The Lilliefors-corrected Kolmogorov–Smirnov test checks normality by comparing the empirical CDF against the normal CDF, with the mean and SD estimated from the data.
The classical Kolmogorov–Smirnov test compares an empirical CDF against a fully specified distribution. When you estimate the parameters (μ, σ) from the same data — as you always do in practice for normality testing — the K–S p-values are too large. The Lilliefors correction adjusts the critical values for this in-sample parameter estimation, giving a properly calibrated test.
K–S statistics are based on the maximum vertical distance between the empirical and theoretical CDFs, so the test is most sensitive in the middle of the distribution and relatively insensitive to tail behaviour. That makes it weaker than Shapiro–Wilk for catching heavy tails, but useful when you specifically care about the centre of the distribution (e.g. calibration of a predicted-vs-observed plot).
One numeric column.
D statistic (maximum CDF gap) and a Lilliefors p-value. Small p (< 0.05) rejects normality.
Less powerful than Shapiro–Wilk in most settings, especially against heavy-tailed alternatives. Reach for K–S only when n is huge or you specifically want the CDF-centre framing — Shapiro–Wilk is the better default for clinical-style data sets.