PPS-PROBABILITY PROPTIONAL to size SAMPLINGDr Anshuli TrivediIInd year Resident

Definition-A probability sampling scheme ,a multi-stage sampling methodology in which every unit in the population has a chance of being selected in the sample, in which the selection probability for each element is set to be proportional to its size measure, minimum of 0,up to a maximum of 1,and this probability can be accurately determined. OrProbability proportional to size (PPS) is a sampling technique for use with surveys or mini-surveys in which the probability of selecting a sampling unit (e.g., village, zone, district, health center) is proportional to the size of its population.(2)

Ref-(1)Wikipedia, the free encyclopedia(2)Instructions for Probability Proportional to Size Sampling TechniquePrepared by Therese McGinnHeilbrunn Department of Population and Family HealthMailman School of Public Health, Columbia University

Calculation- Sampling interval (SI)Calculation=Population size(N)/Predetermined sample size(n).

Select a number between 1&SI randomly. This is starting point of calculation Random Size (RS).

Series is calculated by multiples of SI +Random start=nxSI+RS

Example: Suppose we have six schools with populations of 150, 180, 200, 220, 260, and 490 students respectively (total 1500(N) students), and we want to use student population as the basis for a PPS sample of size three(n).

To do this, we could allocate the first school numbers 1 to 150, the second school 151 to 330 (= 150 + 180), the third school 331 to 530, and so on to the last school (1011 to 1500). We then generate a random start between 1 and 500 (Sampling Interval= N/n= 1500/3) and count through the school populations by multiples of 500.

If our random start was 137, we would select the schools which have been allocated numbers 137(137+0x500), 637(137+500x1), and 1137(137+2x500), i.e. the first, fourth, and sixth schools.

•For example- A mini-survey of a population of 17,619 spread over 100-200 villages ,from which only basic data from 150 females of reproductive age group is required. Methodology -Team-expects to visit 10-15 villages for a total sample size of 150.In this example, we will visit 10 sites to conduct a mini-survey with a desired sample size of 150 women aged 15-44. Thus, 15 women will be interviewed in each of the 10 sites selected.•Divide the total population of the project area of,17,619, by 10, •The result, 1,762, is called the Sampling Interval (SI).•Choose a number between 1 and the SI at random. This is the Random Start (RS).• In this sample, the RS is 1321.•Calculate the following series: RS; RS + SI; RS + 2SI; RS + 3SI; RS + 4SI; RS + 5SI; RS + 6SI;• RS + 7SI; RS + 8SI; RS + 9SI.Example :RS + 2SI is to be calculated as 2 times the sampling interval added to the random start. In this case, 1321 + 2(1762) = 4845.•Each of these 10 numbers corresponds to a site on the list of villages..For example, the first number in the series, 1,321, is contained in village 3,which holds numbers 788 to 1,819. The second number in the series (3,083) is contained in village 6, which holds numbers 2,943 to 3,294.Continuing in this manner, the desired number of sites will be selected. Series calculated-1321,3083,4845,6607,8369,10131,11893,13655,15417,17179. In this example, the selected villages are numbers 3, 6, 9, 11, 15, 18, 21, 22, 25 and 29 .

Instructions for Probability Proportional to Size Sampling TechniquePrepared by Therese McGinnHeilbrunn Department of Population and Family Health Mailman School of Public Health, Columbia University

Various ways of probability sampling have two things in common:(1)•Every element has a known nonzero probability of being sampled •involves random selection at some point.

•Advantages- unbiased, allow stratification.(3)•It is most useful when the sampling units vary considerably in size. •This method also facilitates planning for field work because a pre-determined number of respondents is interviewed in each unit selected, and staff can be allocated accordingly.•The PPS approach can improve accuracy for a given sample size by concentrating sample on large elements.

Demerits- Cannot guarantee “representativeness” on all traits of interest.

(3)TIMOTHY LOStatistician, Inteernational Comparison Program Asian Development Bank

Types of Probability Samples-

Simple Random

Systematic Random

Stratified Random

Random Cluster

Complex Multi-stage Random (various kinds)

Stratified Cluster

Simple Random Sampling• Each element in the population has an equal probability ofselection AND each combination of elements has an equal probability of selection. Ex-Names drawn out of a hat. Random numbers to selection.

Random Numbers;

Select numbers from every third column and every row.  If a number comes up twice or is larger than the population number, discard it.  Be sure to stick to the pattern of movement through the table.

87456 34098 88900 11128

87456 34098 88900 64554

45666 77789 82276 12555

22333 45767 87900 99989

2) Systematic Random Sampling -Systematic sampling is very similar to simple random sampling, except instead of selecting random numbers from tables, you move through the sample frame picking every nth name. In order to do this, it is necessary to work out the sampling fraction.  This is done by dividing the population by the desired sample. Example

For a population of 100,000 and a desired sample of 2,000, the sampling fraction is 2/100 or 1/50.  This means that you would select one person out of every fifty in the population.  With this method, with the sampling fraction of 1/50, the starting point must be within the first 50 people in your list.

3) Stratified SamplingIt is designed to produce a more representative and thus more accurate sample.  A stratified sample is obtained by taking samples from each sub-group of a population.  Example-age, gender or marital status. 

Random Cluster Sampling- Population is divided into groups, usuallygeographic or organizational. Some of the groups are randomly chosen.Types-In pure cluster sampling, whole cluster is sampled. In simple multistage cluster, there is random sampling within each randomly chosen clusterAdvantage-Cost savings of clustering may permit larger sampleCluster sampling is NOT desirable if the clusters are different from each other.

Stratified Cluster Sampling-Reduce the error in cluster sampling by creating strata of clusters. Sample one cluster from each stratumAdvantage-The cost-savings of clustering with the error reduction of stratification.

Sampling errors are larger  when using cluster sampling.

4) Multistage Cluster Sampling

  The entire population is divided into groups, or clusters, and a random sample of these clusters are selected.  Following that, smaller 'clusters' are chosen from within the selected clusters.

Multistage cluster sampling is often used when a random sample would produce a list of subjects so widely scattered geographically that surveying them would prove to be far too expensive. 

Example Stage 1: Define population - (say) adults 16+ living in the South East

of England.

Stage 2: Select (say) 100 electoral wards from the SE at random

Stage 3: Select a member of smaller areas (e.g. EDS) from within each selected ward.

Stage 4: Interview all residents within the smaller areas (alternatively, select a sample from the each smaller area.

Non probability sampling- A method where some elements of the population have no chance of selection (these are sometimes referred to as 'out of coverage'/'under covered'), or where the probability of selection can't be accurately determined. It involves the selection of elements based on assumptions regarding the population of interest, which forms the criteria for selection.

Example: We visit every household in a given street, and interview the first person to answer the door. In any household with more than one occupant, this is a non probability sample, because some people are more likely to answer the door (e.g. an unemployed person who spends most of their time at home is more likely to answer than an employed housemate who might be at work when the interviewer calls) and it's not practical to calculate these probabilities .(1)When every element in the population does have the same probability of selection, this is known as an ‘Equal Probability of Selection' (EPS) design.(1)

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