I have a process wherein human operators (Ops) evaluate some quantity/metric (for simplicity let's say length of a leaf fallen from a tree) for 1000 representative samples and note down it's value on a form.
Main goal is to estimate the 95% CI of mean length of leaf. I can use the usual formula (mean +- z*(standard deviation of observed length)/sqrt(sample size) but...
The evaluation is subject to measurement errors - measuring instrument not calibrated properly, incorrect value noted down on form, leaf may have withered a little bit, skill difference of Ops in doing the measurement
In order to better quantify the measurement errors, the Ops were divided in to 2 mutually exclusive groups and each of these groups measured the same set of leafs - measurement times might be apart by a couple of hours. Within a group a leaf was measured by only one operator.
So the data looks like following:
Note length_groupA - length_groupB and it's absolute difference is zero for 90% of the sampling_id's. But the remaining 10% varies all over the place. Standard deviation of either of length_groupA or length_groupB is much lower than standard deviation of (length_groupA - length_groupB) which again is much lower than standard deviation of |(length_groupA - length_groupB)|
I'm aware of concept of standard error of measurement (SEm) as provided here
a) I want to graphically summarize the distribution of leaf lengths and intend to use boxplot. Would like to add a caveat that there is measurement error. Should I do boxplot on only one of "length_groupA" or "length_groupB" (and supplement it with standard error of measurement for the difference between groupA and groupB for the same sampling_id). Or for each sampling_id should I randomly select length from one of these 2 groups and do a boxplot on that? Does the later option need to be supplemented with SEm?
b) Now to the primary goal - arrive at 95% CI of mean length. Is there an adjustment to the standard error of the mean formula to include standard error of measurement?
PS: I have tried to simplify the problem; in reality this needs to be independently analyzed for different types of tree - maple, oak, poplar etc