Read e-book online Seminaire de Probabilites. Universite de Strasbourg, PDF

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Additional info for Seminaire de Probabilites. Universite de Strasbourg, Novembre 1966 - Fevrier 1967

Sample text

The first contained three illustrations where estimation was not required, while the next had five illustrations where estimation was required. The paper finished with a brief conclusion. Of the illustrations Cochran (1952, p. 319) notes that two of them serve to poke fun at Sir George Airy and Professor Merriman. These two authors presented data sets which they claimed to be normally distributed. Of course, prior to Pearson’s test the claim could only be assessed subjectively. Pearson showed that both data sets were far from normal.

Nevertheless some users will prefer to use an X2 test under these circumstances, perhaps because X2 tests are familiar, available in a computer package, or convenient in that it may be easy to calculate the test statistic and this test statistic has a conveniently tabulated null distribution. 20 Smooth Tests of Goodness of Fit If an X2 test is to be used, then the cells or classes must be constructed. As, for example, Kempthorne (1967) has pointed out, different conclusions may be reached if different constructions are used.

2 , As n increases, the distribution of XP2 tends to be increasingly well approximated by χm−1 the chi squared distribution with m − 1 degrees of freedom. If the distribution specified by the null hypothesis is continuous, then a goodness of fit test appropriate for continuous data could be used, as there is presumably some loss of power in ignoring some of the information and categorizing the data. We discuss several tests appropriate for continuous data in later chapters. Nevertheless some users will prefer to use an X2 test under these circumstances, perhaps because X2 tests are familiar, available in a computer package, or convenient in that it may be easy to calculate the test statistic and this test statistic has a conveniently tabulated null distribution.

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