I have two groups - one group which was presented with one picture of a politician with his wife, one group where the politician was alone. Participants in each group also answered questions (as a Likert-scale item) on how likely they were to vote for that politician.
I need to compare how likely each group was to vote for that politician, and compare.
Which would be the best statistical test to use?
If the number of observations is reasonably large and the distribution of responses not too jammed up one end or the other, a plain two-sample t-test may be reasonable, especially if you would be prepared to add such an item to similar Likert-scale items to produce a scale, were additional items available (this illustrates preparedness to assume that the scale-intervals are equispaced).
It is possible to take a nonparametric approach such as with a Mann-Whitney/Wilcoxon but the heavy ties make this approach only about as good as the $t$ in many cases.
A more easily justified approach might be to deal with the ordered categorical response more directly, and look at a regression model that deal with it (where there's a dummy to signify membership of the second group), such as say proportional odds models, cumulative logit ("grouped-continuous") models, continuation-ratio models, polytomous logistic models, adjacent-category logistic models or stereotype logistic models.
