Shapiro-Francia Test for Normality
Performs the Shapiro-Francia test for the composite hypothesis of normality.
ShapiroFranciaTest(x)
x |
a numeric vector of data values, the number of which must be between 5 and 5000. Missing values are allowed. |
The test statistic of the Shapiro-Francia test is simply the squared correlation between the ordered sample values and the (approximated) expected ordered quantiles from the standard normal distribution. The p-value is computed from the formula given by Royston (1993).
A list of class htest, containing the following components:
statistic |
the value of the Shapiro-Francia statistic. |
p.value |
the p-value for the test. |
method |
the character string “Shapiro-Francia normality test”. |
data.name |
a character string giving the name(s) of the data. |
The Shapiro-Francia test is known to perform well,
see also the comments by Royston (1993). The expected ordered quantiles
from the standard normal distribution are approximated by
qnorm(ppoints(x, a = 3/8)), being slightly different from the approximation
qnorm(ppoints(x, a = 1/2)) used for the normal quantile-quantile plot by
qqnorm for sample sizes greater than 10.
Juergen Gross <gross@statistik.uni-dortmund.de>
Royston, P. (1993): A pocket-calculator algorithm for the Shapiro-Francia test for non-normality: an application to medicine. Statistics in Medicine, 12, 181–184.
Thode Jr., H.C. (2002): Testing for Normality. Marcel Dekker, New York. (2002, Sec. 2.3.2)
shapiro.test for performing the Shapiro-Wilk test for normality.
AndersonDarlingTest, CramerVonMisesTest,
LillieTest, PearsonTest for performing further tests for normality.
qqnorm for producing a normal quantile-quantile plot.
ShapiroFranciaTest(rnorm(100, mean = 5, sd = 3)) ShapiroFranciaTest(runif(100, min = 2, max = 4))
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