NormalityTest Class

Performs a test for normality.

For a list of all members of this type, see NormalityTest Members.

System.Object
Imsl.Stat.NormalityTest

public class NormalityTest

Thread Safety

Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.

Remarks

Three methods are provided for testing normality: the Shapiro-Wilk W test, the Lilliefors test, and the chi-squared test.

Shapiro-Wilk W Test

The Shapiro-Wilk W test is thought by D'Agostino and Stevens (1986, p. 406) to be one of the best omnibus tests of normality. The function is based on the approximations and code given by Royston (1982a, b, c). It can be used in samples as large as 2,000 or as small as 3. In the Shapiro and Wilk test, W is given by

$W = \left( {\sum {a_i x_{\left( i \right)} } } \right)^2 /\left( {\sum {\left( {x_i - \bar x} \right)^2 } } \right)$

where $x_{(i)}$ is the i-th largest order statistic and x is the sample mean. Royston (1982) gives approximations and tabled values that can be used to compute the coefficients $a_i, i = 1, \ldots, n$ , and obtains the significance level of the W statistic.

Lilliefors Test

This function computes Lilliefors test and its p-values for a normal distribution in which both the mean and variance are estimated. The one-sample, two-sided Kolmogorov-Smirnov statistic D is first computed. The p-values are then computed using an analytic approximation given by Dallal and Wilkinson (1986). Because Dallal and Wilkinson give approximations in the range (0.01, 0.10) if the computed probability of a greater D is less than 0.01, the p-value is set to 0.50. Note that because parameters are estimated, p-values in Lilliefors test are not the same as in the Kolmogorov-Smirnov Test.

Observations should not be tied. If tied observations are found, an informational message is printed. A general reference for the Lilliefors test is Conover (1980). The original reference for the test for normality is Lilliefors (1967).

Chi-Squared Test

This function computes the chi-squared statistic, its p-value, and the degrees of freedom of the test. Argument n finds the number of intervals into which the observations are to be divided. The intervals are equiprobable except for the first and last interval, which are infinite in length.

If more flexibility is desired for the specification of intervals, the same test can be performed with class ChiSquaredTest.

Requirements

Namespace: Imsl.Stat

Assembly: ImslCS (in ImslCS.dll)

NormalityTest Class

Thread Safety

Remarks

Requirements

See Also