How do I analyze data for multilevel pairwise comparisons?

Question

I am trying to run a study using Pairwise comparisons.

Essentially, I have two groups of images: Group A (containing 107 different images) and Group B (containing 100 different images). Participants will view two images at a time (one from Group A and one from Group B) and be asked to choose which image they prefer.

My questions are:

1. How can I calculate the total number of possible combinations of Group A and Group B?
2. How many comparisons do I have to make in order to draw adequate conclusions about the differences between Group A and Group B (assuming that showing all possible comparisons is too much)
3. Exactly what analysis would I run to see if there are differences between Group A and Group B (chi-squared goodness of fit?)

Bonus: How do I run the analysis in R?

I have tried calculating the total number of comparisons using n(n-1)/2, but this does not seem correct as I am not interested in comparing images within Groups (I don't care about comparing Image 1 from Group A to Image 2 from Group A).

Answer 1

1. Compute a mean difference for each pair of variables.
2. Find the critical mean difference.
3. Compare each calculated mean difference to the critical mean.
4. Decide whether to retain or reject the null hypothesis for that pair of means.