Chi-square comparison of distributions and question on validity of application:
The experiment: Thirty individuals were given two choices for each of two parameters (based on location). So they could choose a or b and 1 or 2 (giving four choices a1, a2, b1, b2).
Data set: There were four replicates with systematic randomization which yielded about 100 useable data points.
Question: Is it statistically valid to compare the distributions of the data points using a chi-squared test or does this under-estimate the p-value? (given that the number of subjects is only 30)

Question

Chi-square comparison of distributions and question on validity of application:
The experiment: Thirty individuals were given two choices for each of two parameters (based on location). So they could choose a or b and 1 or 2 (giving four choices a1, a2, b1, b2). 
Data set: There were four replicates with systematic randomization which yielded about 100 useable data points.
Question: Is it statistically valid to compare the distributions of the data points using a chi-squared test or does this under-estimate the p-value? (given that the number of subjects is only 30)