Page 175 - Six Sigma Advanced Tools for Black Belts and Master Black Belts
P. 175

OTE/SPH
 OTE/SPH
                               Char Count= 0
         August 31, 2006
 JWBK119-11
        160              2:57  Goodness-of-Fit Tests for Normality
        Table 11.4 Critical values of EDF based statistics (Kolmogorov--Smirnov, Anderson--Darling
        and Cram´er--von Mises).
             (a) Critical values of D statistic (case where F 0 (x) completely specified and mean
                             specified, variance unknown)

                      F 0 (x) completely specified  Mean specified, variance unknown
                      (from exact distribution) 6  (based on Monte Carlo simulation) 15
        Sample
         size, n     α = 5%         α = 10 %         α = 5%            α = 10 %
             5         0.565         0.510             --                  --
            10         0.41          0.368            0.402              0.360
            15         0.338         0.304             --                  --
            20         0.294         0.264            0.288              0.259
            25         0.27          0.240             --                  --
            30         0.24          0.220             --                  --
            35         0.23          0.210             --                  --
                    ⎫              ⎫
            50                                        0.185              0.165
                          √              √
                    ⎬              ⎬
           100        1.36/ n        1.22/ n          0.132              0.118
                                                          √                   √
          >100      ⎭              ⎭                  1.333/ n           1.190/ n
                              2
                                    2
           (b) Critical values for A and W statistics for Anderson--Darling and Cram´er--von Mises
                                         GOF test (n ≥ 5) 15
                                 Case when F 0 (x) completely specified
                                                                           2
                                                Critical values Modified W* and A statistic
                        Modifications           α = 5%            α = 10 %

                                  2
                    2
        W 2  W* = (W − 0.4/n + 0.6/n )(1.0 + 1.0/n)  0.461         0.347
        A 2                  --                  2.492             1.933
                                                                 2           2
           Case when mean specified, variance unknown and estimated from s =  (x i − μ) /n
                                                                      i
                 Critical values at α level of significance
                 α = 5%            α = 10 %

        W 2       0.443              0.329
        A 2       2.323             1.76




        absolute differences where the null hypothesis can be retained at the 5% level of sig-
        nificance is shown in Figure 11.1 as well. This ‘acceptance’band is computed from the
        critical values for the absolute difference based on equation (11.4). The critical values
        d α are given by Barnes and Murdoch. 14  The critical values for the case where F 0 (x)
        is completely specified and the case where the mean is specified and the variance
        unknown given in Table 11.4(a). 6,15
   170   171   172   173   174   175   176   177   178   179   180