THEORY OF SAMPLING

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THEORY OF SAMPLING

• Facilitator
• Assoc. Prof. Dr. Abdul Hamid b. Hj. Mar Iman
• Director
• Centre for Real Estate Studies
• Faculty of Engineering and Geoinformation Science
• Universiti Teknologi Malaysia
• Skudai, Johor

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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

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Concept of sampling Definition

• A process of selecting units from a population
• A process of selecting a sample to determine
  certain characteristics of a population

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Concept of samplingWhy sample

• 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!

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General Types of Sampling

• Probability Sampling
• Non-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

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Probability Sampling

• Simple random
• Stratified random
• Systematic random
• Cluster/area random
• Multi-stage random

• Non-probability Sampling
• Convenience
• Purposive

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Simple random sampling
Population
Sample

• Probability selected ni/N
• When population is rather uniform (e.g.
  school/college students, low-cost houses)
• Simplest, fastest, cheapest
• Could be unreliable, why?

B T G K
A T Y W B P
G E S C
K L G N Q
element
population
Population not uniform
Wrong procedure
?
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Random selection

• Pick any element
• Use random table

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Stratified random sampling
Population
Sample

• 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

3 7 10 16
1 4 8 12 3 6
13 2 10 20
15 7 14 11 16
Stratum 1 odd no.
Stratum 2 even no.
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Stratified random sampling (contd.)Disproportion
ate
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
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Stratified random sampling (contd.)Proportionate

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.
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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

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Systematic sampling (contd.) Example
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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?

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Systematic sampling (contd.)sampling plan

• 500/7 72 shoppers per day
• 72/3 24 per time block
• 24/3 8 shoppers per hour
• 8/4 2 shoppers per ethnic group per hour
• 60/8 7.5th. minutes pick-up interval

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Cluster sampling

• Research involves spatial issues (e.g. do prices
  vary according to neighbourhoods 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

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Cluster samplingExample
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Multi-stage sampling (contd.)

• Among choices
• Two-stage cluster (cluster first, then,
• stratify within cluster).

Tmn Daya
Tmn Perling
Tmn Tebrau
Cluster
Strata
M C I M C I
M C I
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Multi-stage sampling (contd.)

• Three-stage stratified (Locality first,
• then, ethnic, then, family status).

Locality
Inner
Suburb
Outskirt
Ethnic
C
M
I
C
M
M
I
I
C
Family status
MD
UD
MD
MD
UD
UD
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Convenience sampling

• Naïve sampling
• Does not intend to represent the population
• Selection based on ones convenience, by
  accident, or haphazard way
• Common in popular surveys, public view or
  opinion (e.g. by-the-road-side interviews)
• Serious bias only one group included
• Must be avoided

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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

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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
• Populations normal distribution can be analysed

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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

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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.

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Purposive sampling (contd.)Heterogeneity/diversi
ty 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.

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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

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Some tipsDetermining sample size

• Rules of thumb
• anything 30 cases
• smaller population needs greater
• sampling intensity
• type of sample
• Statistical rules
• level of accuracy required
• a priori population parameter
• type of sample

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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.

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Determining sample sizeExample

• 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 ?)
• s std. deviation of population (must be known)
• maximum precision required between sample
  and population mean

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Determining sample sizeNumerical example

• Problem
• A researcher would like to estimate the average
  spending of households in one week
• in a shopping complex for the clients 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

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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?

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• Thank you!