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Comparative Study of Transformed and Concealed Data in Experimental Designs and Analyses

Authors: P. Luangpaiboon, K. Chinda


This paper presents the comparative study of coded data methods for finding the benefit of concealing the natural data which is the mercantile secret. Influential parameters of the number of replicates (rep), treatment effects (τ) and standard deviation (σ) against the efficiency of each transformation method are investigated. The experimental data are generated via computer simulations under the specified condition of the process with the completely randomized design (CRD). Three ways of data transformation consist of Box-Cox, arcsine and logit methods. The difference values of F statistic between coded data and natural data (Fc-Fn) and hypothesis testing results were determined. The experimental results indicate that the Box-Cox results are significantly different from natural data in cases of smaller levels of replicates and seem to be improper when the parameter of minus lambda has been assigned. On the other hand, arcsine and logit transformations are more robust and obviously, provide more precise numerical results. In addition, the alternate ways to select the lambda in the power transformation are also offered to achieve much more appropriate outcomes.

Keywords: Experimental Designs, Box-Cox, Arcsine, Logit Transformations

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[1] M.F. Freeman and J.W. Tukey, "Transformation Related to the Angular and the Square Root", The Annals of Mathematical Statistics, Vol. 10, 1939, pp. 247-253.
[2] G.E.P. Box and D.R. Cox, "An Analysis of Transformation", Journal of the Royal Statistical Society. Series B (Methodological), Vol. 26, No. 2, 1964, pp. 211-252.
[3] J.A. John and N.R. Draper, "An Alternative Family of Transformations", Journal of the Royal Statistical Society. Series C (Applied Statisyics), Vol. 29, No. 2, 1980, pp. 190-197.
[4] L. Kirisci, A.A. Al-Subaihi and R. Tarter, "Effects of the generalized Box-Cox transformation on Type I error rate and power of Hotelling-s T2", Journal of Statistical Computation and Simulation, Vol. 75, No. 3, March 2005, pp. 199-206.
[5] J. Olivier and M.M. Norberg, "Positively Skewed Data: Revisiting the Box-Cox Power Transformation", International Journal of Psychological Research, 2010, Vol. 3, No. 1, pp. 69-78.
[6] M.J. Duran, " The Use of the Arcsine Transformation in the Analysis of Variance when Data Follow a Binomial Distribution", Master Thesis, State Univ. of New York, College of Environmental Science and Forestry Syracuse, New York , May 1997.
[7] G.M. Cordeiro and M.G. Andrade, "Transformed symmetric models", International Journal of Statistical Modelling, Vol. 11(4), 2011, pp. 371- 388.
[8] "General Statistics Transformations" Code No. PSYC-5741 (4), Department of Psychology and Neuroscience, University of Colorado Boulder, USA (Online) Available :
[9] M.S. Bartlett, "The use of Transformation", Biometric Bulletin Vol. 3, 1947, pp. 39-52.
[10] J.L. Rasmussen and W.P. Dunlap, "Dealing with Nonnormal Data: Parametric Analysis of Transformed data VS Nonparametric Analysis", Educational and Psychological Measurement Journal Winter 1991, Vol. 51, pp. 809-820.
[11] Y. Guan, "Variance stabilizing transformations of Poisson, binomial and negative binomial distributions", Statistics and Probability Letters, Vol. 79, 2009, pp. 1621-1629.
[12] F.J. Anscombe, "The Transformation of Poisson, binomial, negative binomial data", Biometrika Journal, Vol. 35, 1948, pp. 246-254.
[13] M.S. Bartlett, "The square root transformation in the analysis of variance", Journal of the Royal Statistical Society, Vol.3, 1936, pp. 68- 78.
[14] G.E.P. Box and D.R. Cox, "An analysis of transformation Revisited", Journal of American Statistical Association, Vol. 77, 1982, pp. 177-182.
[15] P.A. Bromiley and N. A. Thacker, "The effects of an arcsine square root transform on a binomial distributed quantity", TINA memo, 2002, pp. 2002-007.
[16] D.C. Montgomery, Design and Analysis of Experiments, Hoboken, NJ: John Wiley & Sons, Inc., 2001.
[17] S.J. Chapman, MATLAB Programming for Engineers, Pacific Grove, CA: Wadsworth, 2002.