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Normality Test (Anderson-Darling)

Check whether your data follow a normal distribution with the Anderson-Darling test. A histogram with a normal curve is shown and the p-value tells you whether normality holds.

1Data Table

Paste a table copied from Excel into a cell (Ctrl+V). Click a column header (A, B…) before pasting to use the first line as column names. Double-click a header to rename it, right-click to insert/delete rows and columns, and formulas such as =A1*2 work too.

2Normality Test Options

Select the columns to test for normality (multiple allowed):

How to run a normality test

  1. Copy the measurement columns to test (and a group column if needed) together with the header.
  2. Click the column header (A) in the data table and paste - the first line becomes the column name. You can also open a CSV or Excel file.
  3. Select the columns to test, and a group column to test each group separately.
  4. Press Analyze and check the A², p-value and interpretation in the statistics panel.

The Anderson-Darling test

The Anderson-Darling test measures how far the cumulative distribution of the data is from a normal distribution and is especially sensitive to differences in the tails. The larger the A² statistic, the further the data are from normal.

The p-value uses the D'Agostino & Stephens (1986) approximation including the correction for estimating the mean and standard deviation from the sample (the same formula as R's nortest::ad.test).

Decision rule

If the p-value is greater than 0.05, assuming a normal distribution is reasonable; if it is 0.05 or less, there is evidence that the data are not normal. The test is skipped for fewer than 8 values.

How to read the normality test

  • p > 0.05: analyses that assume normality (t-tests, Cpk/Ppk capability, control charts) can be used as is.
  • p ≤ 0.05: there is evidence against normality. With strong skewness, the interpretation also says which tail is long.
  • With very large samples even small departures give small p-values, so look at the histogram shape too.

Frequently asked questions

How is it different from the Shapiro-Wilk test?

Both test normality; Anderson-Darling is more sensitive to the tails. The same Anderson-Darling test as the Qstat desktop program is used.

How many values do I need?

At least 8 to run the test; 20 or more are recommended for a reliable judgment.

Should I also look at a QQ plot?

Yes. Checking on the normal probability plot page whether the points follow a straight line is a good complement.

Is my data sent to a server?

No. All calculations run inside your browser and nothing is transmitted or stored.

Other chart tools

Normal Probability Plot (QQ Plot) MakerCheck whether data follow a normal distribution with a QQ plot and R².Distribution FittingFit 8 candidate distributions by maximum likelihood and find the best one by AIC.Histogram MakerSee the distribution, a fitted normal curve and Pp/Ppk against spec limits at once.

Need process capability, control charts or DOE?

The Qstat desktop program offers about 250 analysis features: histograms and box plots plus process capability (Cp, Cpk), control charts, measurement system analysis (MSA), design of experiments (DOE), regression and machine learning.

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