Effective sample size
More rows do not always mean more independent evidence.
Library note. Check the assumptions and further reading before applying a formula.
What Is This?
Nearby measurements often move together. A thousand readings taken one second apart may tell you less than a thousand readings spread over a year. Effective sample size describes how much information a dependent or weighted sample contains for a particular estimate, compared with independent observations. There is no single effective sample size that works for every statistic.
Try an example
Ten sensors record the same room temperature every second. A shared heat source can move all ten readings together. Treating every row as fresh, independent evidence would make an uncertainty interval too narrow.
Where it needs care
One common adjustment uses the correlation between readings at different time lags. It estimates information about the mean, assuming a stable process with a finite mean and variance and suitably decaying correlations. Heavy tails, regime changes and overlapping labels need more care than a smaller row count.
Historical Context
The idea appears in survey sampling, correlated time series and Markov chain Monte Carlo, with different definitions for different estimators.
Real-World Applications
- Judge how much information repeated measurements add.
- Design block-based validation that respects dependence.
