[Eeglablist] Million dollar question

Wed Nov 7 04:21:09 PST 2007

Rael,

the anova2 routine in the matlab statistics toolbox is not appropriate
for repeated measures anova, since it assumes a fixed effects model,
which is not the case for repeated measures anova
(http://www.mathworks.com/support/solutions/data/1-15PD2.html?product=ST&solution=1-15PD2).

Which ANOVA is appropriate depends on the factorial design (within
factors, between factors,....). 

If you want to calculate repeated measures in Matlab I would suggest to
use the code attached below from A. Trujillo-Ortiz.

At Matlab Central
(http://www.mathworks.com/matlabcentral/fileexchange/loadCategory.do )
you can find
several solutions for calculating ANOVAs and Greenhouse-Geisser
estimation. (Though I see no reason why to use Matlab for statistics if
one has Statistica or R ;-) )

Best regards, Sven.

> A collaborator of mine asked about the different ANOVA calculation in
> Statistica vs. Matlab. He attached numerical inconsistent results
> between the two programs. If any Statistica savvy researcher could
> enlighten us, we would be grateful.
>
> Arno
>
> ------------------------------------------------------------------------
>
> Betreff:
> ANOVA Calculation in Statistica vs. Matlab
> Von:
> "Rael Cahn" <rael at ucsd.edu>
> Datum:
> Tue, 6 Nov 2007 23:36:21 -0800
> An:
> "'Arnaud Delorme'" <arno at salk.edu>
>
> An:
> "'Arnaud Delorme'" <arno at salk.edu>
>
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> Dear List,
>
>  
>
> I have come up with an inconsistency between the repeated-measures ANOVA
> output of Statistica and Matlab for a simple 2 factor analysis of a 2x3 ERP
> dataset with N=16 corresponding to ERP values for two cognitive states at 3
> midline electrodes.
>
>  
>
> The settings in Statisca were "Repeated Measures ANOVA" with factors State
> and Channel.  The statistics script in Matlab was "ANOVA2" - Two way
> analysis of variance with factors State and Channel as above
> (anova2(A1,16)).
>
>  
>
> The ANOVA analyses of these data in Statistica and Matlab generated the
> exact same SS, MS, and dF but the F and p values were significantly
> different as indicated here:
>
>  
>
> For Statistica: 
>
> Main effect of State: F- 3.69898 p- 0.073639
>
> Main effect of Channel: F- 0.71071, p- 0.499382
>
> State X Channel Interaction: F- 0.48295, p- 0.621676
>
>  
>
> For Matlab:
>
> Main effect of State: F- 2.88 p- 0.0932
>
> Main effect of Channel: F- 0.18, p- 0.8338
>
> State X Channel Interaction: F- 0.06, p- 0.9442
>
>  
>
> Does anyone have an idea as to why the two ANOVA in Statistica and Matlab
> generates such different values and, if so, which is more appropriate for
> use with ERP data???
>
>  
>
>  
>
>  
>
> (incidentally a bootstrap/permutation analysis of the significance for state
> run in Matlab generated a p-value of 0.0149 for State1 vs. State2)
>
>  
>
>  
>
> Here's the data:
>
>  
>
> State1 Ch1
>
> 7.768
>
> 5.615
>
> 0.3074
>
> 0.762
>
> 5.4652
>
> 2.6145
>
> 2.5397
>
> 8.2239
>
> 8.4658
>
> -4.9788
>
> 6.0245
>
> 4.0349
>
> 9.6742
>
> 11.5664
>
> 8.3378
>
> 6.6524
>
>  
>
>  
>
>  
>
> State1 Ch2
>
> 7.2829
>
> 4.9909
>
> 0.9792
>
> 2.3317
>
> 5.3813
>
> 4.608
>
> 4.5485
>
> 10.8874
>
> 10.4529
>
> -7.5731
>
> 8.7319
>
> 4.5726
>
> 12.9894
>
> 13.372
>
> 8.6935
>
> 4.3401
>
>  
>
> State1 Ch3
>
> 5.6541
>
> 2.689
>
> 0.9022
>
> 2.4779
>
> 3.9023
>
> 6.1488
>
> 5.0258
>
> 14.2864
>
> 9.7666
>
> -1.8947
>
> 5.7047
>
> 4.0641
>
> 13.8596
>
> 9.012
>
> 7.5569
>
> 6.0009
>
>  
>
> State2 Ch1
>
> 2.2808
>
> 2.7393
>
> 0.4708
>
> -1.2193
>
> 9.3576
>
> 4.1422
>
> 0.5838
>
> 7.6672
>
> 1.4603
>
> 1.9716
>
> 7.359
>
> 3.5934
>
> 5.399
>
> 9.1324
>
> 6.3965
>
> 4.4362
>
>  
>
> State2 Ch2
>
> 3.6114
>
> 3.6278
>
> 3.4012
>
> -2.3031
>
> 5.7399
>
> 3.1817
>
> 1.9795
>
> 9.106
>
> 2.1827
>
> -0.69
>
> 4.7947
>
> 5.1603
>
> 8.158
>
> 13.6168
>
> 4.4405
>
> 2.0521
>
>  
>
> State2 Ch3
>
> 4.5252
>
> 5.7949
>
> 5.5186
>
> -2.5002
>
> 3.0347
>
> 5.237
>
> 1.3336
>
> 11.7375
>
> 2.058
>
> -1.094
>
> 3.0639
>
> 6.0547
>
> 10.9694
>
> 9.8537
>
> 1.5573
>
> 5.0396
>
>  
>
> Here is the data presented in tabular for for ease of manipulation in
> Matlab: 
>
>  
>
> (column 1 corresponds to ERP values at Ch1, column2 to ERP values at Ch2,
> column3 to ERP values at Ch3; Rows 1-16 correspond to ERP values during
> cognitive state 1 and Rows 17-32 correspond to ERP values during cognitive
> state 2)
>
>  
>
> A1 = [ ...
>
> 7.768   7.2829  5.6541;
>
> 5.615   4.9909  2.689;
>
> 0.3074  0.9792  0.9022;
>
> 0.762   2.3317  2.4779;
>
> 5.4652  5.3813  3.9023;
>
> 2.6145  4.608   6.1488;
>
> 2.5397  4.5485  5.0258;
>
> 8.2239  10.8874 14.2864;
>
> 8.4658  10.4529 9.7666;
>
> -4.9788 -7.5731 -1.8947;
>
> 6.0245  8.7319  5.7047;
>
> 4.0349  4.5726  4.0641;
>
> 9.6742  12.9894 13.8596;
>
> 11.5664 13.372  9.012;
>
> 8.3378  8.6935  7.5569;
>
> 6.6524  4.3401  6.0009;
>
> ...
>
> 2.2808  3.6114  4.5252;
>
> 2.7393  3.6278  5.7949;
>
> 0.4708  3.4012  5.5186;
>
> -1.2193 -2.3031 -2.5002;
>
> 9.3576  5.7399  3.0347;
>
> 4.1422  3.1817  5.237;
>
> 0.5838  1.9795  1.3336;
>
> 7.6672  9.106   11.7375;
>
> 1.4603  2.1827  2.058;
>
> 1.9716  -0.69   -1.094;
>
> 7.359   4.7947  3.0639;
>
> 3.5934  5.1603  6.0547;
>
> 5.399   8.158   10.9694;
>
> 9.1324  13.6168 9.8537;
>
> 6.3965  4.4405  1.5573;
>
> 4.4362  2.0521  5.0396 ];
>
>  
>
> anova2(A1,16)
>
>
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>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>Dear List,<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>I have come up with an inconsistency between the
> repeated-measures ANOVA output of Statistica and Matlab for a simple 2 =
> factor analysis
> of a 2x3 ERP dataset with N=3D16 corresponding to ERP values for two =
> cognitive
> states at 3 midline electrodes.<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>The settings in Statisca were “Repeated =
> Measures
> ANOVA” with factors State and Channel.  The statistics script =
