Tahir Mahmood Lecturer Department of Statistics

1. Sampling Theory and Methods Tahir Mahmood Lecturer Department of Statistics

2. Outlines: • Explain the role of sampling in the research process • Distinguish between probability and non probability sampling • Understand the factors to consider when determining sample size • Understand the steps in developing a sampling plan

3. What is Sampling? • Sampling is the procedure a researcher uses to gather people, places, or things to study. • Samples are always subsets or small parts of the total number that could be studied. • Sampling is the process of selecting a small number of elements from a larger defined target group of elements such that the information gathered from the small group will allow judgments to be made about the larger groups

4. What is your population of interest? • To whom do you want to generalize your results? • All doctors • School children • Indians • Women aged 15-45 years • Other • Can you sample the entire population?

6. Why sampling? Get information about large populations • Less costs • Less field time • More accuracy i.e. Can Do A Better Job of Data Collection • When it’s impossible to study the whole population

7. Important Factors in selecting a Sample Design Research objectives Degree of accuracy Time frame Resources Research scope Knowledge of target population Statistical analysis needs

8. Common Methods for Determining Sample Size • Common Methods: • Budget/time available • Executive decision • Statistical methods • Historical data/guidelines

9. Determining Sample Size • How many completed questionnaires do we need to have a representative sample? • Generally the larger the better, but that takes more time and money. • Answer depends on: • How different or dispersed the population is. • Desired level of confidence. • Desired degree of accuracy.

10. IMPORTANT STATISTICAL TERMS Population: a set which includes all measurements of interest to the researcher (The collection of all responses, measurements, or counts that are of interest) Sample: A subset of the population

11. Sampling Frame • A list of population elements (people, companies, houses, cities, etc.) from which units to be sampled can be selected. • Difficult to get an accurate list. • Sample frame error occurs when certain elements of the population are accidentally omitted or not included on the list. • See Survey Sampling like HIES PDHS, PSLM, MICS

12. Sampling Methods probability sampling Nonprobability sampling

13. Probability Sampling • A probability sampling scheme is one in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined.

14. Non-Probability Sampling • Non probability sampling is any sampling 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.

15. Types of Sampling Methods Probability • Simple random sampling • Systematic random sampling • Stratified random sampling • Cluster sampling Non probability • Convenience sampling • Judgment sampling • Quota sampling • Snowball sampling

16. Simple Random Sampling Simple random sampling is a method of probability sampling in which every unit has an equal non zero chance of being selected

17. Simple random sampling

18. Systematic Random Sampling Systematic random sampling is a method of probability sampling in which the defined target population is ordered and the sample is selected according to position using a skip interval

19. Steps in Drawing a Systematic Random Sample • 1: Obtain a list of units that contains an acceptable frame of the target population • 2: Determine the number of units in the list and the desired sample size • 3: Compute the skip interval • 4: Determine a random start point • 5: Beginning at the start point, select the units by choosing each unit that corresponds to the skip interval

20. Systematic sampling

21. Stratified Random Sampling Stratified random sampling is a method of probability sampling in which the population is divided into different subgroups and samples are selected from each.

22. Steps in Drawing a Stratified Random Sample • 1: Divide the target population into homogeneous subgroups or strata • 2: Draw random samples from each stratum • 3: Combine the samples from each stratum into a single sample of the target population

23. Example:

24. Cluster sampling • Cluster sampling is an example of 'two-stage sampling' . • First stage a sample of areas is chosen; • Second stage a sample of respondents within those areas is selected. • Population divided into clusters of homogeneous units, usually based on geographical contiguity. • Sampling units are groups rather than individuals. • A sample of such clusters is then selected. • All units from the selected clusters are studied.

25. Cluster sampling Section 1 Section 2 Section 3 Section 5 Section 4

26. Accidental, Haphazard or convenience sampling members of the population are chosen based on their relative ease of access. To sample friends, co-workers, or shoppers at a single mall, any one on the street • Snowball method The first respondent refers to next and then a chain starts Example: Addicts, HIV etc. • Judgmental sampling or Purposive sampling The researcher chooses the sample based on who they think would be appropriate for the study. This is used primarily when there is a limited number of people that have expertise in the area being researched.

27. Quota sampling: • There are two types of quota sampling: proportional. In proportional quota sampling you want to represent the major characteristics of the population by sampling a proportional amount of each. Non proportional: Non proportional quota sampling is a bit less restrictive. the minimum number of sampled units is specified in each category. not concerned with having numbers that match the proportions in the population • Ad hoc quotas: • A quota is established (say 65% women) and researchers are free to choose any respondent they wish as long as the quota is met. • Expert Sampling • Expert sampling :involves the assembling of a sample of persons with known or demonstrable experience and expertise in some area. • Often, we convene such a sample under the auspices of a "panel of experts." There are actually two reasons you might do expert sampling. First, because it would be the best way to elicit the views of persons who have specific expertise.

28. Errors in sample • Systematic error (or bias) Inaccurate response (information bias) • Selection bias • Sampling error (random error) Sampling error is any type of bias that is attributable to mistakes in either drawing a sample or determining the sample size

29. Type-I Error • The probability of finding a difference with our sample compared to population, and there really isn’t one…. • Known as the α (or “type 1 error”) • Usually set at 5% (or 0.05)

30. Type-II Error • The probability of not finding a difference that actually exists between our sample compared to the population… • Known as the β (or “type 2 error”) • Power is (1- β) and is usually 80%

31. Factors Affecting Sample Size for Probability Designs • Variability of the population characteristic under investigation • Level of confidence desired in the estimate • Degree of precision desired in estimating the population characteristic

32. Comparison b/w Probability and Nonprobability Sampling • The difference between nonprobabilityand probability sampling is that nonprobability sampling does not involve random selection and probability sampling does. • Nonprobability sampling techniques cannot be used to infer from the sample to the general population. • Any generalizations obtained from a nonprobability sample must be filtered through one's knowledge of the topic being studied. • Performing nonprobability sampling is considerably less expensive than doing probability sampling, but the results are of limited value.

33. Probability Sampling and Sample Sizes • When estimating a population mean n = (Z2B,CL)(σ2/e2) • n estimates of a population proportion are of concern n = (Z2B,CL)([P x Q]/e2)

34. Probability Sampling Advantages • Less prone to bias • Allows estimation of magnitude of sampling error, from which you can determine the statistical significance of changes/differences in indicators

35. Probability Sampling Disadvantages • Requires that you have a list of all sample elements • More time-consuming • More costly • No advantage when small numbers of elements are to be chosen

36. Non Probability Sampling Advantages • More flexible • Less costly • Less time-consuming • Judgmentally representative samples may be preferred when small numbers of elements are to be chosen.

37. Non Probability Sampling Disadvantages • Greater risk of bias • May not be possible to generalize to program target population • Subjectivity can make it difficult to measure changes in indicators overtime • No way to assess precision or reliability of data

39. Thank you