Auricle.txt

The table that follows compares the diagnostic accuracy of the 
electrocardiogram (ECG) in detecting abnormalities of the heart.  The data 
show both the diagnostic assessment and the results of postmortem 
examination of the heart in 122 individuals.  The deaths in these 
individuals occurred within three months of the diagnostic test, with an 
average of about two weeks.  [source: Bliss (1967) vol 1, p.  58, citing 
Kaufman, Scott and McGuire (1950).]

. tabi 28  14 \ 30 50, all

           | Postmortem pathology
ECG test   |         +          - |     Total
-----------+----------------------+----------
         + |        28         14 |        42 
         - |        30         50 |        80 
-----------+----------------------+----------
     Total |        58         64 |       122 

          Pearson chi2(1) =   9.3943   Pr = 0.002
 likelihood-ratio chi2(1) =   9.5154   Pr = 0.002
               Cramer's V =   0.2775
                    gamma =   0.5385  ASE = 0.142
          Kendall's tau-b =   0.2775  ASE = 0.087



Expected counts (under the hypothesis of no association):

   m11  =  (42)(58)/122 = 19.97
   m12  =  (42)(64)/122 = 22.03
   m21  =  (80)(58)/122 = 38.03
   m22 =   (80)(64)/122 = 41.97
   
   
Pearson X^2 =  [28-19.97]^2 / 19.97      =  64.48 / 19.97    =   3.23
              +[14-22.03]^2 / 22.03        +64.48 / 22.03      + 2.93
              +[30-38.03]^2 / 38.03        +64.48 / 38.03      + 1.70
              +[50-41.97]^2 / 41.97        +64.48 / 41.97      + 1.54
                                                                -----
                                                                 9.39
                                                                 
LR X^2 = G^2 =  2 x [ 28 log (28/19.97)       =  2 x [ 9.46
                     +14 log (14/22.03)              - 6.35
                     +30 log (30/38.03)              - 7.12
                     +50 log (50/41.97) ]            + 8.75 ]
                                                      -----
                                              =  2 x [ 4.74 ]  = 9.49