In the realm of quantitative measure research, there are those researchers who b
ID: 2907961 • Letter: I
Question
In the realm of quantitative measure research, there are those researchers who believe some small violations of the homogeneity of variance assumption may have little practical effect on the analysis due to the robust nature of parametric tests. However, other researchers believe any violation of the homogeneity of variance assumption can result in tarnished or unbelievable results regardless of the robust nature of parametric tests. Discuss the viability or falsity of both viewpoints and how you would approach one view point versus the other.
Explanation / Answer
Researchers had assembled some evidence that some minimal violations of some assumptions had minimal effects on error rates under certain circumstances. i.e, if your variances are not exactly identical across all groups, but are relatively close, it is probably acceptable to interpret the results of that test despite this technical violation of assumptions.
Box is credited with coining the term “robust” which usually indicates that violation of an assumption does not substantially influence the Type I error rate of the test1.
That analyses such as simple one-factor ANOVA analyses are “robust” to non-normality of the populations and to variance inequality when group sizes are equal.
This means that they concluded that modest violations of these assumptions would not increase the probability of Type I errors.
In particular, when statistical assumptions are violated, the probability of a test statistic may be inaccurate, distorting Type I or Type II error rates.
That these basic assumptions are unimportant. These early studies do not mean, however, that all analyses are robust to dramatic violations of these assumptions, or attest to robustness without meeting the other conditions.
So,in the realm of quantitative measure research, there are those researchers who believe some small violations of the homogeneity of variance assumption may have little practical effect on the analysis due to the robust nature of parametric tests.