I'm not sure that variance is technically the right term, so allow me to explain... I'm measuring two data sets at work, looking at the 50th, 90th, and 99th percentile for each data set on a monthly basis. Data set A generally has about 10x as many observations as data set B.
If any of these metrics changes enough in one month for either data set, my bosses want an explanation for why it changed. The threshold they've historically used for whether an explanation is necessary is a 3% delta month-over-month. (For various long reasons, doing an actual statistical significance test is not possible for our circumstances.) This 3% threshold was established when we were only looking at data set A, where anecdotally it seems to be about right. But is now also being applied to data set B. Obviously since data set B has one tenth as many observations, it breaches this threshold much more frequently.
I want to make the case to say something like "data set B has one tenth as many observations, so we should allow for a threshold that is X times larger". I'm just not sure how to determine what X should be. I have this vague intuitive sense from old stats classes that it should be proportional to sqrt(N), i.e. if data set A is allowed to vary up to 3% from month to month, then data set B should be allowed to vary by up to 3% * sqrt(10) =~ 9.5% per month.
My question is: Am I right? And regardless of whether I'm right, what's the actual statistical argument for whatever the right answer is? How much should data set B be allowed to vary assuming that we allow data set A to vary by 3%?