I have been asked to forward this to the list.
Please reply to the details given and not to me.
>I am struggling with the interpretation of the cutoff value in case of
>unequal sample sizes.
>
>Denote by z the linear discriminant function of Fisher for separating 2
>groups.
>Let z1 be the mean score of the first group and z2 the mean score of the
>second group.
>The standard (very simple) classification rule states than that an
>observation x0 is classified in group 1 if its score z0 is closer to z1
>than to z2 which is equivalent to comparing the score z0 with the
>cutoffvalue (z1+z2)/2...
>
>The problem is that some books (and also the SAS-software?) use another
>cutoff value in case the sample sizes are unequal:
>they compare z0 with (n1z1+n2z2)/(n1+n2)??!!
>This implies that if the first group is much larger than the second
>group (n1 >>n2) the cut-off value is shifted towards z1 and more group1
>observations will be classified in the second (smaller) group ???
>Wouldn't you expect more classifications into the larger group, not into
>the smaller group???
>
>Can anyone explain the logic of this approach or point out where my
>reasoning is incorrect?
>
>
>Thanks!
>Martina Vandebroek
[log in to unmask]
|