Q:

Confidence intervals and different methods of sampling

I have two samples collected from the same population, where each sample is collected using a different method of selection, and both samples are large enough for the distribution of the sample distribution of the mean to be normal.
Now, when calculating two 95% confidence intervals for the mean, using each of the two samples, I get two non-overlapping intervals, so I can be fairly confident that one of the two samples suggest a larger population mean than the other sample suggest, or in other words, they are suggesting two different population means even-though they are sampled from the same population.
So, my question is now, is it valid to conclude that one, or both, of the sampling methods are flawed due to the discrepancy in the population means predicted by the two methods? 

A:

If both samples were random samples, then you would expect the means to be equal and the confidence intervals to overlap. While the mean need not be equal due to small sample size, the confidence intervals---if computed correctly---account for the small sample size and should overlap even for small samples. Only in less than 5% of the cases would you have nonoverlapping confidence intervals if both sampling was random and the population means were the same. 
Hence, yes, you can reject the hypothesis of random sampling at a lower than 5% level. Whether that means the sampling methods are flawed---I don't know, depends on what they are supposed to achieve. If they are supposed to give you a random sample, then you can indeed view at least one of them as flawed.

