Ratio statistics for randomized experiments in precipitation stimulation

A variety of ratio statistics has been used in the design and evaluation of weather modification experiments and their significance has usually been e stimated by rerandomization. These ratios, and especially their logarithms, are asymptotically normal with null expectations and variances that can be readily calculated. This paper reviews and generalizes several useful rati o statistics and derives their variances. The variances presented here shou ld make it easier for users of these ratios statistics in large experiments , 100 or more units, to assess significance without going through a large n umber of rerandomizations. It also shows how these formulas can be used to evaluate power and the required sample sizes. Some illustrations from Israe l and from Puglia, Italy, are given.