How to compute the global precision given the precision calculated for each class? Is it just the average over classes precisions? When I use Weka the global precision is not computed as the average one, but as a "weighted average" and I don't know how this later is computed (weighted by what?). See the example bellow of the results that we get with Weka, can you please tell me how "Weighted Avg." is computed in this result (last line)?
Correctly Classified Instances 608 93.5385 %
Incorrectly Classified Instances 42 6.4615 %
Total Number of Instances 650
=== Detailed Accuracy By Class ===
TP Rate FP Rate Precision Recall F-Measure ROC Area Class
0.889 0.005 0.727 0.889 0.8 0.995 APP05179028
0.991 0.032 0.866 0.991 0.924 0.999 APP05179007
0.633 0.005 0.864 0.633 0.731 0.989 APP05179012
0 0 0 0 0 0.954 APP05179014
0.972 0.013 0.936 0.972 0.954 0.998 APP05179010
0.957 0.002 0.957 0.957 0.957 0.999 APP05179009
0 0 0 0 0 ? APP05179018
0.6 0 1 0.6 0.75 0.988 APP05179027
0 0 0 0 0 ? APP05179023
1 0.002 0.75 1 0.857 1 APP05179025
0.8 0 1 0.8 0.889 0.991 APP05179016
0 0 0 0 0 ? APP05179021
0.889 0 1 0.889 0.941 1 APP05179029
0.918 0 1 0.918 0.957 1 APP05179020
0 0 0 0 0 0.958 APP05179022
1 0.002 0.963 1 0.981 0.999 APP05179015
0.846 0 1 0.846 0.917 0.998 APP05179008
0.992 0.002 0.992 0.992 0.992 1 APP05179011
0.947 0.002 0.973 0.947 0.96 1 APP05179013
1 0 1 1 1 1 APP05179026
0.857 0 1 0.857 0.923 1 APP05179019
0.714 0.011 0.417 0.714 0.526 0.952 APP05179017
0.969 0 1 0.969 0.984 1 APP05179030
1 0 1 1 1 1 APP05179024
0.935 0.008 0.939 0.935 0.933 0.998 **Weighted Avg.**
a b c d e f g h i j k l m n o p q r s t u v w x
8 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | a = APP05179028
0 110 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | b = APP05179007
0 9 19 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | c = APP05179012
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 | d = APP05179014
0 3 0 0 103 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | e = APP05179010
0 1 0 0 0 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | f = APP05179009
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | g = APP05179018
3 0 0 0 0 0 0 6 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | h = APP05179027
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | i = APP05179023
0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | j = APP05179025
0 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | k = APP05179016
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | l = APP05179021
0 0 0 0 0 0 0 0 0 0 0 0 32 0 0 0 0 0 0 0 0 4 0 0 | m = APP05179029
0 1 0 0 0 1 0 0 0 0 0 0 0 45 0 0 0 0 0 0 0 2 0 0 | n = APP05179020
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | o = APP05179022
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 26 0 0 0 0 0 0 0 0 | p = APP05179015
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 1 0 0 | q = APP05179008
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 126 0 0 0 0 0 0 | r = APP05179011
0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 36 0 0 0 0 0 | s = APP05179013
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 | t = APP05179026
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 | u = APP05179019
0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 | v = APP05179017
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 31 0 | w = APP05179030
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 | x = APP05179024