Logarithmic Transformation is Essential for Statistical Analysis of Fungicide EC50 Values. Issue 6 (11th November 2014) - Liang, Hong‐Jie
Abstract: Half maximal (50%) effective concentration (EC50) 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 EC50 values. The results demonstrated that without logarithmic transformation, none of the five sets of epoxiconazole EC50 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 EC50 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 EC50 data to homogeneity but failed to improve the heterogeneity of variance across the five sets of pyraclostrobin EC50 data. For 150 isolates' EC50 values to epoxiconazole and 153 isolates' EC50 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 EC50 data will be greatly enhanced by this kind of transformation.