StatsKendallTauTest

StatsKendallTauTest [/Q/Z] [/T=k] wave1 [,wave2]

The StatsKendallTauTest operation performs the nonparametric Mann-Kendall test, which computes a correlation coefficient τ (similar to Spearman's correlation) from the relative order of the ranks of the data. Output is to the W_StatsKendallTauTest wave in the current data folder.

Flags

/DEST=ktWave	Specify the destination wave for the test results. If you do not specify this flag, the operation saves this output in the wave W_StatsKendallTauTest in the current data folder.
	This flag was added in Igor Pro 10.00.
/FREE	Creates the user-specified destination wave as a free wave.
	/FREE is allowed only in functions, and only if the destination waves are simple names or wave reference structure fields.
	See Free Waves for more discussion.
	The /FREE flag was added in Igor Pro 10.00.
/Q	No results printed in the history area.
/T=k	Displays results in a table. k specifies the table behavior when it is closed.
	k =0: Normal with dialog (default). k =1: Kills with no dialog. k =2: Disables killing.
/Z	Ignores errors. V_flag will be set to -1 for any error and to zero otherwise.

Details

Inputs may be a pair of XY (1D) waves of any real numeric type or a single 1D wave, which is equivalent to using a pair of XY waves where the X wave is monotonically increasing function of the point number. StatsKendallTauTest ignores wave scaling.

Kendall's τ is 1 for a monotonically increasing input and -1 for monotonically decreasing input. The significance of the test is computed from the normal approximation

$$\displaystyle \operatorname{Var}(\tau)=\frac{4 n+10}{9 n(n-1)},$$

where n is the number of data points in each wave. The significance is expressed as a P-value for the null hypothesis of no correlation.

References

Kendall, M.G., Rank Correlation Methods, 3rd ed., Griffin, London, 1962.

See Also

Statistical Analysis, StatsRankCorrelationTest

For small values of n you can compute the exact probability using the procedure WM_KendallSProbability().