## ABSTRACT

The majority of statistical experiments are conducted so as to compare two or more groups. It is understand that the word group is a generic term used by statisticians to label and distinguish the individuals who share a set of experimental conditions. The transformations such as the square root or the logarithm to improve normality can improve the power of the F–test when applied to nonnormal samples. The effect of unequal variances on the F–test of the analysis of variance problem had been investigated by Box. The fundamental assumption in the analysis of group means is that the samples must be independent, as are the observations within each sample. The aforementioned procedures to deal with situations where the usual assumptions of normality and variance heterogeneity are not tenable, several alternatives are available. Nonparametric procedures are designed to have desirable statistical properties when few assumptions can be made about the underlying distribution of the data.