Variance can be defined as a statistical measure of variability obtained by calculating individual deviations from the mean value of a population, squaring them, summing up the squares and finally finding the average of the deviations squared. Homogeneity of variance, also known as equality of variance or homoscedasticity can therefore be defined as the similarity of the variance obtained from two or more populations under comparison (Rafter & Bell, 2003).
A significant emphasis is laid on the homogeneity of variance of populations that have different sizes since it places the two populations on the same platform for the purposes of comparison and analysis. The larger the size of the population, the greater the variance expected. This therefore necessitates the homogeneity of variance in order to draw unbiased inferences from a study of two or more populations (Gravetter & Wallnau, 2000). For example, a population picked from a high school would not have the same age variance as compared to the population of a city and therefore the need for homoscedasticity.
A lack of homogeneity would significantly affect the Analysis of variance (ANOVA) of tests in the sense that hypothesis tests in the linear models of ANOVA would be adversely affected. Equality of the variance will therefore allow for the accurate analysis and application of hypothesis tests in unequal sample sizes (Dowdy et al., 2011). The importance of homoscedasticity is that inferences can be drawn from a wide scope of variables from different populations that differ in size without distorting the characteristic observation throughout a given study. It also allows for future referencing in the case of follow-up studies and improvements on previous studies since the homogenous variance allows for the formulation of equation and functions. These equations and functions used for statistical studies have constants that are not affected by time which would otherwise not have been the case had there not been homogeneity of variance.