the concise encyclopedia of statistics (y. dodge)

[...]... Fellow of the Guggenheim Foundation between 1947 and 1948; Editor of the Annals of Mathematical Statistics from 1950 to 1952; President of the Institute of Mathematical Statistics in 1963; and Vice-President of the American Statistical Association from 1971 to 1973 He is a member of the American Academy of Arts and Sciences, of the National Academy of Sciences, of the Institute of Mathematical Statistics. .. Anderson, Theodore W Anderson, Theodore W Anderson, Theodore Wilbur was born on the 5th of June 1918 in Minneapolis, in the state of Minnesota in the USA He became a Doctor of Mathematics in 1945 at the University of Princeton, and in 1946 he became a member of the Department of Mathematical Statistics at the University of Columbia, where he was named Professor in 1956 In 1967, he was named Professor of Statistics. .. test to compare the mean of several popula- and defined as the quotient of the second esti2 tions This analysis also helps us to test mation of σ to the first) will be equal to 1 certain hypotheses concerning the param- The value of the F ratio, which is generally eters of the model, or to estimate the compo- more than 1 because of the variation from the nents of the variance The sources of vari- sampling,... The arithmetic mean was used by the astronomers to determine the positions of the sun, the moon and the planets According to Plackett (1958), the concept of the arithmetic mean originated from the Greek astronomer Hipparchus In 1755 Thomas Simpson of cially proposed the use of the arithmetic mean in a letter to the President of the Royal Society MATHEMATICAL ASPECTS Let x1 , x2 , , xn be a set of. .. analysis of variance, one- then entered the Faculty of Economics at way analysis of variance, linear multiple the Polytechnic Institute of St Petersburg, regression and simple linear regression where he studied mathematics, statistics and economics FURTHER READING The publications of Anderson, Oskar comDesign of experiments bine the traditions of the Continental School Factor of Statistics with the concepts... 1.533 0.937 distributions if the initial test rejects the null hypothesis for the distribution of a random We then get A2 ∼ 0.436, which gives = variable EXAMPLES The following data illustrate the application of the Anderson–Darling test for the normality hypothesis: Consider a sample of the heights (in cm) of 25 male students The following table shows the observations in the sample, and also wi and... test the precision • H1 : θ1 = θ2 or H1 : θ1 − θ2 = 0 of a new machine that should make bolts During the comparison of more than two 8 mm in diameter populations, the null hypothesis supposes We can use the following null hypothethat the values of all of the parameters are sis: identical If we want to compare k populaH0 : μ = 8 , tions, the null hypothesis is the following: where μ is the mean of the. .. i=1 E [¯ ] = μ x i=1 Proof: We can write: xi − a = (xi − x) + (¯ − a) ¯ x Finding the squares of both members of the equality, summarizing them and then simplifying gives: is still valid, but the variance of x must be ¯ adjusted by a factor that depends on the size N of the population and the size n of the sample: Var (¯ ) = x N−n σ2 · n N−1 , where σ 2 is the variance of the population n (xi − a)2... year, see the examples under the entries for incidence rate, prevalence rate) and the incidence rate of the nonexposed group (57.0/100000 per year) The risk of breast cancer attributable to smoking in the population (PAR) is the ratio of the number of the cases of breast cancer attributable to exposure to tobacco and the number of cases of breast cancer diag- A 24 Autocorrelation nosed in the population... test the validity of the statistical model and to control the assumptions made on the error term It may be used also for outlier detection HISTORY MATHEMATICAL ASPECTS The analysis of residuals dates back to Euler See goodness -of- fit and contingency table (1749) and Mayer (1750) in the middle of A 6 Analysis of Residuals the eighteenth century, who were confronted with the problem of the estimation of . w1 h0" alt="" The Concise Encyclopedia of Statistics Yadolah Dodge The Concise Encyclopedia of Statistics With 247 Tables 1 3 Author Yadolah Dodge Honorary Professor University of Neuchâtel Switzerland yadolah.dodge@uninc.ch A. corresponds to the mean of the variances of each sample; • The second, s 2 Tr , is based on the variation between the means of the samples. Ideally, if the null hypothesis is verified, thesetwoestimationswill. Petersburg, where he studied mathematics, statistics and economics. The publications of Anderson, Oskar com- bine the traditionsof the Continental School of Statistics with the concepts of the English Biometric