[FieldTrip] Antw: Re: ANOVA and tails

Fri Sep 2 11:21:59 CEST 2011

Gregor is correct in what he says. I would like to take it one step further.
I hope future statistics books and even Fieldtrip would remove the option of
doing a two tailed t-test. If you want to do a two tail t then simply use F
=t^2. That removes ever needing to say you are doing a two-tail t. However
in doing the one-tailed t you would need to specify which tail. The default
of the t could be an upper tail default so you would simply switch sign if
wanting to to the lower tail. The benefit of this approach is that it can
minimize the errors and complexity of dealing with cfg structures.
Stan

On Fri, Sep 2, 2011 at 2:01 AM, Gregor Volberg <
Gregor.Volberg at psychologie.uni-regensburg.de> wrote:

>  Dear Olga,
>
> Just to add to my former mail:
>
> Another way to think of F and t tests is that the F-Test is _always_
> two-sided, in the sense that it tests for both differences A>B and B>A. So I
> think you already did the test that you intended to do. But formally, the
> rejection region is on the right side of the F distribution, and so it
> should be indicated in the cfg structure.
>
> Cheers,
>
> 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
>
>
>
> >>> "Gregor Volberg" <Gregor.Volberg at psychologie.uni-regensburg.de>
> 9/2/2011 9:45 AM >>>
>
>   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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