A Statistical Inquiry into Methods for Estimating Numbers of Rhizobia

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Abstract
Plate counts of Rhizobia are very erratic unless especial care is taken to maintain a standardized technique. Even if the latter is made uniform, variability among individual plates is often larger than that attributable to random sampling. In such cases, abnormal variability usually results from one plate in a series, rather than from uniform variation among replicates. This variability can be partially eliminated by increase in number of parallel plates. Also, if 3 or more plates are made in parallel, elimination of any 1 plate that is markedly different from its replicates can be made without bias. Sets of 3 and 4 plate data examined after elimination of any plate decidedly at variance with its replicates, indicated that variations noted in the remaining plates could have arisen by chance alone. The cause of this abnormal variation was not investigated, but other exps. and observations indicated that (1) stages in the life-cycle and (2) unique growth-initiation requirements of individual cells or stages, especially in regard to the oxidation-reduction character of the medium, may be factors involved. In any study requiring a viable count, use of as many parallel plates as possible without introducing an undue time factor is desirable. In all cases, at least 3 replicates are advisable. Direct counts of Rhizobia by a Petroff-Hausser counting chamber can be made under laboratory conditions in such a manner that the variance is that due to chance alone. In this case, distribution of cells per unit area follows the Poissan Exponential Summation, and accuracy of count will be dependent solely on total number of organisms counted. Standard deviation of such a count is equal to m1/2, and standard deviation of the mean= (m/N)1/2, where m is the mean number of organisms per unit area, and N is the total squares counted. Direct count with the Petroff-Hausser or similar counting chambers proved to be the most accurate of all methods investigated and its use whenever possible is advised.