I am conducting a psycholinguistics study for a term paper in which I investigate how young children interpret "ambiguous" sentences such as "The dog ate the food on the table" in my native language.
What I mean by ambiguity is that "on the table" could be referring to the location of the food (noun-location), or it could refer to the location where the dog performs the action of eating (action-location).
I am trying to find out whether children have a bias towards one of these interpretations, i.e., whether there is a difference between the frequency of "noun-location" and "action-location" interpretations.
I have tested all children with 4 such sentences in total. So the number of every individual child's total noun-location and action-location interpretations vary between 0 and 4, depending on their biases. (e.g., a child who had a noun-location bias could have interpreted all sentences like that, and then his/her score for noun-location would be 4, while his/her score for action-location would be 0. But if a child gives random responses, s/he may have interpreted 2 sentences as having noun-location and 2 sentences as having action-location, etc.)
I have detected that there is a considerable bias towards noun-location interpretations at the group level, but I'd like to show that this is statistically significantly different from chance as well. (The group mean is somehwere around 3.4 over 4 for noun-location readings, so I anticipate that it should be indeed significantly different from 2 over 4, which we would expect if the interpretations were completely random.)
But which test would be appropriate to test my data against chance here?