Runs two normality tests on the finite values of `col`:
Value
A tibble with one row per test run: `statistic`, `p.value`, `method`, `distribution.test` (`TRUE` when `p.value >= alpha`, i.e. normality is not rejected), `p_value_sig`, and `distribution`. It has no rows when neither test applies (fewer than 3 values, or all values equal).
Details
* **Shapiro-Wilk** ([stats::shapiro.test()]), for 3 to 5000 values. It is left out above 5000 rather than run on a random subsample, so results never depend on the random number generator. * **Lilliefors** ([nortest::lillie.test()]), for 5 or more values: the Kolmogorov-Smirnov test corrected for estimating the mean and standard deviation from the same data. A plain KS test against `pnorm(mean(x), sd(x))` gives p-values that are far too large.
Both tests are deterministic. In large samples they reject normality for departures too small to matter, so read them alongside a plot such as [distribution_plot()] or a normal Q-Q plot.
References
Lilliefors HW (1967). On the Kolmogorov-Smirnov test for normality with mean and variance unknown. *Journal of the American Statistical Association*, 62(318), 399-402.
Examples
set.seed(1)
is_normal(rnorm(1000, mean = 5, sd = 3))
#> # A tibble: 2 × 6
#> statistic p.value method distribution.test p_value_sig distribution
#> <dbl> <dbl> <chr> <lgl> <chr> <chr>
#> 1 0.999 0.726 Shapiro-Wilk nor… TRUE "" normal
#> 2 0.0178 0.623 Lilliefors (Kolm… TRUE "" normal
is_normal(runif(1000, min = 2, max = 4))
#> # A tibble: 2 × 6
#> statistic p.value method distribution.test p_value_sig distribution
#> <dbl> <dbl> <chr> <lgl> <chr> <chr>
#> 1 0.951 1.20e-17 Shapiro-Wilk no… FALSE *** normal
#> 2 0.0710 6.37e-13 Lilliefors (Kol… FALSE *** normal