The Lilliefors test checks normality with the same statistic as Kolmogorov–Smirnov but the correct null distribution for when μ and σ are estimated from the sample.
When Kolmogorov–Smirnov is applied with sample-estimated parameters (μ̂ = x̄, σ̂ = s) rather than fixed reference values, its p-values are systematically too large — the test becomes too lenient. Lilliefors derived the correct null distribution for this case via simulation and tabulated critical values for it.
In our app, the K–S menu entry already uses the Lilliefors correction by default, so the two entries are effectively the same test under slightly different names. Lilliefors is here for completeness and as the historically correct citation.
One numeric column.
D statistic and Lilliefors-corrected p-value.
Same caveats as K–S: less powerful than Shapiro–Wilk for typical alternatives. Prefer Shapiro–Wilk unless n is very large.