# naginterfaces.library.correg.coeffs_​kspearman¶

naginterfaces.library.correg.coeffs_kspearman(x, itype)[source]

coeffs_kspearman computes Kendall and/or Spearman nonparametric rank correlation coefficients for a set of data; the data array is preserved, and the ranks of the observations are not available on exit from the function.

For full information please refer to the NAG Library document for g02bq

https://www.nag.com/numeric/nl/nagdoc_29/flhtml/g02/g02bqf.html

Parameters
xfloat, array-like, shape

must be set to data value , the value of the th observation on the th variable, for , for .

itypeint

The type of correlation coefficients which are to be calculated.

Only Kendall’s tau coefficients are calculated.

Both Kendall’s tau and Spearman’s coefficients are calculated.

Only Spearman’s coefficients are calculated.

Returns
rrfloat, ndarray, shape

The requested correlation coefficients.

If only Kendall’s tau coefficients are requested (), contains Kendall’s tau for the th and th variables.

If only Spearman’s coefficients are requested (), contains Spearman’s rank correlation coefficient for the th and th variables.

If both Kendall’s tau and Spearman’s coefficients are requested (), the upper triangle of contains the Spearman coefficients and the lower triangle the Kendall coefficients.

That is, for the th and th variables, where is less than , contains the Spearman rank correlation coefficient, and contains Kendall’s tau, for , for .

(Diagonal terms, , are unity for all three values of .)

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: or .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

The input data consists of observations for each of variables, given as an array

where is the th observation on the th variable.

The observations are first ranked, as follows.

For a given variable, say, each of the observations, , has associated with it an additional number, the ‘rank’ of the observation, which indicates the magnitude of that observation relative to the magnitude of the other observations on that same variable.

The smallest observation for variable is assigned the rank , the second smallest observation for variable the rank , the third smallest the rank , and so on until the largest observation for variable is given the rank .

If a number of cases all have the same value for the given variable, , then they are each given an ‘average’ rank – e.g., if in attempting to assign the rank , observations were found to have the same value, then instead of giving them the ranks

all observations would be assigned the rank

and the next value in ascending order would be assigned the rank

The process is repeated for each of the variables.

Let be the rank assigned to the observation when the th variable is being ranked.

The quantities calculated are:

1. Kendall’s tau rank correlation coefficients:

 where sign(u)=1 if u>0 sign(u)=0 if u=0 sign(u)=−1 if u<0

and , being the number of ties of a particular value of variable , and the summation being over all tied values of variable .

2. Spearman’s rank correlation coefficients:

where where is the number of ties of a particular value of variable , and the summation is over all tied values of variable .

References

Siegel, S, 1956, Non-parametric Statistics for the Behavioral Sciences, McGraw–Hill