1. Educational Research
Chapter 4
Selecting a Sample
Gay, Mills, and Airasian

2. Topics Discussed in this Chapter
 Quantitative sampling
 Selecting random samples
 Selecting non-random samples
 Qualitative sampling
 Selecting purposive samples

3. Quantitative Sampling
 Purpose – to identify participants from
whom to seek some information
 Issues
 Nature of the sample
 Size of the sample
 Method of selecting the sample

4. Quantitative Sampling
 Terminology
 Population: all members of a specified group

Target population – the population to which the
researcher ideally wants to generalize

Accessible population – the population to which the
researcher has access
 Sample: a subset of a population
 Subject: a specific individual participating in a
study
 Sampling technique: the specific method used to
select a sample from a population
Obj. 1.1, 1.2, & 1.3

5. Quantitative Sampling
 Important issues
 Representation – the extent to which the sample is
representative of the population

Demographic characteristics

Personal characteristics

Specific traits
 Generalization – the extent to which the results of
the study can be reasonably extended from the
sample to the population
Obj. 1.4

6. Quantitative Sampling
 Important issues (continued)
 Sampling error

The chance occurrence that a randomly
selected sample is not representative of the
population due to errors inherent in the
sampling technique

Random nature of errors

Controlled by selecting large samples
Obj. 6.1

7. Quantitative Sampling
 Important issues (continued)
 Sampling bias

Some aspect of the researcher’s sampling design
creates bias in the data

Non-random nature of errors

Controlled by being aware of sources of sampling bias
and avoiding them

Examples
 Surveying only students who attend additional help
sessions in a class
 Using data returned from only 25% of those sent a
questionnaire
Obj. 6.2

8. Quantitative Sampling
 Important issues (continued)
 Three fundamental steps

Identify a population

Define the sample size

Select the sample
Obj. 1.5

9. Quantitative Sampling
 Important issues (continued)
 General rules for sample size

As many subjects as possible

Thirty (30) subjects per group for correlational,
causal-comparative, and true experimental
designs

Ten (10) to twenty (20) percent of the
population for descriptive designs
Obj. 1.8

10. Quantitative Sampling
 Important issues (continued)
 General rules for sample size (continued)

See Table 4.2 for additional guidelines for survey
research
 The larger the population size, the smaller the percentage
of the population needed to get a representative sample
 For population of less than 100, use the entire population
 If the population is about 500, sample 50%
 If the population is about 1,500, sample 20%
 If the population is larger than 5,000, sample 400
Obj. 1.9

11. Selecting Random Samples
 Known as probability sampling
 Best method to achieve a
representative sample
 Four techniques
 Random
 Stratified random
 Cluster
 Systematic
Obj. 1.7

12. Selecting Random Samples
 Random sampling
 Selecting subjects so that all members of a
population have an equal and independent chance
of being selected
 Advantages

Easy to conduct

High probability of achieving a representative sample

Meets assumptions of many statistical procedures
 Disadvantages

Identification of all members of the population can be
difficult

Contacting all members of the sample can be difficult
Obj. 1.6, 2.2, & 4.9

13. Selecting Random Samples
 Random sampling (continued)
 Selection process

Identify and define the population

Determine the desired sample size

List all members of the population

Assign all members on the list a consecutive number

Select an arbitrary starting point from a table of random
numbers and read the appropriate number of digits

If the number corresponds to a number assigned to an
individual in the population, that individual is in the
sample; if not, ignore the number

Continue until the desired number of subjects have been
selected
Obj. 2.3

14. Selecting Random Samples
 Random sampling (continued)
 Selection issues

Use a table of random numbers
 Need to list all members of the population
 Ignore duplicates and numbers out of range when sampled
 Potentially time consuming and frustrating

Use SPSS-Windows or other software to select a
random sample
 Create a SPSS-Windows data set of the population or their
identification numbers
 Pull-down commands

Data, select cases, random sample, approximate or
exact

15. Selecting Random Samples
 Stratified random sampling
 Selecting subjects so that relevant subgroups in
the population (i.e., strata) are guaranteed
representation
 A strata represents a variable on which the
researcher would like to see representation in the
sample

Gender

Ethnicity

Grade level
Obj. 3.1 & 3.3

16. Selecting Random Samples
 Stratified random sampling (continued)
 Proportional and non-proportional (i.e., equal size)

Proportional – same proportion of subgroups in the
sample as in the population
 If a population has 45% females and 55% males, the
sample should have 45% females and 55% males

Non-proportional – different, often equal, proportions of
subgroups
 Selecting the same number of children from each of the
five grades in a school even though there are different
numbers of children in each grade
Obj. 3.4

