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 estimated 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 ratio statistics and derives their variances. The variances presented here should make it easier for users of these ratios statistics in large experiments, 100 or more units, to assess significance without going through a large number of rerandomizations. It also shows how these formulas can be used to evaluate power and the required sample sizes. Some illustrations from Israel and from Puglia, Italy, are given.