In this paper the first two moments of the ratio (treatment sum of squares)/(treatment sum of squares + error sum of squares) over all possible random assignment of treatments to the experimental plots, for a class of 2 associate PBIBD has been obtained. These two monemts are compared with the corresponding moments of a continuous beta distribution to settle the question of approximating the randomization test by the usualF-test. It has been shown that a reasonable approximation to the randomization test based on the statisticFis equivalent to modifying the normal theory test by multiplying the numbers of d.f. of theF-distribution by a factor depending on the heterogeneity of the blocks.