Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!
Get Started for Free

PearsonTest

Pearson Chi-Square Test for Normality


Description

Performs the Pearson chi-square test for the composite hypothesis of normality.

Usage

PearsonTest(x, n.classes = ceiling(2 * (n^(2/5))), adjust = TRUE)

Arguments

x

a numeric vector of data values. Missing values are allowed.

n.classes

The number of classes. The default is due to Moore (1986).

adjust

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.

Details

The Pearson test statistic is P=∑ (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).

Value

A list of class htest, containing the following components:

statistic

the value of the Pearson chi-square statistic.

p.value

the p-value for the test.

method

the character string “Pearson chi-square normality test”.

data.name

a character string giving the name(s) of the data.

n.classes

the number of classes used for the test.

df

the degress of freedom of the chi-square distribution used to compute the p-value.

Note

The Pearson chi-square test is usually not recommended for testing the composite hypothesis of normality due to its inferior power properties compared to other tests. It is common practice to compute the p-value from the chi-square distribution with n.classes - 3 degrees of freedom, in order to adjust for the additional estimation of two parameters. (For the simple hypothesis of normality (mean and variance known) the test statistic is asymptotically chi-square distributed with n.classes - 1 degrees of freedom.) This is, however, not correct as long as the parameters are estimated by mean(x) and var(x) (or sd(x)), as it is usually done, see Moore (1986) for details. Since the true p-value is somewhere between the two, it is suggested to run PearsonTest twice, with adjust = TRUE (default) and with adjust = FALSE. It is also suggested to slightly change the default number of classes, in order to see the effect on the p-value. Eventually, it is suggested not to rely upon the result of the test.

The function call PearsonTest(x) essentially produces the same result as the S-PLUS function call chisq.gof((x-mean(x))/sqrt(var(x)), n.param.est=2).

Author(s)

Juergen Gross <gross@statistik.uni-dortmund.de>

References

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

See Also

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.

Examples

PearsonTest(rnorm(100, mean = 5, sd = 3))
PearsonTest(runif(100, min = 2, max = 4))

DescTools

Tools for Descriptive Statistics

v0.99.41
GPL (>= 2)
Authors
Andri Signorell [aut, cre], Ken Aho [ctb], Andreas Alfons [ctb], Nanina Anderegg [ctb], Tomas Aragon [ctb], Chandima Arachchige [ctb], Antti Arppe [ctb], Adrian Baddeley [ctb], Kamil Barton [ctb], Ben Bolker [ctb], Hans W. Borchers [ctb], Frederico Caeiro [ctb], Stephane Champely [ctb], Daniel Chessel [ctb], Leanne Chhay [ctb], Nicholas Cooper [ctb], Clint Cummins [ctb], Michael Dewey [ctb], Harold C. Doran [ctb], Stephane Dray [ctb], Charles Dupont [ctb], Dirk Eddelbuettel [ctb], Claus Ekstrom [ctb], Martin Elff [ctb], Jeff Enos [ctb], Richard W. Farebrother [ctb], John Fox [ctb], Romain Francois [ctb], Michael Friendly [ctb], Tal Galili [ctb], Matthias Gamer [ctb], Joseph L. Gastwirth [ctb], Vilmantas Gegzna [ctb], Yulia R. Gel [ctb], Sereina Graber [ctb], Juergen Gross [ctb], Gabor Grothendieck [ctb], Frank E. Harrell Jr [ctb], Richard Heiberger [ctb], Michael Hoehle [ctb], Christian W. Hoffmann [ctb], Soeren Hojsgaard [ctb], Torsten Hothorn [ctb], Markus Huerzeler [ctb], Wallace W. Hui [ctb], Pete Hurd [ctb], Rob J. Hyndman [ctb], Christopher Jackson [ctb], Matthias Kohl [ctb], Mikko Korpela [ctb], Max Kuhn [ctb], Detlew Labes [ctb], Friederich Leisch [ctb], Jim Lemon [ctb], Dong Li [ctb], Martin Maechler [ctb], Arni Magnusson [ctb], Ben Mainwaring [ctb], Daniel Malter [ctb], George Marsaglia [ctb], John Marsaglia [ctb], Alina Matei [ctb], David Meyer [ctb], Weiwen Miao [ctb], Giovanni Millo [ctb], Yongyi Min [ctb], David Mitchell [ctb], Franziska Mueller [ctb], Markus Naepflin [ctb], Daniel Navarro [ctb], Henric Nilsson [ctb], Klaus Nordhausen [ctb], Derek Ogle [ctb], Hong Ooi [ctb], Nick Parsons [ctb], Sandrine Pavoine [ctb], Tony Plate [ctb], Luke Prendergast [ctb], Roland Rapold [ctb], William Revelle [ctb], Tyler Rinker [ctb], Brian D. Ripley [ctb], Caroline Rodriguez [ctb], Nathan Russell [ctb], Nick Sabbe [ctb], Ralph Scherer [ctb], Venkatraman E. Seshan [ctb], Michael Smithson [ctb], Greg Snow [ctb], Karline Soetaert [ctb], Werner A. Stahel [ctb], Alec Stephenson [ctb], Mark Stevenson [ctb], Ralf Stubner [ctb], Matthias Templ [ctb], Duncan Temple Lang [ctb], Terry Therneau [ctb], Yves Tille [ctb], Luis Torgo [ctb], Adrian Trapletti [ctb], Joshua Ulrich [ctb], Kevin Ushey [ctb], Jeremy VanDerWal [ctb], Bill Venables [ctb], John Verzani [ctb], Pablo J. Villacorta Iglesias [ctb], Gregory R. Warnes [ctb], Stefan Wellek [ctb], Hadley Wickham [ctb], Rand R. Wilcox [ctb], Peter Wolf [ctb], Daniel Wollschlaeger [ctb], Joseph Wood [ctb], Ying Wu [ctb], Thomas Yee [ctb], Achim Zeileis [ctb]
Initial release
2021-04-09

We don't support your browser anymore

Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.