probability proportional to size.pptx.By Rc

PPS sampling

1. Sampling II Presented to: Sir Noman Presented by; Roll no 5; Mubeen Ahmed Roll no 13; Rakhshanda kousar

2. Types of sampling Probability Sampling Non-Probability Sampling Known Probability Non-zero Probability Judgement

3. Probability proportional to size: The size measure is the value of an axillary variable (x) which is closely associated with the study variable(y) this is called probability proportional to size. PPS sampling assigns a probability to each unit in the population based on its size and importance. For example, In an agricultural survey, the yield depends upon the total area cultivated. Hence bigger areas have larger production so the value of the area is the size of the axillary variable.

4. When to use PPS sampling? When the population is large and varies according to size and importance. When to study rare events. Limited resources. Heteros groups according to size. When stratified random sampling and simple random sampling are not effective and distinct according to size and importance.

5. Objective: Proportional representation. Efficiency. Simplicity. PPS sampling enables researchers to obtain accurate and reliable information about the population of interest.

6. Efficient allocation of resources. Improved Precision. Flexibility in sample size. Inclusion of rare groups. Overall PPS advantages in terms of efficient allocation of resources, flexibility in sample size, improve Precision, etc. Additional complexity. Dependency variable. Limited flexibility in sampling design. complexity in analysis. Sensitive to outliers. Need high cost Advantages: Dis-Advantages:

7. Method of selection sample using PPS sampling: With Replacement. Without Replacement.

8. Selection of sample using with replacement : In with-replacement, the probability of selection will not change and there is no re-distribution of the probability after a draw. For the selection of sample by using PPS sampling with replacement case there are generally two methods: 1. Cumulative total method 2. Lahiri 's method

9. Lehiri's method: Lahari in 1951 suggested an alternative procedure in which cumulations are avoided completely. In this approach, a pair of random numbers say ( I,j ) is selected such that (1 ≤ I ≤ N) and (1 ≤ j ≤ M) where m is the maximum size of N units in the population. If (x ≥ j) or (j ≤ x) then ith pair will be selected otherwise rejected and another pair of random numbers is chosen. This procedure is continued until n units are selected.

10. Cumulative total method The selection procedure consists of the following steps: