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I have (I think) a relatively basic question concerning paired / unpaired data.

I want to compare the mean number of employees in the same company in the same year across two age groups (under 50 years and over 50 years), using a t-test. My question is simply whether I should be using a paired or unpaired t-test. Clearly, the two groups of employees are composed of different individuals (in the given year), but they also constitute different subgroups of the same workforce / company. Would it be legitimate to apply a paired t-test in this instance, or should the data be treated as unpaired?

Many thanks!

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  • $\begingroup$ What even is your sampling? All I'm seeing is that you have X employees under 50 and Y employees over 50. $\endgroup$ – Dave Aug 20 at 10:39
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There is no variable to pair these people on, as far as I can tell.

So, independent samples t test.

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  • $\begingroup$ Thank you for the quick response. My doubt arises from the fact that the analysis is at the company level across a 100 or so different companies (sorry for lack of clarity in original post); that is, comparing mean total company workforce aged 50 and over vs total workforce aged under 50 across approx 100 companies. So my doubts was whether the 'total company workforce' variable for each age group could be paired on the company/employer variable (although, of course, the individuals in each group are different). $\endgroup$ – Sam Aug 20 at 10:48
  • $\begingroup$ No, it can't be paired. However, if you are worried about homogeneity within companies you might need a multilevel model. $\endgroup$ – Peter Flom - Reinstate Monica Aug 20 at 11:01
  • $\begingroup$ Thank you (and others) for the clarification $\endgroup$ – Sam Aug 20 at 11:04
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Since the individuals in the two groups are independent a paired test is not appropriate. Given that you have partitions in your data it is better to use a linear model, which can return many results for an arbitrary number of groups.

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