Imagine that you want to inspect members of a population to see if they have a target feature. For example, test people to see if they have a certain disease.
One possible approach is to take a sample of fixed size $n$, that is, test $n$ people with $n$ predefined. Another approach is sequential sampling: you keep sampling people one by one until a stopping rule is satisfied (for instance, test until $25$ people with the desease are found).
Assume now that sequential sampling is applied but not one by one. Instead, samples are taken in groups of $k$, and a stopping rule dictates how many such groups you observe. Note that the feature of interest still corresponds to each individual person, not to the groups. That is, in each group of $k$, some people may have the disease and others may not, and each person is tested individually. The group is just a convenient way to perform the sampling.
For a specific example, consider that the population of interest is soldiers, and the sampling plan selects squads of $10$ soldiers. So the sample size will always be a multiple of $10$.
What is the correct statistical term for those groups of size $k$, such that the sample is taken in lumps of $k$ units instead of one by one? The words "lot", "batch" and "group" come to mind, but I think those might have a different meaning here.
