Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

the binary problems, when the choice is restricted to two modes. It
appears that the classification can be done rather successfully in many
cases. However, when rail and truck shipments are compared, a fair
percentage of origins which actually use truck would be mis-allocated.
Table VII gives the probabilities that an origin will be
correctly assigned to the mode it uses as against the two other modes.
They have been computed according to equation (18) of Chapter II. The
probabilities of correct overall classification are not quite as good
as the probabilities of correct binary classification. It could not be
otherwise. The application of a second classification rule to the same
set of observations can only reduce the number of origins correctly ,
classified.
Let us note that the discounting of the net prices contributed
•
to a reduction of the distance between the 5. and rc involved in each
. ij
binary problem, thereby decreasing the probabilities of correct classification. (11
It is now appropriate to examine the assumptions, made in
Chapter II, that the X's normally distributed can be safely used. To
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test if the parent distributions of the X1 .'s sample distributions were
3
normally distributed, Chi-square tests were made for each of the X.. over
the month of January sample. The results were as follows: two of the tests
sustained the hypothesis of normality at the .10 and .50 level of significance
respectively. The four other tests rejected the hypothesis at the .05 level
of significance. When plotted, these four sample distributions were shown
to have tails but otherwise were either irregular or closer to some Chi-
square distributions. As no general pattern of distribution appeared through
that examination, it does not seem that one could find a distribution which
could fit the six samples.
(1) Because only a few days time is involved, the reduction due to
discounting is small.
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