Conducting a two sample t-test using log transformed non-normally distributed data I have two data sets, where sulfate concentrations of groundwater in a specific site are shown for two different years 
2013
1000,1530,694,432,370,750,337,432,1562,469,1520,601,469,439,699,316,372,929,841,810,583,163,286,693,129,313,651
2014
785,584,1270,499,452,452,996,883,737,78,443,253,149,199,401,961,642,824,190,462,404,172,222,526
2013 data is not normally distributed (tested using Shapiro-Wilk normality test p value is 0.003. 2014 data is normally distributed (p-value = 0.26). Used R software. 
Can I log transform both data sets to get a normal distribution for both groups so I can conduct a two sample welch test? Also, will I have to back-calculate the p-value resultant from log-transformed t-test? 
Thank you. 
 A: I don't believe the means (or medians) for the two years differ significantly.
Just looking at side-by-side boxplots of the two samples, I did not expect to find significant differences. The 'notches' in the sides of the boxplots indicate nonparametric confidence intervals for population medians, and the intervals overlap. (It might be worthwhile to find out whether the outliers in 2013 sulfate
levels were due to actual temporary or local spikes in sulfate or whether
they were due to measurement error.)

When I do a Welch t test on the two log-transformed samples, I get about
the same result as for a Welch t test on the original samples. P-values
are about 0.2 in both cases. No significant difference between years.
t.test(log(x1),log(x2))

        Welch Two Sample t-test

data:  log(x1) and log(x2) 
t = 1.2682, df = 46.122, p-value = 0.2111
...

If the results from the logged data were significant, you might have some
trouble explaining why the differences in log(sulfate) are worth studying,
but the P-value for the logged data needs no transformation. 
Also, a 2-sample Wilcoxon rank sum test gave a larger P-value along with a
warning message about ties, and a permutation test showed no significant difference. Neither of these nonparametric tests should be bothered by
the outliers in the data for 2013.
Just to make sure I correctly scraped your data from the screen, my summary
statistics are as follows.
summary(x1)
  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
129.0   371.0   583.0   644.1   780.0  1562.0 
summary(x2)
  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 78.0   245.2   457.0   524.3   749.0  1270.0 

