Suppose I am testing two drugs, I and II. The response profile is either I > II, I < II or I = II. I was trying to figure out if I is in fact better than II.

One way I thought of was to throw out all the ties (I == II), and then assign a 1 where I > II and a 0 where I < II. Then this boils down to a binomial distribution (which I can approximate with the normal).

But I was wondering if throwing away the ties is really appropriate... If I don't throw away ties, I can't use the binomial distribution (so would I switch to some multinomial test)?

The other thing I can think of is some wilcoxon rank sum test or mann whitney u test with ties... but I was wondering if anyone else has an idea? The concern here is that there will be a LOT of ties...

Thanks!