is the same I employ when I argue that the reason we usually use a base-ten number system is that we have ten fingers with which to count. If we had 12 fingers we would have probably ended up using a basetwelve number system. Karl L. Wuensch, August, 2010.