Is the following a reasonable approach to assess the statistical significance of the difference between two groups'
For each group 1) Subsample with replacement 2) Take the mean of the subsample 3) Repeat 10,000 times to build a distribution of means 4) Carry out a t-test to assess the difference between those two distributions
(i.e. bootstrapping to build a distribution of means)
The two datasets are very different in size (~100 vs. 100,000). The alternative approach would be to subsample from each to build two equally sized datasets, and then use a t-test on those two samples. The problem I have with this is I'm not sure if the smaller of the two sets is normally distributed (while the larger is), which may invalidate the t-test assumptions?