The statistical analysis of plant virus assays: a transformation to include lesion numbers with small means

Summary: The numbers of local lesions (x) produced by different leaves when inoculated with the same virus preparation deviate greatly from a normal distribution, and the standard errors of x's depend on their magnitude. Before customary statistical analyses are applicable to results of infectivity assays, x's must be suitably transformed. When mean values of x are greater than about 10, the transformation z = log10 (x + c) (where c is a constant), is satisfactory but inapplicable with smaller numbers. In some work the use of poorly infective inocula is unavoidable, and to allow statistical analysis of results in such work a new transformation z = log101/2 [x + c + √(x 2 + 2cx)] is derived. This operates satisfactorily when mean numbers of x are greater than about 1·5. The results of the two transformations converge as x increases. Values of z are tabulated to make the use of the new transformations as quick as that of the other transformation.