StatReason

Q-Q Plot Maker

Compare your sample's shape against a normal distribution visually, by plotting your sorted values against the values you would expect if the data were exactly normal.

What this answers

This tool answers "does this sample's shape look consistent with a normal distribution?" visually, showing exactly where and how a sample departs from normality, information a single normality-test statistic cannot convey on its own.

How it is calculated

Your values are sorted, and each one is paired with the theoretical quantile a standard normal distribution would produce at that same rank, using the Blom position convention (the same one this site's Shapiro-Wilk engine uses). If your data were drawn from a normal distribution, these pairs would fall close to a straight reference line built from your sample's own mean and standard deviation. Systematic curvature, S-shapes, or a small number of points straying far from the line are each a specific, visually distinct kind of departure from normality.

Worked example

For a right-skewed sample like 2, 4, 5, 7, 8, 9, 12, 15, 18, and 25, the points curve noticeably away from the reference line at the upper end, exactly the pattern a Q-Q plot is designed to reveal: the largest values are farther from the bulk of the data than a normal distribution would predict, consistent with the sample's visible right skew.

Assumption audit

Calculated from your data: the theoretical normal quantile paired with each of your sorted values, and a reference line built from your sample's own mean and standard deviation.
Evidence to review: the specific shape of any departure from the reference line; curvature at both ends suggests heavy or light tails, while curvature concentrated at one end suggests skew, each implying a different kind of follow-up.
You must verify: that your sample is large enough to judge shape meaningfully; very small samples produce Q-Q plots that look irregular even when drawn from a genuinely normal population, simply from sampling variability.

What this result does not mean

A Q-Q plot that looks reasonably straight is evidence consistent with normality, not proof of it; formal statements about normality require a test statistic like the Shapiro-Wilk Normality Test, ideally used alongside this plot rather than instead of it.

Limitations

This calculator compares only against a normal reference distribution; comparing against a different theoretical distribution (uniform, exponential, or another named distribution) is not supported by this specific engine.