The Shapiro–Francia test checks normality from the squared correlation between the sorted data and the expected normal order statistics — a simplification of Shapiro–Wilk.
Shapiro–Francia replaces Shapiro–Wilk's complicated weighting with the simple Pearson r between sorted data and expected normal quantiles. The result is equivalent to the squared correlation in the normal Q-Q plot — W′ is a measure of how straight that plot is.
Computationally cheaper than Shapiro–Wilk and handles very large n (up to 5000 in our implementation), so it's a good choice when you want a Shapiro-style test on a big sample and the strict Shapiro–Wilk implementation hits its size cap. Power against most alternatives is comparable to Shapiro–Wilk.
One numeric column.
W′ statistic (closer to 1 = more normal) and p-value.
Read W′ as the squared correlation between the data and the Q-Q reference line. W′ ≥ 0.99 ⇒ essentially straight; W′ ≤ 0.95 ⇒ visible departure. The p-value formalises the same intuition.