Six Sigma: Tests of Equal Variance

In the video below, we go over tests of equal variance and how they can be used to help you with your Six Sigma project.




By now you’re very familiar with these two vertical bars. We use them to test assumptions when we’re doing ANOVA or when we’re doing 2 to the K factorial switcher, a subset of ANOVA. We checked for equal variances and we checked for normal residuals. Well, there’s a reason that we’ve brought that over here when we’re checking for unequal variance. Let me show you why that works.

Let me designate this is an output and this as an input, and let me pop this up so you can see the whole data set. I’ve got some parameter that I have measured in a sample of frogs and measured the same thing in a sample of toads. If you look at that, the means are very different, but that’s not the question. The question is, are there variances and by inference their standard deviations the same. So let me, having designated those as Y and Xc, click calculate. What I get up here is the answer on two different tests. I get the answer on Levin’s test for equal variances. This test is less susceptible to non normality. I also get the F test, which is the classic Fisher test and this happens to be very sensitive to non-normality. So how do I know which one to use? Well, I look and see if my residuals are normally distributed and if they appear to be normal, then I will use the F test and that’s what will show up over here on the slider bar. If this slider gets down into the non-normal range or flirting with it, then the slider bar over here will automatically use the Levine test, which is less susceptible.

So under the circumstances, we would conclude that there is no evidence, that the standard deviation, or the variance, is different for these two subgroups. Now, we look at the residuals if we like and here’s that shift we were looking at in the data. Obviously toads have a lower mean frogs have a higher mean. But the amount of variation is about the same. If I want to look at that and scatter plot form, yeah sure enough, the box plots here are about equally spread out. So that’s how you check to see if variance or standard deviation is the same in two or more subgroups of data.

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