<div>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.</div>
<div>Stan <br><br></div>
<div class="gmail_quote">On Fri, Sep 2, 2011 at 2:01 AM, Gregor Volberg <span dir="ltr"><<a href="mailto:Gregor.Volberg@psychologie.uni-regensburg.de" target="_blank">Gregor.Volberg@psychologie.uni-regensburg.de</a>></span> wrote:<br>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">Dear Olga,</font> </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">Just to add to my former mail:</font> </p><br>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">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.</font> </p>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">Cheers,</font> </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">Gregor</font> </p>
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<div><br><br><font style="FONT-SIZE: 10pt" face="Dialog"><br>-- <br>Dr. rer. nat. Gregor Volberg <<a href="mailto:gregor.volberg@psychologie.uni-regensburg.de" target="_blank">gregor.volberg@psychologie.uni-regensburg.de</a>> ( mailto:<a href="mailto:gregor.volberg@psychologie.uni-regensburg.de" target="_blank">gregor.volberg@psychologie.uni-regensburg.de</a> ) <br>
University of Regensburg <br>Institute for Experimental Psychology <br>93040 Regensburg, Germany <br>Tel: <a href="tel:%2B49%20941%20943%203862" target="_blank" value="+499419433862">+49 941 943 3862</a> <br>Fax: <a href="tel:%2B49%20941%20943%203233" target="_blank" value="+499419433233">+49 941 943 3233</a> <br>
<a href="http://www.psychologie.uni-regensburg.de/Greenlee/team/volberg/volberg.html" target="_blank">http://www.psychologie.uni-regensburg.de/Greenlee/team/volberg/volberg.html </a><br><br><br></font></div>>>> "Gregor Volberg" <<a href="mailto:Gregor.Volberg@psychologie.uni-regensburg.de" target="_blank">Gregor.Volberg@psychologie.uni-regensburg.de</a>> 9/2/2011 9:45 AM >>><br>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">Dear Olga and Gopa,</font> </p>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">I would like to comment on this discussion because I fear that there could be some misunderstandings.</font> </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">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. </font></p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">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).</font> </p>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">Best regards,</font> </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><font size="2" face="Dialog">Gregor</font> </p>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px"><br><br><span style="FONT-FAMILY: 'Dialog'"><br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt">-- <br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt">Dr. rer. nat. Gregor Volberg <<a href="mailto:gregor.volberg@psychologie.uni-regensburg.de" target="_blank">gregor.volberg@psychologie.uni-regensburg.de</a>> ( mailto:<a href="mailto:gregor.volberg@psychologie.uni-regensburg.de" target="_blank">gregor.volberg@psychologie.uni-regensburg.de</a> )<br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt">
University of Regensburg<br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt">Institute for Experimental Psychology<br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt">93040 Regensburg, Germany<br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt">
Tel: <a href="tel:%2B49%20941%20943%203862" target="_blank" value="+499419433862">+49 941 943 3862</a> <br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt">Fax: <a href="tel:%2B49%20941%20943%203233" target="_blank" value="+499419433233">+49 941 943 3233</a><br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt">
<a href="http://www.psychologie.uni-regensburg.de/Greenlee/team/volberg/volberg.html" target="_blank">http://www.psychologie.uni-regensburg.de/Greenlee/team/volberg/volberg.html</a><br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt">
<br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt"><br style="FONT-FAMILY: Dialog; FONT-SIZE: 10pt"></span>>>> Gopakumar Venugopalan <<a href="mailto:venug001@crimson.ua.edu" target="_blank">venug001@crimson.ua.edu</a>> 9/1/2011 6:58 PM >>><br>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px">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: </p>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px">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. </p>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px">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.. </p>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px">Going back to the conservative versus liberal nature of the statistic. </p></div>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px">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. </p>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px">I hope I have helped. </p></div>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px">Warm regards </p></div>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px">gopa<br><br></p></div>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px">On Thu, Sep 1, 2011 at 7:51 AM, Sysoeva, Olga Vladimirovna <span dir="ltr"><<a href="mailto:sysoevao@psychiatry.wustl.edu" target="_blank">sysoevao@psychiatry.wustl.edu</a>></span> wrote:<br>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" class="MsoNormal">Dear Fieldtrippers, </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" class="MsoNormal">I’ve tried to use between subject ANOVA (independentF) and a bit confused with the tails. </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" class="MsoNormal">I’ve got the following message </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" class="MsoNormal"> “For an independent samples F-statistic, it does not make sense to calculate a two-sided critical value.” </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" class="MsoNormal">Could you explain me why? Why only right tail is possible? </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" class="MsoNormal">Best Regards, </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" class="MsoNormal">Olga. </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" class="MsoNormal">____________________________________________________________________________ </p>
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<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" class="MsoNormal">Psychiatry Department, </p>
<p style="MARGIN-TOP: 0px; MARGIN-BOTTOM: 0px" class="MsoNormal">Washington University School of Medicine </p>
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