Vol. 13 No. 1
Different methods for judging the normality assumption for univariate and bivariate data and its remedial measure
Abstract: Methods of finding density functions for statistics often lead to intractable mathematical expressions but the calculations are relatively simple and a good deal of work has been done using the basic assumption of normality. The most popular tests among practical Statisticians are tests which depend on normality in the parent population. When there is grave doubt about the assumption, non-parametric tests should be used, even at some sacrifice of power. Parametric tests like τ-test, t-test and F-test are applied under the assumption that the data are normally distributed. One should test the data whether they follow normal or not before conducting the parametric tests. If there is reason to suspect non-normality, it is advisable to try a transformation. In this work different methods for testing the normality are discussed and eight data sets are taken and they are tested for normality. The data sets 2 and 5 are found normal. The other data sets i.e.3,4 and 6 are non-normal. The bivariate data set 7 is normal where as bivariate data set-8 is non-normal. Box-Cox- power transformation is used for all non-normal data and it is found that all the transformed data follow normality. But it is not necessary that the Box-Cox-power transformation will always makes the data normal.
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