 |
 |
A slight correction to my original email (thanks to Darren for pointing out my oversimplification of the issue): At the top of the Jeanette's page, the following text can be found: "Also important is that if you have multiple groups (see third model example) you should not mean center within each group separately. The reason for this is that your continuous covariate may actually describe some of the group differences, and then mean centering within group will remove this important aspect of the covariate. For example, if you have two groups and one is significantly younger than the other, this difference in ages between groups may explain brain activation differences. If you mean center age within each group, then each group's set of ages will be centered about the same value, 0, and then you risk detecting group differences that are actually just attributable to age." This is a true statement. However, the other view is that you can miss group differences using this approach as well. Take for example, covariate B. Covariate B differs between two groups. Within each group covariate B does not correlate with the dependent variable. If you do not mean-center within each group, then the group differences are attributed to covariate B, rather than groups. In summary, one should look at several models to understand the relationship of the covariate with the data before including it in the model and recognize how that not mean centering across the entire sample can confound the group differences even when the covariate is unrelated to the dependent variable. See inline responses below. On Sat, Dec 24, 2011 at 11:16 AM, mmkleung <[log in to unmask]> wrote: > Dear Dr. McLaren, > > Thanks for the website. I got some useful materials there to read further. > > If I run model (3) with the covariates zero-meaned within each group and > find that the slopes modelling GMV and Q1 in group1 and group2 are not > different (i.e. no significant result for 0 0 .5 -.5 or 0 0 -.5 .5), then > I go on to test for the common correlation, but is there any difference > between the following two methods? > > 1) group the two groups of image together in a single column (e.g. using > multiple regression) and study the relationship between GMV and Q1 in all > subjects > 2) do the contrast (0 0 .5 .5) using model (3) > > If yes, is it because model (3) allows difference in variance between > groups to be modelled properly? > It allows for different slopes to be modelled, even if they are not significantly different. In doing so, you can for more of the variance in the data. > > Thanks again for your time and help! > > Best wishes, > Meikei > > ________________________________________ > From: MCLAREN, Donald [[log in to unmask]] > Sent: Saturday, December 24, 2011 12:54 PM > To: mmkleung > Cc: [log in to unmask] > Subject: Re: [SPM] correlation in 1 group or both groups of subjects? > > See inline responses below. > > Best Regards, Donald McLaren > ================= > D.G. McLaren, Ph.D. > Postdoctoral Research Fellow, GRECC, Bedford VA > Research Fellow, Department of Neurology, Massachusetts General Hospital > and > Harvard Medical School > Office: (773) 406-2464 > ===================== > This e-mail contains CONFIDENTIAL INFORMATION which may contain PROTECTED > HEALTHCARE INFORMATION and may also be LEGALLY PRIVILEGED and which is > intended only for the use of the individual or entity named above. If the > reader of the e-mail is not the intended recipient or the employee or agent > responsible for delivering it to the intended recipient, you are hereby > notified that you are in possession of confidential and privileged > information. Any unauthorized use, disclosure, copying or the taking of any > action in reliance on the contents of this information is strictly > prohibited and may be unlawful. If you have received this e-mail > unintentionally, please immediately notify the sender via telephone at > (773) > 406-2464 or email. > > > > On Fri, Dec 23, 2011 at 9:11 PM, mmkleung <[log in to unmask]<mailto: > [log in to unmask]>> wrote: > Dear Dr. McLaren, > > Thanks for your reply. For model (3), are the following design and > contrast correct? > > 2 sample t-test with 2 covariate columns: > > scan for group1: 1 1 1 1 1 0 0 0 0 0 > scan for group2: 0 0 0 0 0 1 1 1 1 1 > Q1 for group1: 3 4 1 2 3 0 0 0 0 0 > Q1 for group2: 0 0 0 0 0 8 6 9 7 5 > > > You need to make sure that the group1 and group2 are zero meaned in each > group. If you specify