StatsMultiCorrelationTest

StatsMultiCorrelationTest [/ALPH=alpha /T=k /Z/Q/TUK/CON={controlRow, tails }/CONT=contrastWave ] corrWave, sizeWave

The StatsMultiCorrelationTest operation performs various tests on multiple correlation coefficients. Inputs are two 1D waves: corrWave, containing correlation coefficients, and sizeWave, containing the size (number of elements) of the corresponding samples. Although you can do all the tests at the same time, it rarely makes sense to do so.

Flags

/ALPH=val	Sets the significance level (default val =0.05).
/CDFF=func	Specifies a user function expressing the cumulative distribution function. See Details.
/CON={controlRow,tails }
	Performs a multiple comparison test using the controlRow element of corrWave as a control. It is one- or two-tailed test according to the tails parameter. Output is to the M_ControlCorrTestResults wave in the current data folder.
/CONT=cWave	Performs a multiple contrasts test on the correlation coefficients. The contrasts wave, cWave, contains the contrast factor, ci, entry for each of the n correlation coefficients ri in corrWave, and satisfying the condition that the sum of the entries in cWave is zero. H0 corresponds to
	$\displaystyle \sum_{i=0}^{n-1} c_{i} r_{i}=0 .$
	The test statistic S is
	$\displaystyle S=\left\|\sum_{i=0}^{n-1} c_{i} z_{i}\right\| / \sqrt{\frac{c_{i}^{2}}{n_{i}-3}}$
	where zi is the Fisher z transform of the correlation coefficient ri :
	$\displaystyle z_{i}=\frac{1}{2} \ln \left(\frac{1+r_{i}}{1-r_{i}}\right) .$
	It produces the SE value, the contrast statistic S, and the critical value, which are labeled ContrastSE, ContrastS, and Contrast_Critical, respectively, in the W_StatsMultiCorrelationTest wave.
/DEST=dstWave	Specify the destination wave for the correlation test results. If you do not specify this flag, the results are stored in the wave W_StatsMultiCorrelationTest 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.
/TUK	Performs a Tukey-type multi comparison testing between the correlation coefficients by comparing every possible combination of pairs of correlation coefficients, computing the difference in their z-transforms, the SE, and the q statistic:
	$q=\frac{\left\|z_{j}-z_{i}\right\|}{\sqrt{\frac{1}{2}\left(\displaystyle \frac{1}{n_{i}-3}+\frac{1}{n_{j}-3}\right)}} .$
	The critical value is computed from the q CDF (StatsInvQCDF) with degrees of freedom numWaves and infinity. Output is to the M_TukeyCorrTestResults wave in the current data folder or optionally to a table.
/Z	Ignores errors. V_flag will be set to -1 for any error and to zero otherwise.

Details

Without any flags, StatsMultiCorrelationTest computes

$$\displaystyle \chi^{2}$$

for the correlation coefficients and compares it with the critical value.

$$\chi^{2}=\sum_{i=0}^{n-1} z_{i}^{2}\left(n_{i}-3\right)-\frac{\displaystyle\left(\sum_{i=0}^{n-1} z_{i}\left(n_{i}-3\right)\right)^{2}}{\displaystyle\sum_{i=0}^{n-1}\left(n_{i}-3\right)},$$

where z_i is the Fisher's z transform of the correlation coefficients and n_i is the corresponding sample size. It computes the common correlation coefficient rw and its transform zw.

$$z_{w}=\frac{\displaystyle \sum_{i=0}^{n-1} z_{i}\left(n_{i}-3\right)}{\displaystyle \sum_{i=0}^{n-1}\left(n_{i}-3\right)}$$

These values are calculated even when not appropriate, such as when

$$\displaystyle \chi^{2}$$

exceeds the critical value and H₀ (all samples came from populations of identical correlation coefficients) is rejected.

The operation also computes ChiSquaredP (due to S.R. Paul), a different variant of

$$\displaystyle \chi^{2}$$

that is corrected for bias and should be compared with the same critical value. Output is to the W_StatsMultiCorrelationTest wave in the current data folder or optionally to a table.

References

See, in particular, Chapters 19 and 11 of:

Zar, J.H., Biostatistical Analysis, 4th ed., 929 pp., Prentice Hall, Englewood Cliffs, New Jersey, 1999.

See Also

Statistical Analysis, StatsLinearCorrelationTest, StatsCircularCorrelationTest, StatsDunnettTest, StatsTukeyTest, StatsInvQCDF, StatsScheffeTest

Demos

Open Multi-Correlation Demo.pxp