4 sampling
- 1. Quantitative Research Methods Lecture 4 1. The logic of sampling 2. Classic case of failure and Sampling /Nonsampling Errors 3. Types of Smapling 4. Sample size
- 2. 1.The logic of sampling •Recall that statistical inference permits us to draw conclusions about a population based on a sample. •Sampling is often done for reasons of cost and practicality. •In any case, the sampled population and the target population should be similar to one another.
- 3. 1.The logic of sampling • What we are trying to do: ▫ Study a bunch of people and make discoveries that apply to a larger population we don’t study directly • Topic: E.g. Social Media Use among Kuwait Univ. Students ▫ Methods: survey • What is the population?
- 4. 1. The logic of sampling • Due to limited time, money and resources, we cannot examine an entire population in many situations ▫ We can’t conduct a census ▫ Census: The process of examining every member of the entire citizen population) ▫ A census of UAE citizens would involve millions of participants • What can we do then? • We take a sample from the population
- 5. Sample vs. population • The process of selecting subjects is called sampling Population A Sample A1 Sampling
- 6. Sampling • Sampling is a crucial step because we need to rely on this subset of people to understand the entire population.
- 7. 2.1 Classic case of failure • 1936 U.S. Presidential Election: Literary Digest sent out 10 million ballots to people listed in the magazine subscription, telephone directories, club members, 2.4 million people responded (Response rate?) • Literary Digest predicts: ▫ Roosevelt 43% Landon 57% • Actual results: ▫ Roosevelt 62% Landon 38% • Gallup predicted a Roosevelt victory on the basis of a much smaller sample (50,000)
- 8. 2.1 Classic case of failure • Literary Digest A terrible mistake!! • Editors were all puzzled: ▫ How could the poll be so wrong?! ▫ We had a huge sample (2.4 million people) ! • What went wrong?
- 9. 2.1 Classic case of failure • Bad sampling, Wrong sample! • Sampling methods for Literary Digest Poll— using: ▫ telephone directories ▫ magazine subscriber lists ▫ club and association rosters, etc. • Mailed out 10 million ballots • Can you think of any problems with these sampling methods?
- 10. 2.1 Classic case of failure • Literary Digest's bad sampling problem #1 Selection bias: • Sources for sample lists tended to represent middle- and upper-class voters: ▫ In those days, many poor did not have telephones ▫ They didn’t subscribe to magazines ▫ They didn’t belong to clubs • On the other hand, the poor would be voting heavily for Roosevelt and his social programs • => Selection bias: wrong sample due to exclusion of certain segments of a population
- 11. 2.1 Classic case of failure • Literary Digest's bad sampling problem #2 Nonresponse bias • 10 million ballots were sent out • 2.4 million were returned • Response rate of 2.4/10 = 24% • Fact: those who responded to surveys tended to be: ▫ better educated ▫ in higher economic brackets ▫ Republican! • Nonresponse bias: wrong sample due to low response rate
- 12. 2.2 Errors are considered: Sampling and Non-Sampling Errors Population Sample A1 1) Sampling error 2) Nonsampling errors
- 13. 2.2 Sampling and Non-Sampling Errors •Two major types of error can arise when a sample of observations is taken from a population: 1) sampling error 2) nonsampling error. •Sampling error refers to differences between the sample and the population that exist only because of the observations that happened to be selected for the sample. •Affected by sample size, variability within population, and sampling scheme, increase sample size may solve problem
- 14. 2.2 Nonsampling Error •Non-sampling errors are more serious and are due to mistakes made in the acquisition of data or due to the sample observations being selected improperly. •Three types of non-sampling errors: I. Errors in data acquisition II. Selection bias III. Nonresponse errors/bias Note: increasing the sample size will not reduce this type of error. Sample bias
- 15. I. Errors in data acquisition… …arises from the recording of incorrect responses, due to: • incorrect measurements being taken because of faulty equipment, • mistakes made during transcription from primary sources, • inaccurate recording of data due to misinterpretation of terms, or • inaccurate responses to questions concerning sensitive issues.
