I am doing a Bayesian comparison between two proportions, H0 being Proportion(Protein)> Proportion(Mixed). Here the Proportion is of no. of times a free-ranging dog(s) ate from a box(Protein, Mixed). Being a binary variable (Eat from the box: Yes/No), it is of the beta-binomial family. In experiment 1, I use a uniform prior: Beta(1,1). The no. of successes (x) and the no. of failures(y) for Protein and Mixed are as follows:

x1= 19, y1= 25; x2= 8, y2= 33

So my beta posterior shape parameters for Protein are (19+1, 25+1) and for Mixed are (8+1, 33+1).

I am planning to use these posterior parameters as priors for my current experiment. The two experiments have the same set-up. The only difference being the no. of dogs (individual vs groups). I don't expect to see a radical difference in results.

So my question is, can i use the previous beta posteriors as current priors in the way I have written it down, i.e B(20,26) for protein and B(9,34) for mixed. (where, B stands for beta distribution).

Current experiment info: x1=41, y1= 47; x2= 41, y2= 49

Information about me: I come from a biology background with minimal math and programming knowledge. I have been learning Bayesian on my own for about 2 months now. I am willing to learn but math heavy explanations tend to go over my head. Feel free to point me towards relevant resources. I am using R to do the calculations.