Statistical test should be used for comparing population means of skewed data I am trying to find out if the population means of 2 sets of data is significantly different at the 10% level. The 2 sets of data is the same size (25 sample points each), and is taken from the same sample but at different times. I plotted the data of each set and found that both sets of data is highly skewed towards the left, meaning that I cannot use T-test to compare the means. Does anyone have any suggestions on what test I could use to find if the 2 sets of data are significantly different or not.

Try bootstrapping. Here's one approach. Lump all samples into one bag of 50 observations. Run $k$ simulations as follows. Sample 25 observations $x_{ki}$ with replacement from the bag, and another 25 observations $z_{ki}$ with replacement. Calculate the differences $\Delta_k=\bar x_k-\bar z_k$ for your $k$ simulations, where $\bar x_k,\bar z_k$ are the averages (sample means) of the two samples. Now you can estimate the distribution of $\Delta_k$ and compare to the differences of sample means of original two sample, and run tests of significance. For instance if the original difference of means was $\Delta_o=\hat\mu_1-\hat\mu_2$, then you could compare it to standard deviation of the distribution of $\Delta_k$ or a percentile, under null hypothesis that $\Delta_o=0$
