Dear Donald and Helmut,
OK, let me summarize the series of discussion. My hypothesis is that V1 and V2 predict activity in different parts of MCC, and I also hope to demonstrate a direct statistical assessment of this difference.
(1). Whole-brain analysis, simple linear regression 1 (independent variable: V1)
<Result 1> activity in aMCC is correlated with V1.
(2). Whole-brain analysis, simple linear regression 2 (independent variable: V2)
<Result 2> activity in pMCC is correlated with V2.
(3). Small-volume correction in MCC (because prior whole-brain analyses reveals MCC, and my hypothesis only focus on MCC.)
Multiple linear regression 1 (independent variables :V1, V2)
<Result 3-1> Contrast "1 0" shows that V1 predicts aMCC activity after regressing out V2's effect;
<Result 3-2> Contrast "0 1" shows that V2 predicts pMCC activity after regressing out V1's effect
<Summary 3-1> Activity in different portions of MCC is significantly predicted by V1 and V2, respectively.
<Summary 3-2> V1 and V2 specifically predict activity in aMCC and pMCC, respectively.
(4). The same model as (3)
<Result 4> Contrast "1 -1" shows that, as compared with V2, V1 predicts aMCC activity;
Contrast "-1 1" shows that, as compared with V1, V2 predicts pMCC activity.
<Summary 4> The effects of V1 and V2 are different in aMCC and pMCC.
(5). The signal in aMCC (from the activated cluster in Result 1) was extracted and plotted against V1 and V2. Also, the signal in pMCC (from Result 2) was extracted and plotted against V1 and V2.
<Result 5> In aMCC, activity is correlated with V1 but not V2, and slopes of both regression lines are significantly different.
In pMCC, activity is correlated with V2 but not V1, and slopes of both regression lines are significantly different.
<Summary 5-1> The effects of V1 and V2 are different in aMCC and pMCC.
(6). Same as (5) but signals in aMCC and pMCC are from Results 3-1 and 3-2. The same Result and Summary as in (5).
OK! My data fulfill Results 1~5, so I make these conclusions:
<Conclusion 1> Activity of aMCC is predicted by V1, which has a more significant effect than V2.
Activity of pMCC is predicted by V2, which has a more significant effect than V1.
<Conclusion 2> There is a functional segregation of MCC in its anterior and posterior portions, with the former specifically affected by V1 and the latter by V2.
Am I correct for all statements above?
Also, I wonder when can I say a "double dissociation" exists. If my results only fulfill Results 1~4 but not Result 5, can I declare there is a double dissociation? Or if I want to use the term, my data must fulfill Results 1~5?
Another question is what's the difference between (6) and (5).
Thank you SO MUCH because these analyses have confused me for a long time!