The univariate approach to the analysis of variance typically starts with the arrangement of data in a table where the columns represent the different treatments and the rows represent the subjects. The analysis of variance using this approach is based on the assumption that the data in any particular group has the same mean. Another assumption is that data from the different groups have a similar variance.
Further assumptions are that all the subjects were independently sampled and that the sampled data is normally distributed. The null hypothesis is that all the means are the same, while the alternative hypothesis is that there exists a difference between at least one pair of means among the groups.
The first step in the analysis of variance is to find the sample mean for each group after which the grand mean of the sample is calculated. The analysis of variance requires the statistician to partition the total sum of squares, which is the sum of the average squared difference between every observation and the grand mean calculated during the first step. The analysis of variance is simplified as the double summation of the difference between the observations and the group means added to the difference between the group means and the grand mean.