- 16. II.III. Sample bias III. Nonresponse bias Sample bias II. Selection bias Excluding certain segments of a population Those who respond may possess some characteristics that are different from those who not respond
- 17. 2. How to avoid error in sampling • Consider the population parameters (characteristics) before selecting your sample to make sure you would not leave out important segments
- 18. 3. Two kinds of sampling Sampling Probability sampling Non-probability sampling 1) Simple random sampling 2) Stratified Random Sampling 3) Systematic sampling 4) Multistage cluster sampling 1) Reliance on available subjects 2) Purposive sampling 3) Snowball sampling 4) Quota sampling
- 19. 3.1 Probability sampling 1) Simple Random Sampling • Randomly select the subjects from the the entire population • E.g., randomly select 10,000 UAE citizens out of the 9 millions • Sampling error (that is, the chance of getting a biased sample) is reduced • Each subject has an equal chance (probability) of being selected
- 20. 1) Simple Random Sampling • How it is done • 1) Using Random Numbers Table • Steps: ▫ Get a sampling frame (a list that includes all members of the population) ▫ Assign a number to each of the members ▫ Determine the number of subjects you want to select E.g., 100 ▫ Determine the number of digits E.g., if there are 980 members in the population, you’ll need 3- digit numbers ▫ Go to the random numbers table, determine the left-most 3 digits or the right-most 3 digit ▫ Continue until you reach the 100th subject ▫ Diagram
- 23. Hands on: computer generated random numbers • Excel
- 24. 1) Simple Random Sampling • 2) Telephone surveys • (2a) Random digit dialing (RDD) • Generated by computer • Problem: numbers may be disconnected or have not yet been assigned • General rule: Generate at least 3 times the number of telephone numbers needed
- 25. 1) Simple Random Sampling • (2) Telephone surveys • (2b) Randomly choose a number from the telephone directory • Predetermine a one-digit/ two-digit/ three-digit number (e.g. 678) • E.g., the number randomly picked is 2784-4433 • Add the predetermined number(s) to it • Reduce the possibility of invalid numbers
- 26. 1) Simple Random Sampling • Advantages: • 1) minimized sampling error • 2) a representative sample may be easily obtainable • 3) external validity • Disadvantages: • 1) a complete sampling frame (the complete list of members in the population) not available • 2) the procedure involved is much more expensive and time- consuming
- 27. 2) Stratified Random Sampling •A stratified random sample is obtained by separating the population into mutually exclusive sets, or strata, and then drawing simple random samples from each stratum. Strata 1 : Gender Male Female Strata 2 : Age < 20 20-30 31-40 41-50 51-60 > 60 Strata 3 : Occupation professional clerical blue collar other We can inquire about the total population, make inferences within a stratum or make comparisons across strata
- 28. 2) Stratified Random Sampling… •After the population has been stratified, we can use simple random sampling to generate the complete sample: If we only have sufficient resources to sample 400 people total, we would draw 100 of them from the low income group… …if we are sampling 1000 people, we’d draw 50 of them from the high income group.
- 29. 3) Systematic Random Sampling • Every nth subject is selected from the population • ‘nth’ = sampling interval (e.g., a sampling interval of 6) • E.g., a class list ▫ Randomly select a starting point, then every 6th subject • Evolves from simple random sampling, but saves more time, resources, and effort • Commonly used • However…systematic random sampling is far from perfect…
- 30. Disadvantages of systematic sampling • 1) a complete sampling frame • 2) the order of the sampling frame may bias the selection process • =>Periodicity
- 31. 4) Multistage cluster sampling 1. List all districts and randomly select one 2. List all the streets in that districts and randomly select one 3. List all the buildings on that street and randomly select one 4. List all the households in that buildings and select sample of households (e.g., every 6th household) • Drawback: You need to have the entire lists of districts, streets, buildings, and households
- 32. Random sampling is good, but not without defects • 1) complete sampling frame is not possible sometimes • 2) Cost and time consuming • 3) Random sampling can’t 100% guarantee representativeness
- 33. 3.2 Non-probability sampling • 1) Purpose of the study • Not aimed at generalizing to the entire population • To explore and understand • 2) Cost vs. value • Cost of a probability sampling is too high • 3) Time constraints • When there is a time constraint
- 34. 3.2 Non-probability sample • 1) Reliance on available subjects • “Convenience sample” • Readily-accessible sample • E.g., students, stopping people on the street. • In writing: “Limitation of the present study: Generalizability should be taken with cautions”
- 35. 3.2 Non-probability sample • 2) Purposive/Judgement sampling • Deliberately select subjects on the basis of specific characteristics • E.g. ▫ Taxi driver ▫ Filipinos ▫ Unemployed
- 36. 3.2 Non-probability sample • 3) Snowball sampling • Collect data on a few members-> • Then ask those members to provide the information needed to locate other members • “Snowball”: the process of accumulation as each located subject suggests other subjects
- 37. 3.2 Non-probability sample • 4) Quota sampling • Select subjects to meet a known percentage of some characteristics: e.g. gender, income, education, etc. • E.g. known gender: 60% male; 40% female ▫ To select 1000 subjects ▫ 600 male and 400 female • Gallop vs. Literary Digest ▫ Quota sampling: sample select was based on levels of income
- 38. 4. Sample Size Numerical techniques for determining sample sizes will be described later, but it suffice to say that the larger the sample size is, the more accurate we can expect the sample estimates to be.
- 39. 4. Methods of determining sample size • 1) Arbitrary approach • 2) Conventional approach
- 40. 4. Methods of determining sample size • 1) Arbitrary approach • “A sample should be at least 5% of the population in order to be accurate.” • Population= 10,000 • Sample size = 500 • But what about 2,000,000?
- 41. 4. Methods of determining sample size • 2) Conventional approach • 50: very poor • 100: poor • 200: fair • 300: good • 500: very good • 1,000: excellent
- 42. Week 2 Assignment • Continue reading: Chapter 1-5 • Assignment due on Oct. 30th , sumbit on blackboard. ▫ P63: 3.16 ▫ P74: 3.43 ▫ Use SPSS to do P64: 3.27 P82: 3.70