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if samples are drawn from the same population but under different circumstances (i.e. data collected from different machine rather than single machine, also sample size for each machine varies). From sampling distribution point of view, how to approach to it?

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  • $\begingroup$ Some details would help: How many machines? About how many measurements per machine? Are measurements nearly normally distributed? Do you expect some machines to give systematically different measurements on average than others? (Different means.) Are machines of different types so that the variability of measurements might differ from machine to machine? (Different standard deviations.) $\endgroup$
    – BruceET
    Jul 9, 2018 at 23:32
  • $\begingroup$ This Q&A might suggest some relevant methods. // Still hoping to see your clarifications. $\endgroup$
    – BruceET
    Jul 10, 2018 at 5:52
  • $\begingroup$ as per other comments, the desired solution critically depends on two things. Firstly what you mean by ‘under different circumstances’. And secondly whether the sample size for each of the machines is known or not known. $\endgroup$ Jul 15, 2018 at 10:47
  • $\begingroup$ No of machine: 3 , samples/machine - 30 , data normally distributed. Yes, it is expected to get different average even if instruction is to run the all the machine at a same speed $\endgroup$
    – Mynur R.
    Jul 17, 2018 at 15:20
  • $\begingroup$ @MartinRoberts, "under different circumstances" - data pulled from different machine . Sample size for each machine is known, n=30, for each machine. $\endgroup$
    – Mynur R.
    Jul 17, 2018 at 15:23

1 Answer 1

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You can treat the data as a cluster sample survey, which only makes assumptions that observations within a machine are somehow correlated and have something in common, without making any parametric assumptions like normality about that.

library(survey)
nested_in_machines <- svydesign(id = ~machine, data = mydata)
svymean(whatever, design=nested_in_machines)
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