Premium
THE TRANSFORMATION OF LOCAL LESION COUNTS FOR STATISTICAL ANALYSIS
Author(s) -
KLECZKOWSKI A.
Publication year - 1949
Publication title -
annals of applied biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.677
H-Index - 80
eISSN - 1744-7348
pISSN - 0003-4746
DOI - 10.1111/j.1744-7348.1949.tb06404.x
Subject(s) - kurtosis , transformation (genetics) , standard deviation , biology , statistics , logarithm , mathematics , skewness , normal distribution , distribution (mathematics) , skew , constant (computer programming) , statistical analysis , variance (accounting) , value (mathematics) , biological system , botany , mathematical analysis , computer science , telecommunications , accounting , gene , business , biochemistry , programming language
An analysis of the frequency distribution of local lesions, produced by viruses on half‐leaves of a number of plants, shows that their standard error increases with increasing mean. Hence analysis of variance and statistical tests of significance should not be applied to lesion numbers unless they are suitably transformed. The transformation into logarithms over‐corrects so that the standard error decreases with increasing mean. A satisfactory transformation is y = log 10 ( x + c ), where x is the number of lesions and c is a constant. A method is given of assessing c for different experiments. Great accuracy is not needed; in an experiment discussed in detail a satisfactory transformation is obtained with any value for c between 15 and 80. On individual plants the numbers of lesions formed on half‐leaves are distributed more or less normally, whereas their distribution about the common mean for many plants is skew and ‘leptokurtic’. The distribution of the transformed numbers is almost normal, both for individual plants and about the common mean for a number of plants.