Q-Q Plot
Chart overview
A Q-Q (Quantile-Quantile) Plot is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other.
Key points
- It is primarily used to check if data follows a normal distribution.
- If the data is normally distributed, the points will fall approximately along a straight reference line.
- scipy.
Practical guidance
stats. probplot(data, dist='norm', plot=ax) is the standard recipe; statsmodels' qqplot(data, line='45', fit=True) adds standardized variants. Read the shape of the deviation, not just on/off the line: both ends curving away means heavy tails, an S-shape means skew, and steps or plateaus reveal rounded or discretized measurements. The extremes always wobble - tail quantiles have high variance even for truly normal samples - so judge the middle 90% more strictly than the last few points, or add a pointwise confidence envelope. For small n a Q-Q plot is far more informative than a normality-test p-value: Shapiro-Wilk passes almost anything at n=10 and flags trivial deviations at n=10,000. The same mechanics compare any two samples - plot the sorted quantiles of one condition against another to see exactly where two distributions diverge, which is often the real scientific question.
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Further reading
Python Scatter Plot Tutorial
Build scatter plots with regression overlays, color encodings, and uncertainty bars.
Read the guideExample Visualization
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"Create a Q-Q plot to check if the 'Residuals' of my regression model follow a normal distribution. Generate synthetic residuals (n=100) that are mostly normal but with heavier tails (t-distribution). Plot observed quantiles vs theoretical normal quantiles. Add a red reference line (45 degrees). Title: 'Q-Q Plot of Regression Residuals'. Label axes 'Theoretical Quantiles' and 'Ordered Values'."
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Python Code Example
Console Output
Plot displayed. R-squared value typically shown in title or console.
Common Use Cases
- 1Testing for normality
- 2Comparing two distributions
- 3Identifying outliers
- 4Model residual analysis
Pro Tips
Points on the line indicate normality
S-shaped curves indicate heavy/light tails
Check outliers at the extremes
Frequently asked questions
When should you use a q-q plot?
A Q-Q (Quantile-Quantile) Plot is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other. It is primarily used to check if data follows a normal distribution. Common applications include testing for normality, comparing two distributions, and identifying outliers.
Which Python libraries can create a q-q plot?
A q-q plot can be built in Python with scipy and matplotlib — scipy and matplotlib for precise control over axes, annotations, and journal styling. In Plotivy you describe the figure and it writes the scipy code for you.
Can I make a q-q plot without writing Python code?
Yes. Describe the q-q plot you need in plain language and upload your dataset — Plotivy's AI writes the Python code and renders a publication-ready figure. You still get the full, editable scipy source, so nothing is locked in a black box.
What are best practices for a clear q-q plot?
Points on the line indicate normality. S-shaped curves indicate heavy/light tails.
Library comparison for this chart
scipy
Useful in specialized workflows that complement core Python plotting libraries for qq-plot analysis tasks.
matplotlib
Best when you need full control over axis formatting, annotation placement, and journal-specific styling for qq-plot.
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