levenes_test Subroutine

public subroutine levenes_test(x, stat, p, err)

Computes Levene's test statistic and associated probability.

The statistic is calculated as follows. $$W = \frac{N - k}{k - 1} \frac{ \sum_{i = 1}^{k} N_{i} \left( Z_{i.} - Z{..} \right)^{2}}{ \sum_{i = 1}^{k} \sum_{j = 1}^{n_{i}} \left( Z_{ij} - Z_{i.} \right)^{2} }$$

Where: $$Z_{ij} = |X_{ij} - \overline{X_{i.}}|$$ $$Z_{i.} = \frac{1}{n_{i}} \sum_{j = 1}^{n_{i}} Z_{ij}$$ $$Z_{..} = \frac{1}{N} \sum_{i = 1}^{k} \sum_{j = 1}^{n_{i}} Z_{ij}$$

As the test statistic is approximately F-distributed, the F-distribution is used to calculate the probability term.

See Also

• Wikipedia

Arguments

Type	Intent	Optional	Attributes		Name
type(array_container),	intent(in),		dimension(:)	::	x	The arrays of data to analyze.
real(kind=real64),	intent(out)			::	stat	The Bartlett's test statistic.
real(kind=real64),	intent(out)			::	p	The probability value that the variances of each data set are equivalent. A low p-value, less than some significance level, indicates a non-equivalance of variances.
class(errors),	intent(inout),	optional,	target	::	err

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