The Application of Certain Statistical Criteria to the Problem of Seedling Mortality.

Abstract

The practically important problem of obtaining an adequate crop stand on the agricultural field must depend for its solution on the detailed investigation of a number of factors, physical, chemical, physiological and pathological. While the end purpose of such investigations may be in part practical, they have their bearing upon a number of general biological questions, for example that of the existence of a selective death rate. 1 In suggesting the applicability of certain statistical methods, which, as far as I am aware, have not heretofore been applied to these problems, I have in mind the probability that they will be useful in other investigations involving the problem of mortality.

Problem 1. A criterion of the deviation from a random distribution of an observed distribution of number of seedlings produced.

Lets be the number of seeds planted, g be the number of seeds germinating or surviving to a given stage, f the number of seeds failing to germinate or dying at an early stage, in a large number, N, of small experiments. Then if p be the probability of development of the seed into a seedling, and q be the probability of its failing to develop or of its dying before any given period

where ∑ denotes summation throughout the number, N, of experimental plantings and the bars denote means of g and f.

If the frequency distribution of the number of germinations per experiment (e.g., per hill) were determined solely by chance it should should be given by N (p + q)^s. The agreement of the theoretical and empirical distributions may be tested by Pearson's χ² criterion, 2 using Elderton's 3 table for testing goodness of fit.