Normality diagnostics

TL;DR: Find which metrics depart most from normality using directly visible, SD-scaled quantile gaps. Full explanation at the end ↓

What stands out

The cards below are the largest average departures in the selected group. “Average Q–Q gap” is root-mean-square quantile error in SD units; “tail gap” applies the same measure only to the lowest and highest 10%. These are magnitudes, not pass/fail tests.

Ranked diagnostic scan

Start here instead of hunting for tiny bends in dozens of panels. Skew describes left/right asymmetry; excess kurtosis describes tail weight versus a normal curve (positive = heavier, negative = lighter).

Plots

Data: exact per-value counts over seeds. Each fitted normal uses that metric's exact population mean and SD. Discrete integer counts can produce small stair-steps even when the overall shape is normal-like; that is another reason to read the numeric gap rather than demand a perfectly smooth line.

Full explanation and methodology

A classic Q–Q plot can make every metric look normal when the raw count scale is wide. The recommended deviation view instead plots (actual quantile − fitted-normal quantile) / SD. Zero is a perfect match; +0.05 means the observed quantile is 5% of one standard deviation above the normal reference. Tail points are highlighted, and the classic Q–Q view remains available.

A formal normality p-value is not useful for 2,147,483,647 observations: microscopic departures become significant while remaining practically invisible. Read the SD-scaled average and tail gaps, skewness, excess kurtosis, and where the mismatch is concentrated. Integer-valued metrics can also show small stair-steps from discreteness.