Distribution and Normality Analysis: Check the Shape of Your Data Before You Choose a Method

Distribution and Normality Analysis helps you understand distribution shape before choosing capability, regression or hypothesis test methods. It combines separate stratum tests, a fitted normal histogram and a Q to Q diagnostic in one screen.

Most of the methods you reach for in the Analyse phase carry an assumption about shape. Capability indices built on a normal model assume a normal distribution. Many hypothesis tests assume approximate normality of the data or the residuals. If you skip the shape check, you can produce a number that looks precise and means very little.

Use the tool early in Analyse, as soon as you have a clean measurement column and a sensible way to group it. Use it again later if you transform the data or split it a different way. It sits between data collection and the heavier statistical work, and it takes a few minutes.

The worked example in this guide is fictional. It uses the sample data built into the tool, so you can open the tool and follow along exactly.

A service team records cycle time for 48 orders. Each order is labelled with a process stream. Twenty four orders sit in Standard orders. Twenty four sit in Priority orders. Every row belongs to the same scenario, Baseline.

Look at the raw numbers and a pattern appears without any statistics. Standard orders run from 29.3 to 32.76. Priority orders run from 23.17 to 26.63. The two streams occupy different ranges. That matters, because if you pooled all 48 values into one distribution you would be looking at two populations stacked together, not one process.

The question the team wants to answer is narrow and useful. Does cycle time within each stream behave like a normal distribution, closely enough that a normal based capability study or a parametric test would be reasonable?

The tool asks you to map your columns to roles. In this case the mapping is straightforward.

Observation is set as the observation or period column. It holds the labels Order 01 through Order 48. These labels carry no numeric meaning. They exist so you can trace a point back to a record.

Cycle time is set as the measurement. This is the single numeric column the analysis works on. Process stream is set as the group or stratum. Scenario is set as the series or scenario, and here it holds one value, Baseline.

Three settings control the analysis itself. Analyse is set to each process stratum separately, which is the correct choice when the groups may differ. The significance level alpha is set to 0.05. Scale to assess is set to original values, meaning no transformation is applied before testing.

The result panel reports each stratum on its own tab. Standard orders and Priority orders each get their own set of outputs. The walkthrough below reads the Standard orders tab, which covers original scale and n equals 24.

Two tests appear. Shapiro to Francia returns W equals 0.9837 with p equals 0.9024. Anderson to Darling returns A squared equals 0.2277 with p equals 0.7900. Both report no evidence against normality at alpha equals 0.05.

Read the wording carefully, because the tool states it plainly. This is not proof of normality. The available sample did not show strong contrary evidence. Those are different claims. A sample of 24 values has limited power to detect moderate departures from a normal shape. A high p value means you failed to find a problem, not that no problem exists.

Below the tests sits the histogram with a fitted normal curve. The bars show the selected data across six automatic bins, running from 29.3 to 32.76. The dashed curve shows the normal shape with the same mean and standard deviation. The tool labels the curve as a visual reference, not a normality test.

The normal Q to Q plot sits last. Points close to the diagonal and inside the approximate 95 per cent guide are consistent with a normal shape. Tail departures matter most, because tails drive capability estimates and extreme value predictions. The guide is an approximate visual envelope, not a replacement for the p values or your process knowledge.

The tool also offers an AI review that explains the result in plain language if you want a second read.

A shape check is only worth doing if it changes what you do next. Here it does, in three ways.

First, it supports a method choice. With no evidence against normality in either stratum, a normal based capability study on each stream becomes a defensible option. So does a parametric comparison of the two streams, subject to the other assumptions those tests carry.

Second, it supports a stratification decision. The separate stratum setting is the point of this analysis. Standard orders and Priority orders sit in different ranges, 29.3 to 32.76 against 23.17 to 26.63. Testing them together would describe a shape that neither stream actually has. Running them apart gives you two clean answers.

Third, it supports what you report. When you write up a capability figure later, you can point back to this screen and show the assumption was checked, at what alpha, on what scale, with what sample size. That is the difference between an analysis someone can audit and a number someone has to trust.

The most frequent error is pooling groups that should be separate. If you set the analysis to treat all 48 rows as one distribution, the two streams combine and the shape you see is an artefact of mixing. Always ask whether a grouping column exists before you run the test.

The second error is treating a high p value as a certificate. The tool warns against this twice, once under each test. With n equals 24 per stratum, the test has limited power. Combine the p values with the histogram, the Q to Q plot and what you know about how the process runs.

The third error is the reverse. On very large samples, a normality test can flag a departure that has no practical effect on your decision. A p value below alpha tells you a difference is detectable. It does not tell you the difference matters.

Two more worth naming:

This tool checks shape. It does nothing else, and it is better to know that up front.

It will not prove your data is normal. No test can. It can only report whether the sample showed strong contrary evidence at the alpha you set. Both Standard orders results here, W equals 0.9837 with p equals 0.9024 and A squared equals 0.2277 with p equals 0.7900, are statements about what was not found.

It will not tell you whether your process is stable. Normality and stability are separate questions. A process can produce a tidy normal looking histogram while drifting steadily over time, because a histogram discards the order of the points. Use a control chart for that question.

It will not tell you whether your measurement system is sound. If the gauge is biased or imprecise, the shape you see belongs partly to the measurement, not the process. Resolve that before you draw conclusions.

It will not choose your capability indices, run your regression or compare your two streams. It tells you which family of methods is reasonable. The analysis still has to be done, and the other assumptions of those methods still have to be checked.

It will not explain why a distribution has the shape it has. If a result had shown a departure from normality, the tool would not tell you whether the cause was mixed populations, a floor effect, rounding or a handful of unusual orders. That answer lives in the process, not in the numbers. Go and look.