StatsScheffeTest

StatsScheffeTest [/ALPH=val /T=k /Q/SWN/Z/WSTR=waveListString /CONW=contrastWave ] [wave1, wave2,... wave100 ]

The StatsScheffeTest operation performs Scheffe's test for the equality of the means. It supports two basic modes: the default tests all possible combinations of pairs of waves; the second tests a single combination where the precise form of H₀ is determined by the coefficients of a contrast wave (see /CONT). Output is to the M_ScheffeTestResults wave in the current data folder.

Flags

/ALPH=val	Sets the significance level (default val =0.05).
/CONW=cWave	Performs a multiple contrasts test. cWave has one point for each input wave. The cWave value is 1 to include the corresponding (zero based) input wave in the first group, 2 to include the wave in the second group, or zero to exclude the wave.
	The contrast is defined as the difference between the normalized sum of the ranks of the first group and that of the second group. If cWave ={0,1,1,1,2}, then the contrast hypothesis H0 corresponds to:
	$\displaystyle \frac{\bar{X}_{1}+\bar{X}_{2}+\bar{X}_{3}}{3}-\bar{X}_{4}=0$
	For each pair of waves $\displaystyle (i, j)$ with $\displaystyle i \neq j$, it computes
	$S E_{i j}=\sqrt{s^{2}\left(\frac{1}{n_{j}}+\frac{1}{n_{i}}\right)}, \quad s^{2}=\sum_{i=1}^{W} \sum_{j=0}^{n_{j}-1} X_{j}^{2}-\sum_{i=1}^{W} \frac{\displaystyle \left(\sum_{j=0}^{n_{j}-1} X_{j}\right)^{2}}{n_{j}},$
	the statistic
	$S=\frac{\displaystyle \left\|\sum_{i=0}^{n-1} c_{i} \bar{X}_{i}\right\|}{S E},$
	the critical value, and a result field which is set to 1 if H0 should be accepted or 0 if it should be rejected. W is the total number of waves, ni and $\displaystyle \bar{X}_{i}$ are respectively the number of data points and the average of wave i.
/DEST=dstWave	Specify the destination wave for the Scheffe test results. If you do not use this flag, the results are stored in the wave M_ScheffeTestResults in the current data folder.
	This flag was added in Igor Pro 10.00.
/DSTL=labWave	Specify the destination text wave for the descriptors of the test results (see /SWN). If you do not use this flag, the operation saves the text in the wave T_ScheffeDescriptors in the current data folder.
	This flag was added in Igor Pro 10.00.
/FREE	Creates the user-specified destination waves as free waves.
	/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.
/SWN	Creates a text wave, T_ScheffeDescriptors, containing wave names corresponding to each row of the comparison table (Save Wave Names). Use /T to append the text wave to the last column.
/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.
	The table is associated with the test, not the data. If you repeat the test, it will update any existing table with the new results.
/WSTR=waveListString
	Specifies a string containing a semicolon-separated list of waves that contain sample data. Use waveListString instead of listing each wave after the flags.
/Z	Ignores errors. V_flag will be set to -1 for any error and to zero otherwise.

Details

The default of StatsScheffeTest (also known as the S test) tests the hypotheses of equality of means for each possible pair of samples. It is not as powerful as Tukey's test (StatsTukeyTest) and is more useful for hypotheses formulated as multiple contrasts (see /CONT).

References

See, in particular, Chapter 11 of:

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

See Also

Statistical Analysis, StatsANOVA1Test, StatsDunnettTest, StatsTukeyTest

Demos

Open Scheffe-Test Demo.pxp