[FieldTrip] Antw: Re: ANOVA and tails

[Gregor Volberg]

Dear Olga and Gopa, 

I would like to comment on this discussion because I fear that there could be
some misunderstandings. 
Unlike t, the F statistic is not sensitive to the direction of a difference.
The  t value gets positive if means of group A > group B, and negative if B >
A. Therefore, the hypothesis that A >< B can be tested on both tails of the t
distribution. On contrast, the F value gets positive if A > B as well as if B >
A. Small values of F, on the left tail of the distribition, indicate that there
is no difference between means of A and B. This is why a left tail or a
two-tailed test does not make sense with an F-Test.  
So Olga, if you have a two-group design, and if you want to apply a left- or
two-tailed test, then use the t statistic. Beware that the two-sided test is
usually considered more (not less) conservative that the one-sided test. This
is because the critical value of t increases for two-sided tests. It is the
size if the rejection region for H0 that needs to be halved, not the one-sided
critical value of your test statistic. For example, a result of t(20)= 1.9 is
significant in a one-tail right-sided test where it exceeds the critical value
of 1.72 (the 0.95 quantile of a t distribution with 20 df). But it is not
significant in a two sided test where the critical values are 2.09 (0.975
quantile) and -2.09 (0.025 quantile). 

Best regards, 
Gregor 




-- 
Dr. rer. nat. Gregor Volberg <gregor.volberg at psychologie.uni-regensburg.de> (
mailto:gregor.volberg at psychologie.uni-regensburg.de )
University of Regensburg
Institute for Experimental Psychology
93040 Regensburg, Germany
Tel: +49 941 943 3862 
Fax: +49 941 943 3233
http://www.psychologie.uni-regensburg.de/Greenlee/team/volberg/volberg.html


>>> Gopakumar Venugopalan <venug001 at crimson.ua.edu> 9/1/2011 6:58 PM >>>

Dear Olga, this does not mean only right tail is possible. You could have a
positive or negative sign for your test statistic, which is acceptable. That
can be fixed in Fieldtrip or EEGLAB by the order you enter Condition1 and
Condition 2. But to answer your question more substantively: 

A one-tail test is more consevervative than a two-tail test. A two-tail test
is when you have no a priori expectation where you expect the condition 1 -
condition 2 to be higher or lower. Using a non EEG example if you have two
groups treatment and control, you will expect yoga to lower the depression
rates in treatment group and not the control group. 

Similarly if you have two groups treatment and control, you will expect some
protein shake to yield higher muscle mass in the treatment group and not the
control group. In both cases the outcome (negative or lower in scenario one,
higher or positive on scenario two) is an a priori expectation. So in a EEG
sense we know that the Incongruent or deviant word will have a higher
displacement than the congruent or expected word.. 

Going back to the conservative versus liberal nature of the statistic. 

If the tabled value of the F (df1=1, df2=11) is 4.84 that is the size of the
tail or the reject region, however when you halve that you tabled value is half
of it. So you obtained value in the first case would have to be greater than
4.85, while in the two-tail case it slide with anything over 2.43. Therefore
the two-tail is not only for exploratory purposes, but is also less
conservative. 


I hope I have helped. 


Warm regards 

gopa


On Thu, Sep 1, 2011 at 7:51 AM, Sysoeva, Olga Vladimirovna
<sysoevao at psychiatry.wustl.edu> wrote:



Dear Fieldtrippers, 
I’ve tried to use between subject ANOVA (independentF) and a bit confused with
the tails. 
I’ve got the following message 
“For an independent samples F-statistic, it does not make sense to calculate a
two-sided critical value.” 
Could you explain me why? Why only right tail is possible? 
Best Regards, 
Olga. 
____________________________________________________________________________ 
Olga Sysoeva, 
Research Associate, PhD 
Psychiatry Department, 
Washington University School of Medicine 
Campus Box 8134 
660 South Euclid Ave 
Saint Louis, MO 63110-9909 


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