> in
> Matlab was “ANOVA2” – Two way analysis of variance =
> with
> factors State and Channel as above =
> (anova2(A1,16)).<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>The ANOVA analyses of these data in Statistica and =
> Matlab
> generated the exact same SS, MS, and dF but the F and p values were
> significantly different as indicated here:<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>For Statistica: <o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>Main effect of State: F- 3.69898 p- =
> 0.073639<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>Main effect of Channel: F- 0.71071, p- =
> 0.499382<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>State X Channel Interaction: F- 0.48295, p- =
> 0.621676<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>For Matlab:<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>Main effect of State: F- 2.88 p- =
> 0.0932<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>Main effect of Channel: F- 0.18, p- =
> 0.8338<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>State X Channel Interaction: F- 0.06, p- =
> 0.9442<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>Does anyone have an idea as to why the two ANOVA in
> Statistica and Matlab generates such different values and, if so, which =
> is more
> appropriate for use with ERP data???<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>(incidentally a bootstrap/permutation analysis of the =
> significance
> for state run in Matlab generated a p-value of 0.0149 for State1 vs. =
> State2)<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>Here’s the data:<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>State1 Ch1<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>7.768<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.615<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>0.3074<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>0.762<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.4652<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.6145<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.5397<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>8.2239<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>8.4658<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>-4.9788<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>6.0245<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.0349<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>9.6742<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>11.5664<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>8.3378<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>6.6524<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'> <o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>State1 Ch2<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>7.2829<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.9909<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>0.9792<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.3317<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.3813<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.608<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.5485<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>10.8874<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>10.4529<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>-7.5731<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>8.7319<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.5726<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>12.9894<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>13.372<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>8.6935<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.3401<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>State1 Ch3<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.6541<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.689<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>0.9022<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.4779<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>3.9023<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>6.1488<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.0258<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>14.2864<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>9.7666<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>-1.8947<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.7047<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.0641<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>13.8596<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>9.012<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>7.5569<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>6.0009<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'> <o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>State2 Ch1<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.2808<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.7393<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>0.4708<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>-1.2193<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>9.3576<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.1422<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>0.5838<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>7.6672<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>1.4603<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>1.9716<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>7.359<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>3.5934<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.399<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>9.1324<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>6.3965<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.4362<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'> <o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>State2 