I work in the microelectronics industry, and I commonly work with tools that remove material from the surface of a wafer. Furthermore, we typically measure the amount of material removed from a single wafer at multiple sites on the wafer (usually 10 - 20 sites). From this data, we calculate various statistics. For example, we calculate a within wafer (WIW) mean and standard deviation. This metric is very straightforward, and we just calculate the mean and standard deviation of all the sites measured on a single wafer. However, people in my industry also talk about wafer-to-wafer (WTW) standard deviations, which I don't fully understand. Is it common in statistics to look at standard deviations of two groups/samples? If so, what would be the methods used to calculate this? Does it make sense to calculate the standard deviations of all of the wafer means, or is there some better method?

I hope this question is not too vague. If it is, please let me know and I will try to provide more information.


1 Answer 1


You could certainly compute the SD of a set of group means, and this is done with some frequency. More complicated notions related to this also appear, such as, in a mixed model, estimating the SD of a set of per-group random intercepts. But you could also compute the common SD of all the units in several groups, disregarding the existence of the groups. It all depends on what question you're trying to answer. I don't know enough about your subject area to guess what that is.

  • $\begingroup$ I believe that our goal is to reduce the amount of variability in data for sites measured on a given wafer and across multiple wafers. Expressed in a different way, the ideal state would be to remove the exact same amount of material at each site and on each wafer. $\endgroup$
    – johncarter
    Commented Mar 11, 2017 at 1:00
  • $\begingroup$ @johncarter All right, but how were you hoping to use these metrics to accomplish that? $\endgroup$ Commented Mar 11, 2017 at 1:39
  • $\begingroup$ I guess that kind drills down to the essence of my question. I am no stats guru. I ask the question to get a sense of why these metrics are important, and I was curious about the best way to calculate these metrics. $\endgroup$
    – johncarter
    Commented Mar 13, 2017 at 17:24
  • $\begingroup$ @johncarter You would have to ask somebody who does these analyses in order to find out why they do it. It may just be tradition. In practice, many data-analytic traditions are just that, tradition, with no special justification beyond inertia. $\endgroup$ Commented Mar 13, 2017 at 17:27
  • $\begingroup$ @johncarter Although, to be clear, you're asking about what metric to use, not how to calculate the metrics. How to calculate, e.g., the SD of the group means is clear enough. $\endgroup$ Commented Mar 13, 2017 at 17:28

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