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

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

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.

- 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.

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

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.

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

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