Comparison of Transformations used in the Analysis of Data From Agricultural Experiments - PriyaMenon K (Department of Agricultural Statistics, College of Horticulture, 1997)
A study was undertaken to empirically examine the suitability of the various commonly used transformation techniques on the analysis enumerative data relating to agricultural experiments or surveys. The possibility of evolving better transformations for the analysis of data pertaining to certain specific environments was also explored. Data for the study were gathered from the available records of the project on pest surveillance survey on paddy, those on the project on early stage pest control on paddy of Regional Agricultural Research Station, Pattambi and those of the post emergence herbicidal evaluation trial for the control of Pennisetum pedicel/atum of the All India Co-ordinated Research Project on Weed Control, College of Horticulture, Vellanikkara. Comparisons among the various commonly used transformations were made either on the basis of a single criterion viz., Bartlett's chi-square test, Tukey's test of non-additivity, Levene's residual F test or Taylor's power low or on the basis of multiple criteria viz., likelihood method of Box and Cox (1964) or the graphical method of Draper and Hunter (1969). The results of the analysis of the data relating to pest surveillance study on paddy showed that logarithmic transformation was the most desirable in the analysis of data on the counts of all the major types of insects on rice (stem borer, jassid, gall fly, leaf folder, BPH) the only exception being case worm for which a squareroot transformation was indicated. Box-Cox approach undoubtedly emphasised the utility of the logarithmic transformation in analysing data on counts of insects and weeds. The graphical plot of the log likelihood function against the exponent of the power transform had a maximum value around zero for all sets of data indicating the superiority of the logarithmic transformation over the others. The graphical method of Draper and Hunter failed to suggest a unique transformation for all sets of data. However, in most cases, the choice lied between squareroot and logarithmic transformations with a slight superiority for the squareroot transformation. As per the method suggested by Berry (1987) a suitable location parameter 'C' was estimated for the analysis of sets of data involving extreme observations including zero values. The estimated value of the additive constant was found to be approximately 2.8 for all the different sets of data. The analysis of transformated data after incorporating the estimated value of the additive constant to each observation showed slightly better results than the ordinary analysis after incorporating the additive constant 'one' to each datum. An alternative estimate of the parametric constant in the inverse hyperbolic sine squareroot transformation was developed and the resultant estimate produced better results than those by the estimate proposed by Beal (1942). Assuming a non-linear relationship between mean (u) and standard deviation (σ) a new transformation x' = log(x2+k) where x = original observation, k = a parametric constant to be estimated from the data, was derived theoretically. The best estimate (k^) of the parameter k was derived to be ^ ∑σ/μ - n k = ----------- where n is the number of observations. ∑ (1/μ2) This transformation is expected to be useful in the analysis of data when the mean- standard deviation relationship is approximately parabolic. In general, the new transformation was found to be slightly better than the inverse hyperbolic sine