SummaryThe first two randomization moments of W = Tt.S. S./(Tt.S.S. + Error S.S.) are derived in case of (a) a completely randomized design with one observation missing using (I) Yates method of fitting constants and (11) the available observations only and in case of (b) a randomized block design in which one treatment is tested twice by mistake in a block and another treatment is not tested at all in that block using (I) all the available observations and (11) the data after deleting the observation due to the treatment tested by mistake in place of another treatment in a block.It is concluded that in each of the two cases for a completely randomized design, the F-test is unbiased whereas in each of the two cases for a randomized block design the F-test is in general not unbiased. However, if one treatment is tested twice by mistake in randomly chosen plots of some block, the F-test is unbiased in both cases for a randomized block design.For a completely randomized design the F-test is found to be a good approximation to the corresponding randomized test if N 2 80 in case (I) whereas in case (11) this approximation is of the same accuracy as that of case (I) if N 2 90. For a randomized block design it is seen that in case (I), the F-test provides a good approximation to the corresponding randomization test if u 2 r 2 7 and in case (11) this approximation is of the same accuracy if r 2 6 and r ( u -1) 2 45.The analysis of several uniformity trial .data shows that for values of "N" in the neighbourhood of 50 the agreement of the first two moments of "W" under the randomization theory and normal theory are reasonably close in all the four cases considered.