What sources of uncertainty are included in a (95%) confidence interval? Today, I came across an interpretation of 95% confidence interval (thereafter "CI"). The text has been written from education science perpective saying that, beside a (1.) random sampling error of randomly selected cases from a given population, CI also accounts for "(2.) different conditions in which the test was administrated and (3.) which tasks were included into a test (4.) etc."
I am bit confused now, since I have never seen that CI could also account for this other sources of uncertanaity (lets say all of them have stochastic character). Is my knowledge about CI not complete or the author just misinterpreted the meaning of CI?
Thank you in advance.


(1.) random sampling error of randomly selected cases from a given population...

Random sampling error is what most statistical methods are about.

The other sources of error,

...also accounts for "(2.) different conditions in which the test was administrated and (3.) which tasks were included into a test (4.) etc."

, are not part of the random sampling procedure*. These are more like systematic errors. When confidence intervals are computed/estimated then these type of errors are typically not accounted for (e.g an interval based on the t-statistic does not).

* At least they are often are not part of the sampling. You can make it part of the random sampling by performing tests with different settings like changing conditions and tasks. But the text using a phrase like 'beside a (1.) random sampling error...' seems to regard these errors implicitly as different types of error that are not random sampling error. Potentially it could be that they see them as different from 'random error' as they can be seen as 'random effects' and the text might wants to put them aside because of that? There is some duality to random effects and they can be seen as both part of the deterministic part of the model as well as the random part of the model. For these potential subtleties it is better when you provide a link to the original text, even when it is not English.
