_r22#

pycafee.sample.outliers.Dixon._r22(self, x_exp, which)#

The equation to calculate the Dixon statsitic for the r22 ratio as described at [1]

Parameters

x_expnumpy array

One dimension numpy array with the data ordered.

whichstr

The value that should be evaluated.

If it is "max" (or None), the highest value is checked if it is a possible outlier.
If it is "min", the lowest value is checked.

Notes

If which=="min", the equation used is:

\[r_{22} = \frac{x_3-x_{1}}{x_{n-2}-x_1}\]

If which=="max", the equation used is:

\[r_{22} = \frac{x_n-x_{n-2}}{x_{n}-x_3}\]

References

1: DIXON, W. J. Processing Data for Outliers. Biometrics, v. 9, n. 1, p. 74–89, 1953.

Examples

>>> from pycafee.sample.dixon import Dixon
>>> import numpy as np
>>> x_exp = np.array([159, 153, 184, 153, 156, 150, 147])
>>> x_exp.sort(kind='quicksort')
>>> teste = Dixon()
>>> result = teste._r22(x_exp, which="min")
>>> print(result)
0.6666666666666666
>>> result = teste._r22(x_exp, which="max")
>>> print(result)
0.9032258064516129

>>> from pycafee.sample.dixon import Dixon
>>> import numpy as np
>>> x_exp = np.array([15.42, 15.51, 15.52, 15.53, 15.68, 15.52, 15.56, 15.53, 15.54, 15.56])
>>> x_exp.sort(kind='quicksort')
>>> teste = Dixon()
>>> result = teste._r22(x_exp, which="min")
>>> print(result)
0.7142857142857089
>>> result = teste._r22(x_exp, which="max")
>>> print(result)
0.7499999999999944

_r21

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