**PPS sampling**

Sampling with PPS provides a practical technique when sampling from populations with large variation in the values of the study variable and often gives a considerable gain in efficiency. Efficiency varies considerably according to the type of parameter to be estimated. Under PPS sampling an auxiliary size measure (z) must be available and for efficient estimation the size measure should be strongly related to the study variable y. A condition for this is that the variable pair (z, y2/z) is positively correlated. The ratio Yk/Zk must also remain constant over the population. See pages 49 to 61 in Lehtonen, R & Pahkinen, E. (2004)