bartletts_test Subroutine

public subroutine bartletts_test(x, stat, p)

Computes Bartlett's test statistic and associated probability.

The statistic is calculated as follows.

$$\chi^{2} = \frac{(N - k) \ln(S_{p}^{2}) \sum_{i = 1}^{k} \left(n_{i} - 1 \right) \ln(S_{i}^{2})}{1 + \frac{1}{3 \left( k - 1 \right)} \left( \sum_{i = 1}^{k} \left( \frac{1}{n_{i} - 1} \right) - \frac{1}{N - k} \right)}$$

Where $N = \sum_{i = 1}^{k} n_{i}$ and $S_{p}^{2}$ is the pooled variance.

The probability is calculated as the right-tail probability of the chi-squared distribution.

Bartlett's test is most relevant for distributions showing strong normality. For distributions lacking strong normality, consider Levene's test instead.

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.

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