Univariate Test of Normality by Shapiro and Wilk (1965)

Given an univariate sample \(x\), it tests $$H_0 : x\textrm{ is from normal distribution} \quad vs\quad H_1 : \textrm{ not } H_0$$ using a test procedure by Shapiro and Wilk (1965). Actual computation of \(p\)-value is done via an approximation scheme by Royston (1992).

norm.1965SW(x)

Arguments

x

a length-\(n\) data vector.

Value

a (list) object of S3 class htest containing:

statistic

a test statistic.

p.value

\(p\)-value under \(H_0\).

alternative

alternative hypothesis.

method

name of the test.

data.name

name(s) of provided sample data.

References

Shapiro SS, Wilk MB (1965). “An Analysis of Variance Test for Normality (Complete Samples).” Biometrika, 52(3/4), 591. ISSN 00063444.

Royston P (1992). “Approximating the Shapiro-Wilk W-test for non-normality.” Statistics and Computing, 2(3), 117--119. ISSN 0960-3174, 1573-1375.

Examples

## generate samples from several distributions
x = stats::runif(28)            # uniform
y = stats::rgamma(28, shape=2)  # gamma
z = stats::rlnorm(28)           # log-normal

## test above samples
test.x = norm.1965SW(x) # uniform
test.y = norm.1965SW(y) # gamma
test.z = norm.1965SW(z) # log-normal