Assess normality and distribution fit with quantile-quantile plots
Data Source
Generator Parameters
Enter Custom Data
Enter one number per line
Theoretical Distribution
Q-Q Plot
Statistical Tests
Histogram (Sample Data)
Sample Statistics
Interpreting Q-Q Plots
How to Read: Each point compares a sample quantile (y-axis) to the corresponding theoretical quantile (x-axis). If data matches the distribution, points fall on the reference line.
Common Patterns:
Points on line: Data follows the theoretical distribution well
S-curve (left low, right high): Right-skewed data (long right tail)
S-curve (left high, right low): Left-skewed data (long left tail)
Points above line on right: Heavier right tail than expected
Points below line on right: Lighter tails than expected
Points far from line at extremes: Outliers present
Points in curved pattern: Wrong distribution family
Shapiro-Wilk Test for Normality
Null Hypothesis: The data comes from a normal distribution.
Interpretation:
p > 0.05: Fail to reject null - data consistent with normality
p < 0.05: Reject null - significant departure from normality
Caution: Large samples may show statistical significance for trivial departures
Always use Q-Q plot visual inspection alongside the test
Sample Size: Shapiro-Wilk works best with n = 3 to 5000. For larger samples, use other tests or rely on visual inspection.