LOGRITHMIC TRANSFORMATION: A TOOL FOR NORMALIZING RESIDUALS IN ANOVA MODELS

This study investigates the statistical significance of the difference in cost of production of potato, tomato and cauliflower in district Mansehra, Pakistan by using linear and semi-logarithm ANOVA models. The linear model suggests that the average cost of production of potato per acre is Rs. 23460 while that of tomato and cauliflower is Rs. 3284.8 more and Rs. 3188 less than that of potato. These differences are statistically significant. The semilogarithm model indicates that the median cost of production per acre of potato, tomato and cauliflower is Rs.22471.4, Rs. 26135.2 and Rs. 19920.8 respectively. The estimated semielasticities reveal that the median cost of production of tomato and cauliflower is 16.3% more and 11.35% less than that of potato respectively. The difference in cost of production between potato and tomato is statistically significant (P 0.05) while that between potato and cauliflower is insignificant (P 0.05) -based upon the results of the log model. Various normality tests show that the residuals are normally distributed in the semi-log model which is not the case in linear model suggesting that log transformation is an effective technique for normalization of residuals. The non normal distribution of residuals in the linear model undermines the validity of t and F statistics and thus the hypothesis testing can potentially be misleading, especially in small samples. However in the log transformed model t and F statistics can be used with confidence for hypothesis testing.