Normal Q-Q Plot Maker

Created:September 20, 2024

Last Updated:January 18, 2025

The Q-Q (Quantile-Quantile) Plot helps you assess whether your data follows a normal distribution by comparing your sample quantiles against theoretical normal quantiles. Combined with the Shapiro-Wilk normality test, it provides both visual and statistical evidence of normality. It's particularly useful for validating assumptions in statistical tests, analyzing regression residuals, and identifying potential outliers. Simply input your data to create an Q-Q plot and calculate the corresponding Shapiro-Wilk test statistics.

Calculator

1. Load Your Data

2. Select Columns & Options

Select Column to Test

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What is a Q-Q Plot?

A Q-Q (Quantile-Quantile) plot is a graphical tool used to assess whether a dataset follows a normal distribution. It plots the quantiles of your data against the theoretical quantiles of a normal distribution, creating a visual way to identify departures from normality.

How to Interpret Q-Q Plots

Normal Data Patterns

Points follow the diagonal reference line closely
Minor random deviations are acceptable
No systematic curves or patterns
Points near center of line often fit better than extremes

Common Deviations

S-shaped curve: Indicates skewness
Points above line at ends: Heavy tails
Points below line at ends: Light tails
Outliers: Points far from line at either end

When to Use Q-Q Plots

Q-Q plots are particularly useful in these situations:

Checking assumptions for statistical tests (t-tests, ANOVA, etc.)
Validating normality of regression residuals
Assessing the distribution of continuous variables
Identifying potential outliers and their impact

Using with Shapiro-Wilk Test

The Q-Q plot is often used alongside the Shapiro-Wilk test, which provides a numerical assessment of normality. While the test gives a p-value, the Q-Q plot shows how and where the data deviates from normality, making them complementary tools:

Visual Assessment (Q-Q Plot)

Shows pattern and location of deviations
Helps identify specific issues (skewness, outliers)
Useful for any sample size
Provides context for test results

Statistical Test (Shapiro-Wilk)

Provides objective measure (p-value)
Very sensitive to small deviations
Best for small to medium samples (3-5000)
May reject normality for large samples

Sample Size Considerations

The effectiveness of Q-Q plots and normality tests can vary with sample size:

Small samples (n < 30): May not show clear patterns, harder to detect non-normality
Medium samples (30-1000): Ideal range for both visual and statistical assessment
Large samples (n > 1000): May show significant deviations even for approximately normal data

Making Decisions

When assessing normality, consider both the Q-Q plot and Shapiro-Wilk test results:

If both show normality: Proceed with normal-theory statistics
If both show non-normality: Consider transformations or non-parametric methods
If results conflict: Examine sample size and consider practical significance of deviations
For large samples: Give more weight to visual assessment than test p-values