Covariance is a measure of association between two random variables. It has several applications in the design and analysis of surveys.
The covariance of two random variables, X and Y, is equal to the expected product of the deviations between the random variables and their means:
Under a design-based perspective to surveys, the sample inclusion indicators are random variables, and covariance is present when the probabilities of inclusion are correlated.
For a simple random sample of n units from a population of size N, the covariance between the means x and y is estimated as:
This is equivalent to the variance formula when xi and yi are the same for each unit in the sample. For complex sample surveys, standard variance estimation techniques, such as Taylor series linearization, balanced ...