Probability and NonProbability Sampling Dr Carina King carina

Probability and Non-Probability Sampling Dr. Carina King carina. king@ki. se @Carina. TKing

Sampling Why is it important? Research question: What is the proportion of children under 5 that sleep under bed nets in Malawi? • Population of Malawi (2016 estimate): • 16 million population • ~3 million children less than 5 years of age If 1 survey team could collect data on 25 children/day 6 teams would take 54. 8 years to complete data collection Time and money constraints prevent us from measuring everyone in the population… 2

Sampling Why is it important? § But what if you have access to the whole population? à Hospital records à Electoral register à Birth/death records § § Time and effort in analysis Diminishing returns Computational capacity Ethical concerns 3

Sampling Why is it important? § § Reduce cost Reduce time More accuracy When it’s impossible to study the whole population Sampling is needed to try and make the estimate as representative of the population as possible Population 1 Sample 1 4

Sampling Methods 5

Non-probability sampling Convenience samples Sample is selected from elements of a population that are easily accessible Example: consumer feedback surveying at a local shopping centre Snowball sampling Example: (friend of friend…. etc. ) Purposive sampling Selecting who should be in the study based on their characteristics (often used in qualitative research) Good for hard to reach populations, can get your first sampling unit to recruit more 6

Non-probability sampling Quota The sampling procedure that ensure that a certain characteristic of a population sample will be represented to the exact extent that the investigator desires Example: a school with 60% boys, our sample would also be 60% boys Self selection sampling When we allow sampling units (people or organisations) to take part in research of their own accord Example: putting a survey link of a webpage 7

Non-probability sampling § § Probability of being chosen is unknown Can be cheaper… … but unable to generalise Potential for bias Non-probability sampling is often used in qualitative studies Need to justify your decision for using this type of sampling 8

Sampling Methods 9

Probability sampling 1. Simple random sampling 2. Systematic random sampling 3. Stratified sampling Can be simple or systematic 10

Probability sampling Random sampling § Everyone has an equal probability of being selected § Allows the results of the statistical analysis to be: à Generalizable à Test a hypothesis Random sampling allows the sample to meet the assumptions needed to carry out hypothesis testing during statistical analysis. It should be used when you intend to carry out statistical analysis 11

Probability Sampling 1. Simple Random Sampling I need to select 10 students at random from a class of 40: 1. 2. 3. 4. 5. 6. Define the population Choose the sample size List the population Assign numbers to each sampling unit Generate random numbers Select your sample 12

Probability Sampling 1. Simple Random Sampling 1. Jones 2. Baraitser 3. Hamzah 4. Rezel 5. Wilson 6. Syred 7. Barnard 8. Nelson 9. Smith 10. Allen 1. 2 s 11. Lovi 12. Sofield 13. Bob 14. Dunlop 15. Cubitt 16. Hahn 17. Nichols 18. Wong 19. Law 20. Scudder 21. Wezgren 31. Pavlou 22. Nicholls 32. Farquhar 23. Fall 33. Benny 24. Leather 34. Hall 25. Charlie 35. Olley 26. Barge 36. Baird 27. Shahabi 37. Rankin 28. Gaskin 38. Barker 29. Blandin 39. Booth 30. Brandl 40. Steel 29/06/2015 13

Note household 4 was picked twice… If you can pick the sampling unit more than one this is sampling with replacement. If you can only select it once, this is sampling without replacement 1. 2 s http: //graphpad. com/quickcalcs/random. N 1. cfm 14

Probability Sampling 1. Simple Random Sampling Pros Cons § Removes potential for selection bias and gives a sample that is representative of the population § Need a complete list of the population which may be à Access may be difficult à Costly à Time consuming § Need to be able to contact everyone on the list 15

Probability Sampling 2. Systematic Random Sampling § Systematic random sampling is often used to select large samples from a long list of sampling units. § Instead of using a random number table, you select units directly from the sampling frame 16

Probability Sampling 2. Systematic Random Sampling I need to select 10 students at random from a class of 40. . 1. 2. 3. 4. 5. 6. 7. Define the population Choose the sample size List the population Assign numbers to each sampling unit Calculate the sampling fraction Select the first unit with a random number table Select your sample 17

Probability Sampling 2. Systematic Random Sampling § 18

Probability Sampling 2. Systematic Random Sampling Selecting the first unit…. § We then select a number between 1 and the sampling interval from a random number table § … or a random number generator 72 9 3 10 33 55 7 37 6 14 80 79 21 80 16 62 2 11 27 47 19

Probability Sampling 2. Systematic Random Sampling Student #3 is the first student. We then count down the list starting with student #3 and select each 4 th student. For example, the second selected student is 3 + 4, or #7. 1. Jones 2. Baraitser 3. Hamzah 4. Rezel 5. Wilson 6. Syred 7. Barnard 8. Nelson 9. Smith 10. Allen 11. Lovi 12. Sofield 13. Bob 14. Dunlop 15. Cubitt 16. Hahn 17. Nichols 18. Wong 19. Law 20. Scudder 21. Wezgren 31. Pavlou 22. Nicholls 32. Farquhar 23. Fall 33. Benny 24. Leather 34. Hall 25. Charlie 35. Olley 26. Barge 36. Baird 27. Shahabi 37. Rankin 28. Gaskin 38. Barker 29. Blandin 39. Booth 30. Brandl 40. Steel 20

Probability Sampling 2. Systematic Random Sampling Pros Cons § Removes potential for selection bias and gives a sample that is representative of the population § Need a complete list of the population which may be à Access may be difficult à Costly à Time consuming § Need to be able to contact everyone on the list 21

Probability Sampling 3. Stratified Sampling § Stratified sampling is a probability sampling technique where the entire population is divided into different subgroups or strata, then the final subjects are proportionally sampled from the strata. § E. g. villages, classes in a school, hospital wards 1. 2 s 22

Probability Sampling 3. Stratified Sampling It is important to note that the strata must be non- overlapping. Having overlapping subgroups will grant some individuals higher chances of being selected… 4

Probability Sampling 3. Stratified Sampling Example: Select 50 pupils from 1000 pupils of year 7 -11. 1. Calculate probability for sampling: 50/1000=0. 05 2. Count the pupils in each year

Probability Sampling 3. Stratified Sampling 3. Calculate the number of the pupils that should be sampled in each year. 4. Use simple random sampling or systematic sampling method to select pupils in each year

Probability Sampling 3. Stratified Sampling Proportionate stratified random sampling To make sure the original proportion is maintained Non-proportionate stratified random sampling To make sure enough number in each group

Probability Sampling 3. Stratified Sampling The most common strata used in stratified random sampling are: • Age • Gender • Socio-economic status • Nationality • Educational attainment.

Probability Sampling 3. Stratified Sampling

Probability Sampling 3. Stratified Sampling Pros • Focuses on important subpopulations and ignores irrelevant ones. • Allows use of different sampling techniques for different populations • Improves the accuracy/efficiency of estimation • Permits greater balancing of tests of differences between strata by sampling equal numbers from strata varying widely in size Cons • Requires selection of relevant stratification variables which can be difficult. • Is not useful when there are no homogeneous subgroups. • Can be expensive to implement. • Oversampling in some situation.

Summary § Sampling can either be probabilistic of nonprobabilistic § Probabilistic allows you to make inferences beyond the sample in the study, non-probability sampling does not § The sampling method will depend on resources, setting and research question