Performs the Pearson chi-square test for the composite hypothesis of normality.
PearsonTest(x, n.classes = ceiling(2 * (n^(2/5))), adjust = TRUE)a numeric vector of data values. Missing values are allowed.
The number of classes. The default is due to Moore (1986).
logical; if TRUE (default), the p-value is computed from
a chi-square distribution with n.classes-3 degrees of freedom, otherwise
from a chi-square distribution with n.classes-1 degrees of freedom.
A list of class htest, containing the following components:
the value of the Pearson chi-square statistic.
the p-value for the test.
the character string “Pearson chi-square normality test”.
a character string giving the name(s) of the data.
the number of classes used for the test.
the degress of freedom of the chi-square distribution used to compute the p-value.
The Pearson test statistic is \(P=\sum (C_{i} - E_{i})^{2}/E_{i}\),
where \(C_{i}\) is the number of counted and \(E_{i}\) is the number of expected observations
(under the hypothesis) in class \(i\). The classes are build is such a way that they are equiprobable under the hypothesis
of normality. The p-value is computed from a chi-square distribution with n.classes-3 degrees of freedom
if adjust is TRUE and from a chi-square distribution with n.classes-1
degrees of freedom otherwise. In both cases this is not (!) the correct p-value,
lying somewhere between the two, see also Moore (1986).
Moore, D.S., (1986) Tests of the chi-squared type. In: D'Agostino, R.B. and Stephens, M.A., eds.: Goodness-of-Fit Techniques. Marcel Dekker, New York.
Thode Jr., H.C., (2002) Testing for Normality. Marcel Dekker, New York. Sec. 5.2
shapiro.test for performing the Shapiro-Wilk test for normality.
AndersonDarlingTest, CramerVonMisesTest,
LillieTest, ShapiroFranciaTest for performing further tests for normality.
qqnorm for producing a normal quantile-quantile plot.
# NOT RUN {
PearsonTest(rnorm(100, mean = 5, sd = 3))
PearsonTest(runif(100, min = 2, max = 4))
# }
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