Normal 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.

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

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:

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

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