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Sample size (n) refers to the number of participants or observations included in a study through which statistical inferences for the whole population are made. Can sample size have measurement unit, such as $km^2$ (kilometre square)?

In a paper on hydrology, researchers collected data from some areas, but they didn't specify the number of areas, rather said they collected the data from a area of size $20km^2$. Is this $20km^2$ the sample size in the study? I didn't find any other information in the paper which can be potential as a sample size.

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Yes, $km^2$ can be used as a measurement unit but I would say that 20$km^2$ is not the sample size but rather than these 20 $km^2$ are part of the sample area of the study. For example, if we have 10 areas of 2 $km^2$ each, our sample size is $n$=10 with a total sample area of 20 $km^2$.

Usually in cases where the sampling area (or time) is varying among our samples we would consider using that information as an offset in our analysis. As such we would not have to explicitly transform our response variable; see the CV.SE: When to use an offset in a Poisson regression? for more details.

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  • $\begingroup$ Thank you for your reply. If another study report $12km^2$ of area with $3km^2$ for each, then it will become $n=4$. Is that the region behind using offset since each area size is variant? $\endgroup$ – user232597 Apr 18 at 3:51
  • $\begingroup$ Will the adjustment for including an offset is always dividing the response by the offset? That is, (response/area size) in my particular case? $\endgroup$ – user232597 Apr 18 at 3:53
  • $\begingroup$ In this example: while the original study would have an offset of 2 this new study would have an offset of 3 ($km^2). It does not necessarily "divide" our response, rather it controls for proportional changes across a dimension (usually time or area) that are irrelevant to our research question. $\endgroup$ – usεr11852 Apr 18 at 4:01

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