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Logarithmic Transformation is Essential for Statistical Analysis of Fungicide EC50 Values
Author(s) -
Liang HongJie,
Li JinLi,
Di YaLi,
Zhang AnSheng,
Zhu FuXing
Publication year - 2015
Publication title -
journal of phytopathology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.53
H-Index - 60
eISSN - 1439-0434
pISSN - 0931-1785
DOI - 10.1111/jph.12342
Subject(s) - logarithm , statistics , mathematics , homogeneity (statistics) , transformation (genetics) , sclerotinia sclerotiorum , biology , analysis of variance , multiplicative function , standard deviation , botany , genetics , mathematical analysis , gene
Half maximal (50%) effective concentration ( EC 50) values are widely used to express fungicide potency and sensitivity of plant pathogens. This study explored the necessity of logarithmic transformation for statistical analysis of EC 50 values. The results demonstrated that without logarithmic transformation, none of the five sets of epoxiconazole EC 50 data ( n = 26–33) against Sclerotinia sclerotiorum fitted a normal distribution. But after logarithmic transformation, four of the five datasets became normally distributed. Of the five sets of pyraclostrobin EC 50 data ( n = 29–32), only one dataset fitted a normal distribution. After logarithmic transformation, four datasets became normally distributed. Logarithmic transformation transformed the heterogeneity of variance across the five sets of epoxiconazole EC 50 data to homogeneity but failed to improve the heterogeneity of variance across the five sets of pyraclostrobin EC 50 data. For 150 isolates' EC 50 values to epoxiconazole and 153 isolates' EC 50 values to pyraclostrobin, the intervals of arithmetic means ± standard deviations ( SD ) covered 85.3% and 90.2% of data points, respectively, whereas the intervals of geometric means (X *) multiplied/divided by the multiplicative SD (S*) covered 69.3% and 70.9% of data points, respectively, which approximated the theoretical value of 68.3%. Distribution normality and homogeneity of variance are prerequisites for analysis of variance ( anova ) and the two parameters could be improved by logarithmic transformation, therefore, power and efficiency of statistical tests on EC 50 data will be greatly enhanced by this kind of transformation.