Paste a column of data and find out whether it follows a normal distribution. Get the Anderson-Darling A² statistic, an approximate p-value, a normal probability plot and a histogram — all client-side.
Paste your data and press Calculate to run the Anderson-Darling normality test.
Many tools assume your data is normal — but is it? Enter the lab to check 40 readings with the Anderson-Darling test.
Paste a single column of measurements. The calculator sorts them and puts them on a common scale (using the average and spread) so they can be compared to a standard normal (bell-curve) distribution.
The calculator compares your data's shape to a normal (bell) curve, paying extra attention to the extremes (high and low ends) where non-normality usually shows up.
You get a p-value that tells you whether your data looks like a normal (bell-curve) distribution. If the p-value is higher than your chosen threshold (usually 0.05), the data passes the normality check. A plot and a chart let you see the shape with your own eyes.
Many statistical tools — capability indices, t-tests, control charts — assume your data is normally distributed. A normality test checks that assumption objectively so you know whether to trust those tools or switch to a nonparametric alternative.
A normality test asks whether a sample could plausibly have come from a normal (Gaussian) distribution. The Anderson-Darling test compares the empirical distribution of your data with the theoretical normal CDF, giving more weight to the tails than older tests. A large A² statistic and small p-value mean the data departs from normality.
The Anderson-Darling test checks how well your data matches a normal (bell-shaped) curve. It lines your sorted values up against what a perfect normal distribution would predict and measures the gap, paying special attention to the tails where non-normality usually shows. That gap becomes the A² statistic, which is turned into a p-value. A p-value above 0.05 means it is safe to treat the data as normal; below 0.05 means it is not, so you would use a transformation or a rank-based method instead.
Before calculating process capability (Cpk), the team checks whether fill-weight data is normally distributed. They collect 30 measurements and run an Anderson-Darling test. The p-value is 0.08 — above 0.05, so they can't reject normality.
The probability plot confirms it: points stay close to the reference line, no obvious curves or outliers. Safe to proceed with standard Cpk.
What to do with this: Always check normality before using Cpk. If your p-value is below 0.05, use a non-normal capability method or transform the data first — otherwise Cpk will give you the wrong answer.
Capability indices (Cp, Cpk), Shewhart control limits and t-tests all assume normal data. If the assumption is wrong, those numbers can mislead — a process that looks capable may not be. Testing normality first protects you from drawing the wrong conclusion from the right calculation.
Run a normality test in the Measure and Analyse phases before any analysis that assumes a normal distribution. If the data passes, continue with standard tools. If it fails, transform the data, use a nonnormal capability method, or switch to a rank-based nonparametric test.
Checking normality is a routine gate in DMAIC. The Anderson-Darling test is the default normality test in most Six Sigma software because of its sensitivity in the tails, where capability and risk decisions are most affected.
If the data is normal, proceed with capability analysis, control charts or parametric tests with confidence. If it is not normal, first check for outliers or a mixture of two processes (visible as a second peak). Consider a Box-Cox or Johnson transformation, a nonnormal capability method, or a nonparametric test such as Mann-Whitney or Kruskal-Wallis. Always pair the p-value with the probability plot before deciding.
Combine the normality test with histograms, capability analysis and a DMAIC project structure to make sound, assumption-checked decisions.
A paired t-test is used when the same items (machines, patients, stations) are measured twice — before and after, or under two conditions. Because each pair shares variability, the test eliminates that source of noise and is more powerful than a 2-sample test. A 2-sample (independent) t-test is used when the two groups are completely separate, with no natural pairing between observations.
Data is paired when there is a natural one-to-one correspondence between each before and after value — the same machine, the same patient, the same workstation. Examples: cycle time on 10 machines before and after a process change; blood pressure in 20 patients before and after treatment; inspection times for the same parts under two methods. If the items in the two groups are different, use a 2-sample t-test.
The paired t-test assumes: (1) observations are independent of each other (one pair does not influence another); (2) the differences (after minus before) are approximately normally distributed — for small samples use a normality test; (3) there are no extreme outliers in the differences. Violations of normality with small samples suggest using a nonparametric alternative such as the Wilcoxon signed-rank test.
The minimum recommended is about 10–15 pairs, though the test works with fewer if the differences are normally distributed. The required sample size depends on the expected mean difference, the standard deviation of differences, and the desired power (typically 80%). For a kaizen study where you expect a 10% improvement with moderate variability, 20–30 pairs typically gives adequate power. Use a sample size calculator to plan your study.
A normality check tells you which tools you can trust. Structured training shows you how to analyse and improve your process from there.
More calculators for statistics, quality, and improvement.
Want to test assumptions properly inside a full DMAIC project? The Black Belt course covers advanced statistics, hypothesis testing, and the full analytical toolkit.
View Black Belt →