Lean to run variance tests using Minitab. Variance is a measure of variation or lack of consistency. Whether the question is if the variance is consistent enough, less than a target value? Or are variances comparably the same across two groups or multiple groups? Statistical tests such as ANOVA requires that a test for equal variances be carried out first. Minitab can be used to run all these variance tests, from the one-variance test to compare to a target value, to testing for equality between two variances and across multiple variances.
- [Voiceover] In this movie, I will show you how to compare variances using Minitab. Open Exercise File 04-02. Here, we have four locations, A, B, C, D, or four businesses and the processing times, for example. And we are interested in comparing variances. Let's assume we wanna compare variance to a target value of 9.0 and see how office location A performs against that target. So, go to Stat, Basic Statistics, 1 Variance.
And our data is A, and we'd like to perform a hypothesis test against the variance of 9.0. And let's specify the hypothesis test in more detail with Options. Our alpha is 0.05, that's fine, we can change this number if you like. The alternate hypothesis, less than, not equal to, or greater than target value. Let's choose less than, because you'd like to test whether A is more consistent than the allowed maximum target.
OK and OK. Let's bring this down a little more and get a bigger print of this. Here we have it, Variance Test, Null hypothesis, Alternate. There are two methods shown here, one for normal distribution, the other is not. And the confidence intervals are shown, and the P-Values are shown for both types of tests, Chi-Square if it's normal, the Bonett if it's not. In either case, the value is 0.012 or 0.015, both of which are less than 0.05, our alpha, therefore we reject the null hypothesis, in which case we can say safely that the variance of A is less than our target.
So, office A is in good shape. What if I want to compare two variances, let's say office A and office D, and see which one has a higher variance or if they're equally consistent. So, to compare two variances, I run a two-variance test. Go up to Stat, Basic Statistics, 2 Variances, and since our data is in its own column, we can select this, Sample 1 being A, Sample 2 being D.
Specify in the Options, we are comparing variances. And alpha value is fine. Hypothesized ratio is 1, we are comparing the two. The alternate of not equal to is fine, and we select OK. And in the graph, we see the ratio of variances, and then the two variances, continuous intervals, and boxplot themselves. And these two tests show that the p-values are 0.4, which is greater than 0.05, therefore we fail to reject the null hypothesis.
And the null hypothesis is equal variances. Let's go to the printout, and the confidence intervals are shown here, as well as the P-Values. So, there you have it. That's how you compare two variances. What if I wanna compare all four locations, essentially testing for equality of variances across these four locations? Then, I would do Stat, ANOVA, Test For Equal Variances. Our data is not in one column, it's in multiple columns, therefore let's select that.
And select all four locations, and press OK. Here you have a graph showing the confidence intervals, as well as the Test for Equal Variances. As you can see, there is some overlap, but there's some that are different, too. And the P-Value speaks very loudly, at 0.000, it's less than 0.05, therefore we reject the null hypothesis. And the null hypothesis is equal variances, and the alternate is at least one variance is different.
As you saw from the graph, they are different. And the confidence intervals are reported. You get that with the P-Values. So, that's how you compare multiple variances. So, in summary, to compare one variance to a target, go to Stat, Basic Statistics, 1 Variance test. For two variances, select 2 Variances. For multiple variances, go to Stat, ANOVA, Test For Equal Variances. So, that's how you compare variances in Minitab.
Dr. Richard Chua shows how to import and organize data; open, save, and share Minitab worksheets and projects; create graphs and charts; and use descriptive statistics and statistical tests in Minitab to make inferences and data-driven decisions. Then learn how to make inferences on continuous data—running normality tests, variance tests, correlations, and simple regression tests. Finally, discover how to share your findings with others using reports and simple copy-and-paste techniques. Start watching to learn why Minitab is one of the world's most popular statistical software tools.
- Determine how to utilize display graphs and charts including bar, Pareto charts, and scatterplots.
- Recognize how to compare variance and multiple means.
- Identify how to compare medians.
- Explore how to run a multiple regression test and examine the resulting data.
- Break down how to compare inferences on continuous data.
- Differentiate how to compare proportions.