# One way ANOVA Analysis: Completely Randomized

In a lot of situations in research there is a need to examine the differences that occur among more than two groups. The involved groups have to be distinguished in accordance with the levels of a factor interest. When in a particular study, there is only one factor the experimental design is called a Completely Randomized Design.

When a numeric variable is being analysed and certain assumptions are being taken care of, the Analysis of Variance which is ANOVA is used in order to compare the means of the groups. One Way ANOVA is the procedure of ANOVA that is used for a completely randomized design. It is a step forward to the pooled variance T Test that is used for difference between two means. As explained earlier, the acronym ANOVA expands as Analysis of Variance but in research it is used to analyse the differences among the means and not the variance. So the term is slightly misleading. The variation in the groups in study is further subdivided in ANOVA to identify the variance that is among the groups and the variance that is within the groups. The within the group variation is a random measure and the among group variation which is due to differences from group to group, it is indicated as the number of groups. The symbol c is used to represent the number of groups. In a given situation for c it is assumed that the values are selected randomly and independently and follow a normal distribution, having equal variances. In this situation, the null hypotheses formulated would be that there is no difference in the population means and the alternate would be that all the population means of c are not equal.

When the ANOVA test of equality of population means has to be performed, the total variation in the values is subdivided into two parts. These two parts are, one which is due to the variation among the groups and the other which is due to the variation within the groups. This total variation representation is depicted by SST which is the total sum of squares. Sum of Squares Among Groups (SSA) is the squared difference between the sample mean of each group.