# Random sampling at two different frequencies

In a production line, random samples are drawn to be tested for properties A and B. A has to be tested at a higher cadence than B and the assumption is that A and B have zero correlation.

Since the testing destroys the product, it is desirable to test a sample for both A and B, so my questions is, would it be statistically correct to extract the samples needed to test for A, and then from this subset extract the samples needed to test for B, so that for each sample that is tested for A there is a certain chance that it will also be tested for B? Would the samples that are tested for B truly be a random subsample of the production or would I introduce a bias?

The testing is a continuous and ongoing process, where every product has a certain (small) chance of being selected for testing, such that, on average, 0.1% is tested for A and 0.02% is tested for B.

• Strictly speaking, neither procedure produces "random" samples: these are examples of systematic samples. This fact might shed some light on the solution. – whuber Nov 15 '18 at 13:23
• Is that also true if each product on the line has a certain truly random chance of being selected for testing? It is my understanding that systematic sampling is when you take the first of a batch or one sample every hour or every tenth product or something like that. – Christian Brinch Nov 15 '18 at 13:41
• You are correct. But if you are selecting from A randomly and then subselecting from that to obtain B, I hope it's obvious that this is identical to selecting B randomly. The only difference between separate and independent selections of A and B is that the results for A and B will (just as obviously) be physically dependent. This is why I initially interpreted your question as concerning some kind of systematic sampling procedure. – whuber Nov 15 '18 at 13:46