By G. A. Barnard (auth.), Samuel Kotz, Norman L. Johnson (eds.)
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Additional resources for Breakthroughs in Statistics: Methodology and Distribution
3. Starting with Student's own paper, questions were raised regarding the effect of violation of the model assumptions. The resulting investigations of these effects on the t-test have spearheaded and motivated the subject of robustness that has played a central role in statistical practice and theory during the last 50 years. The history of the t-test described in this introduction illustrates a surprisingly common pattern of discovery. A first scientist, dealing with a very specific situation, introduces a new idea either in the formulation of the problem or its solution.
III. The equation is determined of the curve representing the frequency distribution of a quantity z, which is obtained by dividing the distance between the mean of a sample and the mean of the population by the standard deviation of the sample. IV. The curve found in I. is discussed. V. The curve found in III. is discussed. 35 The Probable Error of a Mean VI. The two curves are compared with some actual distributions. VII. Tables of the curves found in III. are given for samples of different size.
L. Lehmann A crucial feature of the above approach is to act as if S2/(n - 1) were a constant (the true value of (J2) rather than a random variable. However, ifthe sample size n is small, S2 will be subject to considerable variation. S. Gosset, a chemist working for Guiness breweries. * He pointed out that if the form of the distribution of the X's is known, this variation can be taken into account since for any given n, the distribution of t is then determined exactly. He proposed to work out this distribution for the case in which the X's are normal.