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THEORY OF SAMPLING
Facilitator:Assoc. Prof. Dr. Abdul Hamid b. Hj. Mar Iman
DirectorCentre for Real Estate Studies
Faculty of Engineering and Geoinformation Science
Universiti Teknologi MalaysiaSkudai, Johor
Objectives
Overall: Reinforce your understanding from the main lecture
Specific: * Concept of sampling * Types of sampling techniques * Some useful tips in sampling
What I will not do: To teach every bit and pieces of sampling techniques
A process of selecting units from a population A process of selecting a sample to determine
certain characteristics of a population
Concept of sampling
“Definition”
Economy Timeliness The large size of many populations Inaccessibility of some of the population Destructiveness of the observation –
accuracy
In most cases, census is unnecessary!
Concept of sampling“Why sample”
General Types of Sampling
Probability SamplingNon-probability Sampling
Probability Sampling: utilizes some form of random selection
Non-probability sampling: does not involve random selection
Random/non-random→ issue of bias, sample validity, reliability of results, generalization
Probability Sampling
Simple randomStratified randomSystematic randomCluster/area randomMulti-stage random
Non-probability SamplingConveniencePurposive
Simple random sampling
Probability selected = ni/N
When population is rather uniform (e.g. school/college students, low-cost houses)
Simplest, fastest, cheapestCould be unreliable, why?
A T Y W
B P G E S C K L
G N Q
B T
G K
Population Sample
elementpopulation
Population not uniform
Wrong procedure
?
Random selection
Pick any “element” Use random table
Stratified random sampling
Break population into “meaningful” strata and take random sample from each stratum
Can be proportionate or disproportionate within strata When: * population is not very uniform (e.g. shoppers, houses) * key sub-groups need to be represented → more precision * variability within group affects research results * sub-group inferences are needed
1 4 8 12
3 6 13 2 10 20 15 7 14 11 16
3 7
10 16
Population Sample
Stratum 2 = even no.
Stratum 1 = odd no.
Stratified random sampling (contd.)“Disproportionate”
Type of company
Sole Proprietor
Partnership Private Limited
Sample frame
150 58 82
Sample stratum
150/290 X 250
58/290 x 250
82/290 x 250
Sample 129 50 71
Let say a sample of 250 companies is required to conduct a research on “strategic planning” practices among the managers. Total company population is 550, but a sample frame obtained is 290. Sampling intensity = 45.5%
Stratified random sampling (contd.)“Proportionate”
Type of company
Sole Proprietor
Partnership Private Limited
Sample frame
150 58 82
Sample stratum
25/100 x 150
25/100 x 58
25/100 x 82
Sample 38 15 21
Let say a sample of 250 companies is required to conduct a research on “strategic planning” practices among the managers. Total company population is 550, but a sample frame obtained is 290. Researcher decides to take 25% cases from each stratum. Sampling intensity = 13.5%.
Systematic sampling
Simple or stratified in nature Systematic in the “picking-up” of element. E.g.
every 5th. visitor, every 10th. House, every 15th. minute
Steps:
* Number the population (1,…,N)
* Decide on the sample size, n
* Decide on the interval size, k = N/n
* Select an integer between 1 and k
* Take case for every kth. unit
Systematic sampling (contd.) “Example”
Systematic sampling (contd.) “Example”
In a face-to-face consumer survey, a sample of 500 shoppers is planned for a 7-day (Mon. – Sun.) period at a shopping complex. The sampling is planned for 3 time blocks: 12-3 p.m.; 3-6 p.m.; and after 6-9 p.m. Respondents are sub-divided into 4 ethnic groups: Malays (30%), Chinese (30%), Indian (30%), and Others (10%). Finally, they are categorized into “Family” and “Single”. Repeat persons are not allowed in the sampling. Determine you sampling plan and determine the timing for respondent “pick-up” interval?
Systematic sampling (contd.)sampling plan
500/7 = 72 shoppers per day72/3 = 24 per time block24/3 = 8 shoppers per hour8/4 = 2 shoppers per ethnic group per
hour60/8 = 7.5th. minutes “pick-up” interval
Cluster sampling
Research involves spatial issues (e.g. do prices vary
according to neighbourhood’s level of crime?) Sampling involves analysis of geographic units Sampling involves extensive travelling → try to
minimise logistic and resources Steps:
* Divide population into “clusters” (localities)
* Choose clusters randomly (simple random,
stratified, etc.)
* Take all cases from each cluster Efficient from administrative perspective
Cluster sampling“Example”
Multi-stage sampling (contd.)
Among choices:
* Two-stage cluster (cluster first, then,
stratify within cluster).
Tmn Perling
Tmn Daya Tmn Tebrau
M C I M C I M C I
Cluster
Strata
Multi-stage sampling (contd.)