your covariate as single column, choose interaction > with factor 1, and choose centering Factor 1 mean, then this will happen > automatically. For your example, the covariates should be: > .4 1.4 -1.6 -.6 .4 0 0 0 0 0 > 0 0 0 0 0 1 -1 2 0 -2 > > > contrast for common correlation between groups: 0 0 1 1 > contrast for different correlations between groups: 0 0 1 -1 or 0 0 > -1 1 > > These are correct. However, if you want the actually mean slope, then you > want to use 0 0 .5 .5. The statistics won't change, just the con_ image > values. > > > I have a further question: what does this contrast, 1 -1 0 0, mean? Does > it mean group1>group2 while ignoring the Q1 scores in both groups? For the > Q1 scores differ significantly in both groups in my case, is it an > inappropriate contrast to look at since the assumption of ANCOVA is > violated...? > > You can not interpret the main effect in the presence of an interaction. > For a more detailed explanation, please see: > http://mumford.fmripower.org/mean_centering/ > > If the slopes are not different, then you could use a single covariate > across the two groups. Then you are controlling for Q1 when assessing group > differences, but that is a different question than what you initially asked > about, which was how can I increase the power of detecting an effect of a > covariate. > > Each question potentially requires a different model. > > > Thanks again and Merry Christmas! > > Best wishes, > Meikei > > ________________________________________ > From: MCLAREN, Donald [[log in to unmask]<mailto: > [log in to unmask]>] > Sent: Saturday, December 24, 2011 2:08 AM > To: mmkleung > Cc: [log in to unmask]<mailto:[log in to unmask]> > Subject: Re: [SPM] correlation in 1 group or both groups of subjects? > > There are a number of options: > (1) Do the analysis separately for each group. > > (2) Use a two-sample t-test with a single covariate (assumes same slope > with your covariate across groups) > > (3) Use a two-sample t-test with 2 covariates (one for each group; allows > for a separate slope in each group). > > Depending on what your trying to show you can choose model (2) or (3). > Model 3 will have slightly better results as the error will be lower if the > slopes are slightly, but not significantly different. With model (3), you > can test the average slope. It has the advantage that the results will not > be skewed by group size differences. > > Hope this helps. > > Best Regards, Donald McLaren > ================= > D.G. McLaren, Ph.D. > Postdoctoral Research Fellow, GRECC, Bedford VA > Research Fellow, Department of Neurology, Massachusetts General Hospital > and > Harvard Medical School > Office: (773) 406-2464<tel:%28773%29%20406-2464> > ===================== > This e-mail contains CONFIDENTIAL INFORMATION which may contain PROTECTED > HEALTHCARE INFORMATION and may also be LEGALLY PRIVILEGED and which is > intended only for the use of the individual or entity named above. If the > reader of the e-mail is not the intended recipient or the employee or agent > responsible for delivering it to the intended recipient, you are hereby > notified that you are in possession of confidential and privileged > information. Any unauthorized use, disclosure, copying or the taking of any > action in reliance on the contents of this information is strictly > prohibited and may be unlawful. If you have received this e-mail > unintentionally, please immediately notify the sender via telephone at > (773) > 406-2464 or email. > > > > On Fri, Dec 23, 2011 at 10:58 AM, mmkleung <[log in to unmask]<mailto: > [log in to unmask]><mailto:[log in to unmask]<mailto:[log in to unmask]>>> wrote: > Dear all, > > I'm studying the relationship between grey matter volume (GMV) and > questionnaire scores (Q1, Q2, Q3, Q4). I have two groups of subjects (all > are healthy subjects), whose GMV differ in some regions as revealed by VBM. > They also differ in Q1, Q2 and Q3. Then I extracted the mean GMV values out > from these regions of all subjects. I found two sig. negative correlations > between: GMV values and Q1, GMV values and Q2. However, these correlations > were not found when the analysis is done on each group of subjects > separately. > > Is there any problem to look at the above relationship in all subjects > (for the sake of power), but provided that the 2 groups of subjects have > sig. group difference in GMV in these regions and Q1-3? > > Thanks for your advice! > > Best wishes, > Meikei > > >