# Standard Error of the Mean for Pools of Multiple Individuals

I have conflicting instructions about which value to use for n when calculating the standard error of the mean for pools.

The scenario: Sixty individuals are involved in a study measuring a chemical in the body. Randomly assigned groups of 12 individuals were pooled to create five composite samples that were submitted for chemical analysis. The results look like this:

           n Individuals     Test result
Pool1      12                5.39
Pool2      12                7.08
Pool3      12                4.47
Pool4      12                5.87
Pool5      12                2.56


I am calculating the mean and 95% confidence interval for the mean for these pools. Normally this procedure is straightforward. However, when calculating the standard error of the mean (SEM) I was instructed to use n = 60 (total individuals). Normally I would use n = 5 (total pools) for the SEM calculation.

Mean = 5.074
SD (sample) = 1.691


This is how I was told to calculate SEM

SEM = SD / SQRT(60) = 0.218


This is how I would normally calculate SEM

SEM = SD / SQRT(5) = 0.756


My argument against using n = 60 is that both the mean and standard deviation calculations use n = 5. I have searched online and cannot find any justification for using n = 60. Is there something going on I don't know about?