norm.1965SW {SHT}

Univariate Test of Normality by Shapiro and Wilk (1965)

Description

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).

Usage

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