* Three-stage stratified (Locality first,
then, ethnic, then, family status).
Outskirt Inner Suburb Locality
EthnicM C I I C M IC M
Family status
MD UD MD MDUD UD
Convenience sampling
Naïve samplingDoes not intend to represent the populationSelection based on one’s “convenience”, by
“accident”, or “haphazard” wayCommon in popular surveys, public “view”
or “opinion” (e.g. by-the-road-side “interviews”)
Serious bias – only one group includedMust be avoided
Purposive sampling
Sampling involves “pre-determined” criteria. E.g. house buyers (25-45 years old), low-cost house buyers (income ≤ RM 2,500)
Proportionality is not critical Achieve sample size quickly More likely to get the required results about the
target population. E.g. what cause tax defaults? → sample those who have not paid tax for, say, over 3 years.
Can be useful if designed properly Types of purposive sampling: modal instance,
expert panel, quota, heterogeneity/diversity, snowball
Purposive sampling (contd.)“Modal instance”
“Typical”, “most frequently”, or “modal” cases. E.g. * 60% of Malaysian population earns ≤ RM 4,000 per month. * 65% of residential properties comprises single- and double-storey terrace units. * First-time house buyers have mean age of 27 years. * Modal home is a single-storey terraced priced at RM 120,000 per unit. Sample is taken to represent the population Population’s normal distribution can be analysed
Purposive sampling (contd.)“Expert panel”
A sample of persons with known or demonstrable experience and expertise in some area. E.g.
* Economic growth next two years → ? * Challenges in ICT in Malaysia → ? * Best practices in corporate management → ? Advantages: * Best way to elicit the views of persons who have specific expertise. * Helps validate other sampling approaches Disadvantages: * Even experts can be, and often are, wrong. * May be group-biased
Purposive sampling (contd.)“Quota sampling”
Select cases non-randomly according to some fixed quota. Proportional quota * Represent major characteristics of the population by proportion. E. g. 40% women and 60% men * Have to decide the specific characteristics for the quota (e.g. gender, age, education race, religion, etc.) Non-proportional quota * Specific minimum size of cases in each category. * Not concerned with upper limit of quota, simply to have enough to assure enumeration. * Smaller groups are adequately represented in sample.
Purposive sampling (contd.)“Heterogeneity/diversity sampling”
Almost the opposite of modal instance sampling Include all opinions or views Proportionate representation of population is not
important Broad spectrum of ideas, not identifying the
"average" or "modal instance“. E.g. * Challenges in ICT: different user groups have or perceive different challenges. What is sampled not people, but perhaps, ideas Ideas can be "outlier" or unusual ones.
Purposive sampling (contd.)“Snowball sampling”
Identify a case that meets criteria for inclusion in the study.
Find another case, that also meets the criteria, based on the first one.
Next, search for others based on the previous ones, and so on.
Hardly leads to representative sample, but useful when population is inaccessible or hard to find. E.g.
* the homeless * forced sales properties * wound-up companies
Rules of thumb: * anything ≥ 30 cases * smaller population needs greater sampling intensity * type of sampleStatistical rules: * level of accuracy required * a priori population parameter * type of sample
Some tips“Determining sample size”
Why sample size matters?
Too large → waste time, resources and money Too small → inaccurate results Generalizability of the study results Minimum sample size needed to estimate a
population parameter.
Determining sample size“Example”
Many ways One way → use statistical sample Different sample types have different formula Based on simple random sampling:
n = required sample size
Z/2 = known critical value, based on level of confidence (1 – )
σ = std. deviation of population (must be known)
= maximum precision required between sample and population mean
Problem
A researcher would like to estimate the average spending of households in one week in a shopping complex for the client’s business plan and model. How many households must we randomly select to be 95% sure that the sample mean is within RM 25 of the population mean. Information on household shows that variation in average weekly spending per household = RM 160
Tips for solution
* We are solving for the sample size n.* A 95% degree confidence corresponds to = 0.05.* Each of the shaded tails in the following figure has an area of = 0.025* Region to the left of and to the right of Z = 0 is 0.5 - 0.025, or 0.475* Table of the Standard Normal ( ) Distribution: area of 0.475 → ‘critical value’ = 1.96.* Margin of error = 25, std. deviation = 160
Determining sample size“Numerical example”
Test yourselves!1. A hypothesis in a research says that “investment yields is insignificantly
influenced by risk attitude of the investor”. How would you determine your sample to prove or disprove it?
2. Some issues are posed in a social research, among other things, as follows:
* What constitutes “good governance”? * What is “good leadership”? * What is an “effective strategy” Suggest how would you design your sample to obtain a wide-spectrum
but yet valid answers to these issues?
Thank you!