By Ralph B. D'Agostino, Michael A. Stephens

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The first (Figure 2 . 5a) is a plot of the first ten observations of the NOR data set. 42. The second ecdf (F igure 2 . 42, replaced by an outlier equal to 140. This example is an exaggeration GRAPHICAL ANALYSIS 15 of what usually happens in practice, but it illustrates w e ll the type of con figuration that results in an ecdf plot of a sym m etric distribution such as the normal distribution when an outlier o r outliers a re present. 3 b). W e w ill illustrate later in this chapter the use of the probability plotting technique for detecting outliers.

947. The fit o f these data to a straight line obviously leaves much to be desired. In addition to the use of program s as described above to do probability plotting, many standard software packages ( e . g . , SAS) have specific routines for probability plotting. These should be used when available. 19) where G "^(*) is the inverse transformation of the standardized distribution of the population (hypothesized distribution) under consideration. W e recom mend for Fjj(X^i)) ^n("(i)> = Pi = ( 2 .

From these we estimate ii = 99 and a = 17. 2 O th erP ro ced u res A second procedure fo r obtaining the line and estimates is to recognize that from (2 . 16) and estimates of and a can be obtained by using unweighted least squares (sim ple linear re g re ssio n ). The general solution for these are ^ Z (z - z)x ,-4 ^S ( Z - Z ) Z and Í. 70. 14), is to use x and s, the sample mean and standard deviation, as estim ates. 67. Notice fo r the LOG data there are very little d iffer ences among the results of these different procedures.