Can Chi Square be Used for a Mixed Design with Repeated Measures?

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My lab partner and I are trying to recreate this experiment:
http://www.blackwell-synergy.com/doi/pdf/10.1111/j.1467-9280.2006.01731.x?
This appears to be a mixed design.
Half the participants were put in a positive mood and half were put into a neutral mood. After the mood induction, each group solved two moral dilemmas (the Footbridge Dilemma and the Trolley Dilemma).
The type of dilemma is one of the independant variables and is a repeated measure because each group has to solve both moral dilemmas.

Now, it seems the authors use a chi square to analyze the results, and my lab partner and I are really struggling because neither of us ever learned to use chi squares (just ANOVA). I called up a friend who is a stats prof and he says that he seems to recall that a chi square can't be used if there are repeated measures in the design.

But somehow the authors are doing it. From the table on the 2nd page of article, it looks like they only analyze one level of the "type of dilemma" IV at a time. (i.e., they just looked only at responses to the Footbridge Dilemma and then looked only at reponses to the Trolley Dilemma).
So, I guess you can use chi square for a design that involves repeasted measures for one of the IVs?
thanks.
 
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oh, and we were planning on only two reponse choices for a dilemma: "appropriate" or "inappropriate", just as the authors did.
 
ok, never mind. we are going to use a different measure for the dependent variable.
 
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