The SURVEYSELECT Procedure

Murthy’s PPS Method

Murthy’s method (METHOD=PPS_MURTHY) selects two units from each stratum, with probability proportional to size and without replacement. The selection probability for unit i in stratum h is

upper P Subscript h i Baseline equals upper Z Subscript h i Baseline left-parenthesis 1 plus upper K Subscript h Baseline minus left-parenthesis upper Z Subscript h i Baseline slash left-parenthesis 1 minus upper Z Subscript h i Baseline right-parenthesis right-parenthesis

where upper Z Subscript h i Baseline equals upper M Subscript h i Baseline slash upper M Subscript h dot and

upper K Subscript h Baseline equals sigma-summation Underscript j equals 1 Overscript upper N Subscript h Baseline Endscripts left-parenthesis upper Z Subscript h j Baseline slash left-parenthesis 1 minus upper Z Subscript h j Baseline right-parenthesis right-parenthesis

Murthy’s algorithm first selects a unit with probability upper Z Subscript h i. Then a second unit is selected from the remaining units with probability upper Z Subscript h j Baseline slash left-parenthesis 1 minus upper Z Subscript h i Baseline right-parenthesis, where unit i is the first unit selected. The joint selection probability for units i and j in stratum h is

upper P Subscript h left-parenthesis i j right-parenthesis Baseline equals upper Z Subscript h i Baseline upper Z Subscript h j Baseline left-parenthesis StartFraction 2 minus upper Z Subscript h i Baseline minus upper Z Subscript h j Baseline Over left-parenthesis 1 minus upper Z Subscript h i Baseline right-parenthesis left-parenthesis 1 minus upper Z Subscript h j Baseline right-parenthesis EndFraction right-parenthesis

For more information, see Cochran (1977, pp. 263–265) and Murthy (1957).

Last updated: March 08, 2022