No. You will likely get different results due to the unbalanced group
size even without the interaction. Remember the lack of an interaction
does not mean that the groups have the same value. Here is some data
to illustrate the point:
Values:
- +
control 0.3 0.1
MCI 0.2 0
Sample sizes:
- +
control 55 80
MCI 9 27
Two-sample t-test contrasts
control 0.181481481
MCI 0.05
DIFFERENCE 0.131481481 * This is greater than the ANOVA difference of .1
- 0.2859375
+ 0.074766355
DIFFERENCE 0.211171145 * This is greater than the ANOVA difference of .2
As you can see, depending on the distribution of the sample, the
differences in the t-tests can be greater than the ANOVA.
Best Regards, Donald McLaren
=================
D.G. McLaren, Ph.D.
Research Fellow, Department of Neurology, Massachusetts General Hospital and
Harvard Medical School
Postdoctoral Research Fellow, GRECC, Bedford VA
Website: http://www.martinos.org/~mclaren
Office: (773) 406-2464
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On Sun, Jul 29, 2012 at 4:23 PM, Bedda Rosario <[log in to unmask]> wrote:
> Hello,
>
> I have 2 Groups (independent) and 2 levels for Status (independent). In
> addition, I have two covariates, age and gender (coded as 0 and 1).
> I ran two separate t-tests to determine if there was a significance
> difference between the two groups and the two status levels. I found
> significant differences between the two groups (FDR).
>
> However, I thought it will be more appropriate to run a full factorial model
> to determine if there are differences between the groups, differences
> between the status levels and if there is an interaction between Group and
> Status, adjusting for age and gender.
>
> I defined the factorial model as follow.
>
> Factor 1: two levels for Group
> Factor 2: two levels for Status
> For both, independece yes and variance unequal.
>
> Cell 1 1 - Group 1 Status 1
> Cell 1 2 - Group 1 Status 2
>
> Cell 2 1 - Group 2 Status 1
> Cell 2 2 - Group 2 Status 2
>
> I included two covariates: age and gender.
>
> The design matrix is attached.
>
> The t contrasts that I defined were
> Main effects: Group -1 -1 1 1 0 0 (or 1 1 -1 -1 0 0)
> Main effects: Status -1 1 -1 1 0 0 (or 1 -1 1 -1 0 0)
> Interaction between Group and Status 1 -1 -1 1 0 0 (I think this is
> correct?)
>
> After running the analysis, the interaction term was not significant. Since
> the interaction was not significant, I checked the main effects for group
> and status level but there is nothing significant. I thought I will get the
> same results as the t-test since the interaction term was not significant.
>
> Is this correct? I will appreciate any help.
>
> Thank you,
> Bedda
>
>
>
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