# Intuition behind clustering standard errors

Intuitively, why does a lack of clustering standard errors lead to erroneously smaller standard errors? Looking at the calculations and seeing the difference between SEs that are clustered and not clustered gives me an idea of the mathematics, but not really an intuition.

• The variance between statistical units belonging to the same class is usually lower (intraclass correlation is positive) than the variance in the total sample, and this is mostly due to unobservable effects (e.g., teacher effect in classes nested in schools, cognitive bias in individuals measured at different point in time, etc.). Ignoring that information yield biased estimates for the standard errors (unless the sample is very large, measurement are very accurate and/or there's no real cluster in the data, i.e. statistical units are really too different). – chl Sep 24 at 12:49

Suppose I sample 3 people from the population of CV users, and I just happen to include Student, Kjetil, and myself. Now I take another sample, which just includes myself three times (perhaps sampled on different days). I think you would agree that in some sense the second sample contains fewer observations, even though $$N=3$$ in both cases. My usage behavior over time may be very correlated.