2. Chapter 11
Sampling Design

3. Chapter Objectives
define sampling, sample, population, element, subject and sampling frame
describe and discuss the different probability and non-probability sampling designs
identify the use of appropriate sampling designs for different research purposes
discuss precision and confidence
estimate sample size
discuss efficiency in sampling
discuss generalisability in the context of sampling designs

4. The Principles of Sampling Design

5. Population, Element, Sampling Frame, Sample and Subject
Population (or target population)
entire group of people, events or things of interest that the researcher wishes to investigate
Element
a single member of the population
Sampling Frame
a listing of all the elements in the population from which the sample is drawn
Sample
a subset of the population
Subject
a single member of the sample

6. Relationship between Population, Sampling Frame and Sample

7. Relationship between Sample Statistics and Population Parameters

8. Advantages of Sampling
Less costs
cheaper than studying whole population
Less errors due to less fatigue
better results
Less time
quicker
Destruction of elements avoided
eg bulbs

9. Normal Distibution in a Population
As the sample size n increases, the means of the random samples taken from practically any population approach a normal distribution with mean μ and standard deviation 

10. Representativeness of Samples
If the sample mean is much > than the population mean μ then the sample would overestimate the true population mean
If the sample mean is much < than the population mean μ then the sample would underestimate the true population mean
The more representative the sample is of the population, the more generalisable are the findings of the research.

11. Preparing a Sampling Design

12. Probability & Non-probability Sampling
the elements in the population have some known chance or probability of being selected as sample subjects
Non-probability Sampling
the elements do not have a known or predetermined chance of being selected as subjects

13. Probability Sampling Simple random sampling
every element in the population has a known and equal chance of being selected as a subject
Complex (or restricted) probability sampling
procedures to ensure practical viable alternatives to simple random sampling, at lower costs, and greater statistical efficiency

14. Simple Random Sampling
Is the most representative of the population for most purposes
Disadvantages are:
Most cumbersome and tedious
The entire listing of elements in population frequently unavailable
Very expensive
Not the most efficient design

15. Complex Probability Sampling
Systematic sampling
Stratified random sampling
Cluster sampling
Area sampling
Double sampling

16. Systematic Sampling
Every nth element in the population starting with a randomly chosen element
Example:
Want a sample of 35 households from a total of 260 houses. Could sample every 7th house starting from a randomly chosen number from 1 to 10. If that random number is 7, sample 35 houses starting with 7th house (14th house, 21st house, etc)
Possible problem is that there could be systematic bias. eg every 7th house could be a corner house, with different characteristics of both house and dwellers.

17. Stratified Random Sampling
Comprises sampling from populations segregated into a number of mutually exclusive sub-populations or strata. Eg
University students divided into juniors, seniors, etc
Employees stratified into clerks, supervisors, managers, etc
Homogeneity within stratum and heterogeneity between strata
Statistical efficiency greater in stratified samples
Sub-groups can be analysed
Different methods of analysis can be used for different sub-groups.

18. Stratified Random Sampling Example
Stratum Motivation Level
Clerks Low
Middle Managers Very high
Top Managers Medium
Combined X would not discrimate among groups
Stratified Sampling
Proportionate sampling
Disproportionate sampling

19. Proportionate & Disproportionate Stratified Random Sampling

20. Cluster Sampling Take clusters or chunks of elements for study
Eg, sample all students in MGMT 303 and MGMT 304 to study the characteristics of Management Science majors
Advantage of cluster sampling is lower costs
Statistically it is less efficient than other probability sampling procedures discussed so far
Area Sampling:
Cluster sampling confined to a particular area
Eg, sampling residents of a particular locality, county, etc

21. Double Sampling
Collect preliminary data from a sample, and choose a sub-sample of that sample for more detailed investigation.
Example:
Conduct unstructured interviews with a sample of 50.
Repeat a structured interview with 30 from the 50 originally sampled.

22. Non-probability Sampling
Convenience sampling
Survey whoever is easily available
Used for quick diagnosis of situations
Simplest and cheapest
Least reliable
Purposive sampling
Judgement sampling
Snowball sampling
Quota sampling

23. Judgement Sampling
Involves the choice of subjects who are in the best position to provide the information required
Experts’ opinions could be sought
Eg, Doctors surveyed for cancer causes

24. Snowball Sampling
Used when elements in population have specific characteristics or knowledge, but are very difficult to locate and contact.
Initial sample group can be selected by probability or non-probability methods, but new subjects are selected based on information provided by initial subjects.
Eg, used to locate members of different stakeholder groups regarding their opinions of a new public works project.

25. Quota Sampling
Quotas for numbers or proportion of people to be sampled, established.
Examples:
survey for research on dual career families: 50% working men and 50% working women surveyed.
Women in management survey: 70% women surveyed and 30% men surveyed.

26. Choice Points in Sampling Design

27. Precision and Confidence
refers to how close the sample estimate eg X is to the true population characteristic( ) depends on the variablity in the sampling distribution of the mean, ie the standard error ( S X )
indicates the confidence interval within which the population mean can be estimated (= X + KS X )
Confidence
reflects the level of certainty that the sample estimates will actually hold true for the population
bias is absent from the data
accuracy is reflected by the confidence level ( K )

28. Standard Error = standard deviation of the sample = sample size
= standard error or standard deviation of the sample mean

29. Characteristics of the Standard Error
The smaller the standard deviation of the population, the smaller the standard error and the greater the precision
The standard error varies inversely with the square root of the sample size. Hence the larger the n, the smaller the standard error, and the greater the precision.

30. Confidence Interval for the Mean
= population mean
= sample mean
= standard error
= z statistic for large samples ≥ 30
= t statistic for small samples < 30

31. Confidence Levels μ = 105 ± 1.96*1.43 = 105 ± 2.80
For large samples, K = z score
= for 90% confidence level
= for 95% confidence level
= for 99% confidence level
Example: a 95% confidence interval for mean purchases (μ) by customers based on a sample mean of $105 with a standard error of $1.43 is:
μ = 105 ± 1.96*1.43 = 105 ± 2.80
Hence μ would fall between $ and $107.80

32. Trade-off between Precision and Confidence

33. Determining the Sample Size
Example: Suppose a manager wants to be 95% confident that withdrawals from a bank will be within a confidence level of ± $500. From a sample of customers the standard deviation S was calculated as $ What sample size is needed?
The expression is equivalent to the precision or admissible margin of error. Let this be E. or

34. Determining the Sample Size (cont’d)
Rearranging these terms, a formula for the sample size n is:
Substituting K=1.96 (95% confidence), S=3500, and E=500 into this equation, provides the sample size n:

35. Roscoe’s Rules of Thumb for Determining Sample Size
Sample sizes larger than 30 and smaller than 500 are appropriate for most research
Minimum sample size of 30 for each sub-category is usually necessary
In multivariate research, the sample size should be several times as large as the number of variables in the study
For simple experimental research, successful research is possible with samples as small as 10 to 20

36. Efficiency in Sampling
If n is constant, you should get a smaller or
For the same , you should use a
smaller n

37. Review of Sample Size Decisions
How much precision is wanted in estimating the population characteristics, ie what is the margin of admissible error or confidence interval?
How much confidence is really needed. How much risk can we take of making errors in estimating the population parameters (ie confidence level)?
How much variability is in the population? The greater the variability, the larger the sample size needed.
Cost and time constraints
The size of the population (N) itself