Ch2<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>3.6114<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>3.6278<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>3.4012<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>-2.3031<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.7399<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>3.1817<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>1.9795<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>9.106<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.1827<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>-0.69<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.7947<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.1603<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>8.158<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>13.6168<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.4405<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.0521<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>State2 Ch3<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.5252<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.7949<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.5186<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>-2.5002<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>3.0347<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.237<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>1.3336<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>11.7375<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.058<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>-1.094<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>3.0639<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>6.0547<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>10.9694<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>9.8537<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>1.5573<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.0396<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>Here is the data presented in tabular for for ease of
> manipulation in Matlab: <o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'> <o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>(column 1 corresponds to ERP values at Ch1, column2 =
> to ERP
> values at Ch2, column3 to ERP values at Ch3; Rows 1-16 correspond to ERP =
> values
> during cognitive state 1 and Rows 17-32 correspond to ERP values during
> cognitive state 2)<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>A1 =3D [ ...<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>7.768   7.2829  =
> 5.6541;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.615   4.9909  =
> 2.689;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>0.3074  0.9792  =
> 0.9022;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>0.762   2.3317  =
> 2.4779;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.4652  5.3813  =
> 3.9023;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.6145  4.608   =
> 6.1488;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.5397  4.5485  =
> 5.0258;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>8.2239  10.8874 =
> 14.2864;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>8.4658  10.4529 =
> 9.7666;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>-4.9788 -7.5731 -1.8947;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>6.0245  8.7319  =
> 5.7047;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.0349  4.5726  =
> 4.0641;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>9.6742  12.9894 =
> 13.8596;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>11.5664 13.372  =
> 9.012;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>8.3378  8.6935  =
> 7.5569;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>6.6524  4.3401  =
> 6.0009;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>...<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.2808  3.6114  =
> 4.5252;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>2.7393  3.6278  =
> 5.7949;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>0.4708  3.4012  =
> 5.5186;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>-1.2193 -2.3031 -2.5002;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>9.3576  5.7399  =
> 3.0347;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.1422  3.1817  =
> 5.237;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>0.5838  1.9795  =
> 1.3336;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>7.6672  9.106   =
> 11.7375;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>1.4603  2.1827  =
> 2.058;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>1.9716  -0.69   =
> -1.094;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>7.359   4.7947  =
> 3.0639;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>3.5934  5.1603  =
> 6.0547;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>5.399   8.158   =
> 10.9694;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>9.1324  13.6168 =
> 9.8537;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>6.3965  4.4405  =
> 1.5573;<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>4.4362  2.0521  5.0396 =
> ];<o:p></o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'><o:p> </o:p></span></font></p>
>
> <p class=3DMsoNormal><font size=3D2 face=3DArial><span =
> style=3D'font-size:10.0pt;
> font-family:Arial'>anova2(A1,16)<o:p></o:p></span></font></p>
>
> </div>
>
> </body>
>
> </html>
>
> ------=_NextPart_000_0009_01C820CD.D648D120--
>
>
>   
> ------------------------------------------------------------------------
>
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-- 
Sven Hoffmann

Institut für Arbeitsphysiologie 
an der Universität Dortmund (IfADo) 

Ardeystr. 67 
44139 Dortmund
Germany

[phone]		+49 (0)231 1084 338
[fax]		+49 (0)231 1084 401
[email]		shoffmann at ifado.de
[web] 		http://www.ifado.de/neurophys

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