Homogeneity of Variance

Homogeneity within Populations

Within research, it is assumed that populations under observation (e.g., the population of female college students, the population of stay-at-home fathers, or the population of older adults living with type 2 diabetes) will be relatively similar and, therefore, will provide relatively similar responses or exhibit relatively similar behaviors. If two identifiable samples (or subpopulations) are each extracted from a larger population, the assumption is that the responses, measurable behaviors, and so on, of participants within both groups will be similar and that the distribution of responses measured within each of the groups (i.e., variance) will also be similar. It is important to note, however, that it would be unreasonable to expect that the variances be exactly equal, given fluctuations based on random sampling. When testing for homogeneity of variance, the goal is to determine whether the variances of these groups are relatively similar or different. For example, is the variation in responses of female college students who attend large public universities different from the variation in responses of female college students who attend small private universities? Is the variation in observable behaviors of older adults with type 2 diabetes who exercise different from that of older adults with type 2 diabetes who do not exercise? Is the variation in responses of 40-year-old stay-at-home fathers different from 25-year-old stay-at-home fathers?

Assumptions of t Tests and ANOVAs

When the null hypothesis is H0: μ1 = μ2, the assumption of homogeneity of variance must first be considered. Note that testing for homogeneity of variance is different from hypothesis testing. In the case of t tests and ANOVAs, the existence of statistically significant differences between the means of two or more groups is tested. In tests of homogeneity of variance, differences in the variation of the distributions among subgroups are examined.

The assumption of homogeneity of variance is one of three underlying assumptions of t tests and ANOVAs. The first two assumptions concern independence of observations, that scores within a given sample are completely independent of each other (e.g., that an individual participant does not provide more than one score or that participants providing scores are not related in some way), and normality (i.e., that the scores of the population from which a sample is drawn are normally distributed). As stated, homogeneity of variance, the third assumption, is that the population variances (σ2) of two or more samples are equal (σ21 = σ22). It is important to remember that the underlying assumptions of t tests and ANOVAs concern populations not samples. In running t tests and ANOVAs, the variances of each of the groups that have been sampled are used in order to test this assumption.

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