Statistics
This guide walks through the Equal Variance Test in the Analyse phase of RDMAICS using one fictional three team dataset. You will see how the tool picks a method, what the output means, and where the tool stops being useful.
The Equal Variance Test compares process spread across groups. It selects a robust or normal theory method automatically, then tells you which downstream test to use. In the words of the product, it gives you the correct downstream test recommendation.
You reach for it in the Analyse phase of RDMAICS, usually at a specific moment. You have grouped data. You are about to compare group means. Before you do that, you need to know whether the groups vary by similar amounts, because a pooled comparison assumes they do.
Spread matters on its own terms as well. Two teams can produce the same average and feel completely different to a customer. One is predictable. The other swings. The Equal Variance Test puts a number on that difference and tells you whether the difference is bigger than sampling noise would explain.
This worked example is fictional. It is the sample data that loads with the tool, and it exists to show you the mechanics rather than to describe a real organisation.
Three teams each contribute ten observations of a single response measurement. Team A records values between 47 and 52. Team C records values between 48 and 52. Team B records values from 35 to 66.
Look at the means and you would be forgiven for seeing nothing. Team A sits at 49.5. Team B sits at 50. Team C sits at 49.8. If your whole analysis stops at the average, the three teams look interchangeable. The question the Equal Variance Test asks is whether that reading survives a look at the spread.
The data table is deliberately plain. Each row is one observation. The Response column holds the measurement. The Group column holds the team label. The remaining columns, including second factor, pair ID and notes, stay empty for this analysis.
You then set four inputs. The first is what you plan to do after the check, which is set here to compare group means. That choice shapes the recommendation at the end. The second is the test method, left on Automatic from groups and normality. The third is the significance level, set to 0.05. The fourth and fifth map the columns: Response is the response, Group is the factor.
Leaving the method on automatic is the point of the tool. You do not have to decide in advance whether Bartlett's test or a robust alternative suits your data. The tool checks sample sizes and normality first, then chooses.
The output opens with a distribution and variance comparison chart. Boxes show the middle fifty per cent of each group, the centre line is the median, and whiskers stop at the most extreme value inside 1.5 times the interquartile range. Individual dots stay visible. The axis runs from 33.14 to 67.86. Team A and Team C appear as narrow boxes. Team B stretches across most of the range.
The method note explains the choice. All groups had at least eight observations and no Anderson-Darling result below 0.05, so Bartlett's chi-square test for approximately normal groups was selected. The assumption checks list each group: Team A Anderson-Darling p = 0.788691, Team B p = 0.943047, Team C p = 0.535722. Group balance is reported as balanced with a largest to smallest N ratio of 1.
Then the numbers. Team A has a standard deviation of 1.5811 and a variance of 2.5. Team C has a standard deviation of 1.3166 and a variance of 1.7333. Team B has a standard deviation of 10.4456 and a variance of 109.1111. The chi-square statistic is 40.6246 on 2 degrees of freedom, with a p-value below 0.000001.
The practical figure sits alongside the statistical one. The largest to smallest standard deviation ratio is 7.934. One team varies nearly eight times as much as another while producing almost the same average.
The decision ready conclusion is direct. Use Welch's t-test or ANOVA, or another robust method, rather than a pooled equal variance comparison. That is the recommendation flowing from the stated intent to compare group means.
Three next actions follow. Use Welch's t-test or Welch's ANOVA for the downstream mean comparison. Investigate outliers and mixed process populations before transforming data. Report the selected test, the significance level, the group sizes and the spread ratio.
The second action deserves attention. A standard deviation ratio of 7.934 is not only a statistical inconvenience. It is a signal about the process. Team B may be running two different methods, two different inputs or two different sets of conditions mixed into one label. That is an improvement question, not a statistics question, and the test has just pointed you at it.
The tool also offers an AI review that explains the result in plain language if you want a second reading before you take it to a stakeholder.
The first mistake is skipping the check entirely. Pooled methods assume comparable spread. In this dataset, the means differ by less than one unit, so a pooled comparison would almost certainly report no difference and you would move on. You would have missed a standard deviation ratio of 7.934.
The second mistake is overriding the automatic method without a reason. The tool reported that every group passed its normality check and that all groups had at least eight observations. Those conditions are why Bartlett's test was used. Forcing a different method when the stated conditions hold discards the logic you came for.
The third mistake is jumping to a transformation. The next actions put outlier and mixed population investigation ahead of transforming data for a reason. A transformation can hide a structural cause rather than fix it.
The fourth mistake is reporting only the p-value. A p-value below 0.000001 tells a reader the result is unlikely under equal variance. It says nothing about magnitude. Report the ratio of 7.934 alongside it.
The Equal Variance Test will not tell you why Team B varies. It reports a variance of 109.1111 and a standard deviation of 10.4456. It cannot tell you whether that comes from two operators, a drifting input, a measurement system problem or a single unusual period. That answer lives in the process, not the dataset.
It will not compare the means for you. The output recommends Welch's method. It does not run it. You still have to carry out the mean comparison in a separate step and interpret that result on its own terms.
It will not fix thin data. Ten observations per group is enough for Bartlett's test under the stated conditions, and the Anderson-Darling results supported normality. That is not the same as confidence about long run behaviour. Ten points per team is a snapshot.
It will not tell you whether the variation matters to a customer. Nothing in the output knows your specification limits, your tolerances or your service promise. A ratio of 7.934 is large in statistical terms. Whether it is large in business terms is a judgement you make.
Finally, it will not validate your measurement system. If the response values are unreliable, the spread you are testing may belong to the gauge rather than the process. Check that first, then come back to this tool and trust the answer.
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