*Based on the information provided, its obvious the participants were asked same question, but have different backgrouds. If I may say you are trying to find if answers given by participants from different groups have anything to do with their backgrouds. I also assume you hope to find the probability that an answer given by a participant is most likely to come from a particular group in a given situation. In cases like this, one of the groups is usually used as a control group
In order to compare the two groups of the participants, we need to establish that there is a significant association between two groups with regards to their answers. Chi-square is normally used for this.
Then, once we are convinced that association exists between the two groups; we need to find out how their answers influence their backgrounds .
From your example, say the G1 represent children with formal education and while G2 represents children without formal education. A picture was presented to each child and asked to identify the event in the picture. Those who identified the event in the picture were coded 1 and those who got theirs' wrong were coded 0.
A good model used for this analysis is logistic regression model, given by log(p/(1-p))=β_0+β_1 X,where p is a binomail proportion and x is the explanantory variable.
The parameters of logistic model are β_0 and β_1. In this case, n= 10 samples each group. The explanatory variable is children groups, coded ‘1’ if the children have formal education, ‘0’ if no formal education. The response variable is also an indicator variable which is "occupation identfication" – coded ‘1’ if they were identified correctly, ‘0’ if not. The model says that the probability ( p) that an occupation will be identifed by a child depends upon if the child has formal education(x=1) or no formal education( x = 0).
So there are two possible values for p, say, p_(formal education) and p_(no formal education) .
The logistic regression model specifies the relationship between p and x.
Since there are only two values for x, we write both equations. For children groups with formal education,
For children groups with no formal education
log(P_(noformaleducation)/(1-P_(no formal education) ))=β_0
Note that there is a β_1term in the equation for children group with formal education because x = 1, but it is
missing in the equation for children group with no formal education because x = 0.*