2.3 SAMPLING TECHNIQUES

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2.3 SAMPLING TECHNIQUES

• In statistics, the term POPULATION is used to
  define ALL individuals or items that belong to
  the group under study.
• The researcher defines the population.
• Examples could be
• All students that are enrolled at Highland
  (small)
• All the people in Ontario that hold a valid
  drivers license (large)
• All the students in Mr. Lenart MDM4U class (very
  small)
• All trucks with a valid ownership and
  registration in Hamilton

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2.3 SAMPLING TECHNIQUES

• A census is a study that measures all members or
  items in a population.
• Populations can be small or large.
• In many cases, populations are large and it may
  not be cost effective to measure every member of
  item in the population to conduct a study.

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2.3 SAMPLING TECHNIQUES
In many cases it is not feasible to conduct a
study using every item in the population, that is
why we use a sample to make predictions or
inferences about the population
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2.3 SAMPLING TECHNIQUES

• If selected carefully, a relatively small SAMPLE
  can give quite accurate results about the
  characteristics of the POPULATION.
• The following are some of the most commonly used
  sampling techniques.

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2.3 SAMPLING TECHNIQUES

• Simple Random Sampling
• Every member of the population has equal chance
  of being selected for the sample
• Choosing a sample randomly reduces the risk of
  BIAS (sample not being representative of the
  population)

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2.3 SAMPLING TECHNIQUES

• Systematic Random Sampling
• You go through the population sequentially and
  select individuals at equal intervals
• INTERVAL

POPULATION SIZE
SAMPLE SIZE
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2.3 SAMPLING TECHNIQUES

• Systematic Random Sampling

1. Number the items in your population sequentially
2. Determine the interval size, k.
3. Select the starting point at random. Between 1
   and k.
4. Select every kth item in the population.

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2.3 SAMPLING TECHNIQUES

• Systematic Random Sampling

• The school administration is planning to conduct
  a study about school uniforms.
• They would like to take a systematic sample of 50
  students from the student population of about
  920.
• Suggest a method for selecting the sample.

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2.3 SAMPLING T TECHNIQUES

• Stratified Sample

• Sometimes a population includes groups of members
  that share a common characteristic such as
  gender, grade, ethnicity
• Such groups are called strata
• A stratified sample has the same proportion of
  members from each strata as the population does

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2.3 SAMPLING TECHNIQUES

• Stratified Sample

Design a stratified sample for a survey of 50
students.
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2.3 SAMPLING TECHNIQUES

• CLUSTER SAMPLE

• Sometimes it is too expensive to spread a sample
  across the population as a whole. Travel costs
  can become expensive if interviewers have to
  survey people from one end of the country to the
  other. To reduce costs, statisticians may choose
  a cluster sampling technique
• If certain groups are likely to be representative
  of the entire population, you can use a random
  selection of such groups as a cluster sample

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2.3 SAMPLING TECHNIQUES

• CLUSTER SAMPLE - example

• Suppose you are a representative from an athletic
  organization wishing to find out which sports
  Grade 12 students are participating in across
  Canada. It would be too costly and lengthy to
  survey every Canadian in Grade 12, or even a
  couple of students from every Grade 12 class in
  Canada. Instead, 100 schools are randomly
  selected from all over Canada.
• These schools provide clusters of samples. Then
  every Grade 12 student in all 100 clusters is
  surveyed. In effect, the students in these
  clusters represent all Grade 12 students in Canada

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2.3 SAMPLING TECHNIQUES

• MULTI-STAGE SAMPLE

• Uses several levels of random sampling.
• Multi-stage sampling is like the cluster method,
  except that it involves picking a sample from
  within each chosen cluster, rather than including
  all units in the cluster.

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2.3 SAMPLING TECHNIQUES

• MULTI-STAGE SAMPLE - example

• Consider our cluster sample of grade 12 students
• In multi-stage sampling, you could get a list of
  all Grade 11 students from these selected schools
  and select a random sample of students from each
  school. This would be a two-stage sampling
  design.

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2.3 SAMPLING TECHNIQUES

• VOLUNTARY RESPONSE SAMPLE

• The researcher simply invites any member of the
  population to participate in the survey.
• The results from such sample can be biased
  because people who choose to respond are not
  always representative of the population.
• Call-in shows and mail-in surveys rely on
  voluntary response.

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2.3 SAMPLING TECHNIQUES
CONVENIENCE SAMPLE

• A sample that is easily accessible.
• The researcher makes no attempt, or only a
  limited attempt, to insure that this sample is an
  accurate representation of some larger group or
  population.
• The classic example of a convenience sample is
  standing at a shopping mall and selecting
  shoppers as they walk by to fill out a survey.

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