This result shows that positive correlation between n a units in the same sample inflates the variance of the sample mean. Even a small positive correlation may have a large effect, because of the multiplier (n-1).
The two preceding theorems express V in terms of s, hence relate it to the variance for a simple random sample. There is an analogue of theorem 8.2 that expresses v in terms of the variance for a stratified random sample in which the strata are composed of the first k units, the second k units, and so on. In our natation the subscript j in y denotes the strata. The stratum mean is written y