Population & Sampling

1. Population & Sampling by Moazzam Ali Malik

2. Population & Sampling

3. What is a Population? • Population is a large group of people which you specify to conduct the research and to answer the research question. • It is the whole or the entire group; the research study is being conducted to get information about, whose properties are analyzed to find the answer or the solution and the results are drawn.

4. What is a Sample? • A sample is a finite part of a statistical population whose properties are studied to gain information about the whole (Webster, 1985). • Sampling is the process of obtaining information from a subset (sample) of a larger group (population) • Number of the sample depends upon the requirements or the scope of the research.

5. Why to Chose a Sample? • The very large populations • The economic advantage • The time factor • The partly accessible populations • The destructive nature of the populations When might you sample the entire population? • When your population is very small • When you have extensive resources • When you don’t expect a very high response

6. Characteristics of a Good Sample Good sampling design should: • Relate to the objectives of the investigation • Be practical and achievable; • Be cost –  effective in terms of equipment and labour; • Provide estimates of population parameters that are truly representative and unbiased. Ideally, representative samples should be: • Taken at random so that every member of the population of data has an equal chance of selection; • Large enough to give sufficient precision; • Unbiased by the sampling procedure or equipment. Factors that influence sample representativeness • Sampling procedure • Sample size • Participation (response)

7. Sampling Terminology The Population/Universe • The class, families living in the city or electorates from which you select you select your sample are called the population or study population, and are usually denoted by the letter N Sampling Design • The way you select students, families or electors is called the sampling design or sampling strategy.

8. Sampling Terminology Sampling elements/Units/Cases/Respondents • The unit about which information is collected • Typically the elements are people • However, schools, universities, corporations, etc. Any of them could be elements. Sampling Frame • The actual list of sampling units (or elements). e.g. if you want to study “Students at the University of Gujrat/Lahore”, there is a list of such sampling units (but there are a number of definition issues to be resolved here)

9. Sampling Terminology Sample/Study Population • Almost impossible to guarantee that every element meeting your definition of “the population” has a chance to be selected into the sample. • Thus the “study population” will be somewhat smaller than “the population” • A subset of a population selected to estimate the behaviour or characteristics of the population. Sample Statistics • Your findings based on the information obtained from your respondents (sample) are called sample statistics. Population Parameters • The estimates arrived at from sample statistics are called population parameters or the population mean.

10. Sampling Terminology Sampling Errors • Errors that occurs when we use a statistic based on sample to predict the value of a population parameter • Approval rating: 63-68% by different polling agencies; population 66% (unknown) • Random sampling: ±3% (margin of error) Response Bias • Due to the way a question is asked or worded • The order of questions • Incorrect response (characteristics of interviewees • (race); lying) Nonresponse bias: missing data • Unreachable; refuse to participate; fail to answer Qs

11. Sampling Designs Basically two sampling strategies available: • Probability sampling • Non-probability Sampling

12. Probability Sampling In Probability Sampling, each member of the population has a certain probability to be selected into the sample Types of Probability Sampling • Random • Stratified Random • Systematic • Cluster • Multistage Sampling

13. Random Sampling • Population members are selected directly from the sampling frame • Equal probability of selection for every member (sample size/population size) • 400/10,000 = .04 • Use random number table or random number generator

14. Systematic Sampling • Order all units in the sampling frame based on some variable and number them from 1 to N • Choose a random starting place from 1 to N and then sample every k units after that

15. Systematic Sampling

16. Stratified Sampling • The chosen sample contains a number of distinct categories which are organized into segments, or strata • equalizing "important" variables • year in school, geographic area, product use, etc. • Steps: • Population is divided into mutually exclusive and exhaustive strata based on an appropriate population characteristic. (e.g. race, age, gender etc.) • Simple random samples are then drawn from each stratum.

17. Stratified Sampling • The sample size is usually proportional to the relative size of the strata. • Ensures that particular groups (e.g. males and females) within a population are adequately represented in the sample • Has a smaller sampling error than simple random sample since a source of variation is eliminated

18. Stratified Sampling

19. Cluster Sampling • The Population is divided into mutually exclusive and exhaustive subgroups, or clusters, usually based on geography or time period • Each cluster should be representative of the population i.e. be heterogeneous. • Means between clusters should be the same (homogeneous) • Then a sample of the clusters is selected. • then some randomly chosen units in the selected clusters are studied.

20. Cluster Sampling • Procedure • Divide population into clusters (usually along geographic boundaries) • Sample clusters randomly • Measure units within sampled clusters

21. Cluster Sampling Two types of cluster sampling methods. One-stage sampling. All of the elements within selected clusters are included in the sample. Two-stage sampling. A subset of elements within selected clusters are randomly selected for inclusion in the sample.

22. MULTISTAGE SAMPLING • Complex form of cluster sampling in which two or more levels of units are embedded one in the other. This technique, is essentially the process of taking random samples of preceding random samples. • Not as effective as true random sampling, but probably solves more of the problems inherent to random sampling. It is an effective strategy because it banks on multiple randomizations. As such, extremely useful. Example • First stage, random number of districts chosen in all states. • Followed by random number of villages. • Then third stage units will be houses. • All ultimate units (houses, for instance) selected at last step are surveyed.

23. Non-probability Sampling Members selected not according to logic of probability (or mathematical rules), but by other means (e.g. convenience, or access) Types of Non-Probability Sampling • Convenience sampling • Purposive/Judgment sampling • Snowball sampling • Quota sampling

24. Convenience Sampling • Convenience Sampling • A researcher's convenience forms the basis for selecting a sample. • Sometimes known as grab or opportunity sampling or accidental or haphazard sampling. • A type of nonprobability sampling which involves the sample being drawn from that part of the population which is close to hand. That is, readily available and convenient Examples • People in my classes • People with some specific characteristic (e.g. tall) • People living in cities

25. Purposive/Judgment Sampling • Select the sample on the basis of knowledge of the population: your own knowledge, or use expert judges to identify candidates to select • Typically used for very rare populations, such as deviant cases.

26. Snowball Sampling • Typically used in qualitative research • When members of a population are difficult to locate, for covert sub-populations, non-cooperative groups • Recruit one respondent, who identifies others, who identify others,…. • Primarily used for exploratory purposes Research design - sampling

27. Quota Sampling • A stratified convenience sampling strategy. The population is first segmented into mutually exclusive sub-groups, just as in stratified sampling. It begins with a table that describes the characteristics of the target population • e.g. the composition of postgraduate students at UOG/UOL in terms of faculty, race, and gender • Then select on a convenience basis, postgraduate students in the same proportions regarding faculty, race, and gender than in the population • In quota sampling the selection of the sample is non-random. For example interviewers might be tempted to interview those who look most helpful. The problem is that these samples may be biased because not everyone gets a chance of selection. This random element is its greatest weakness and quota versus probability has been a matter of controversy for many years.

28. Thank You