17. Selecting Random Samples
 Stratified random sampling (continued)
 Advantages

More precise sample

Can be used for both proportional and non-proportional
samples

Representation of subgroups in the sample
 Disadvantages

Identification of all members of the population can be
difficult

Identifying members of all subgroups can be difficult
Obj. 3.2 & 4.9

18. Selecting Random Samples
 Stratified random sampling (continued)
 Selection process

Identify and define the population

Determine the desired sample size

Identify the variable and subgroups (i.e., strata)
for which you want to guarantee appropriate
representation

Classify all members of the population as
members of one of the identified subgroups
Obj. 4.1

19. Selecting Random Samples
 Stratified random sampling (continued)
 Selection process (continued)

For proportional stratified samples
 Randomly select a number of individuals from each
subgroup so the proportion of these individuals in the
sample is the same as that in the population

For non-proportional stratified samples
 Randomly select an equal number of individuals from
each subgroup
Obj. 4.1

20. Selecting Random Samples
 Stratified random sampling (continued)
 Selection process for proportional samples

Identify and define the population

Determine the desired sample size

Identify the variable and subgroups (i.e., strata) for which
you want to guarantee appropriate representation

Classify all members of the population as members of
one of the identified subgroups

Randomly select an equal number of individuals from
each subgroup
Obj. 4.1

21. Selecting Random Samples
 Cluster sampling
 Selecting subjects by using groups that have
similar characteristics and in which subjects can
be found

Clusters are locations within which an intact group of
members of the population can be found

Examples
 Neighborhoods
 School districts
 Schools
 Classrooms
Obj. 4.3

22. Selecting Random Samples
 Cluster sampling (continued)
 Multistage sampling involves the use of
two or more sets of clusters

Randomly select a number of school districts
from a population of districts

Randomly select a number of schools from
within each of the school districts

Randomly select a number of classrooms from
within each school
Obj. 4.6

23. Selecting Random Samples
 Cluster sampling (continued)
 Advantages

Very useful when populations are large and spread over
a large geographic region

Convenient and expedient

Do not need the names of everyone in the population
 Disadvantages

Representation is likely to become an issue

Assumptions of some statistical procedures can be
violated
Obj. 4.9

24. Selecting Random Samples
 Cluster sampling (continued)
 Selection process

Identify and define the population

Determine the desired sample size

Identify and define a logical cluster

List all clusters that make up the population of clusters

Estimate the average number of population members per
cluster

Determine the number of clusters needed by dividing the
sample size by the estimated size of a cluster

Randomly select the needed numbers of clusters

Include in the study all individuals in each selected
cluster Obj. 4.4

25. Selecting Random Samples
 Systematic sampling
 Selecting every Kth
subject from a list of the
members of the population
 Advantage

Very easily done
 Disadvantages

Susceptible to systematic exclusion of some subgroups

Some members of the population don’t have an equal
chance of being included
Obj. 4.7 & 4.9

26. Selecting Random Samples
 Systematic sampling (continued)
 Selection process

Identify and define the population

Determine the desired sample size

Obtain a list of the population

Determine what K is equal to by dividing the size of the
population by the desired sample size

Start at some random place in the population list

Take every Kth
individual on the list

If the end of the list is reached before the desired sample
is reached, go back to the top of the list
Obj. 4.8

27. Selecting Non-Random Samples
 Known as non-probability sampling
 Use of methods that do not have random
sampling at any stage
 Useful when the population cannot be
described
 Three techniques
 Convenience
 Purposive
 Quota
Obj. 5.1

28. Selecting Non-Random Samples
 Convenience sampling
 Selection based on the availability of
subjects

Volunteers

Pre-existing groups
 Concerns related to representation and
generalizability
Obj. 5.2 & 5.3

29. Selecting Non-Random Samples
 Purposive sampling
 Selection based on the researcher’s experience
and knowledge of the individuals being sampled

Usually selected for some specific reason
 Knowledge and use of a particular instructional strategy
 Experience
 Being in a specific setting such as a school changing to a
teacher-based decision-making process
 Need for clear criteria for describing and defending
the sample
 Concerns related to representation and
generalizability
Obj. 5.2 & 5.4

30. Selecting Non-Random Samples
 Quota sampling
 Selection based on the exact
characteristics and quotas of subjects in
the sample when it is impossible to list all
members of the population
 Concerns with accessibility, representation,
and generalizability
Obj. 5.2 & 5.5

31. Quantitative Sampling Comments
 Both probability and non-random sampling
techniques are used in quantitative research
 Probability models are desired due to the selection
of a representative sample and the ease with
which the results can be generalized to the
population
 Non-random (i.e., non-probability) models are
frequently used due the reality of the situations in
which the research is being conducted

Concerns with representation

Concerns with generalization

32. Qualitative Sampling
 Unique characteristics of qualitative research
 In-depth inquiry
 Immersion in the setting
 Importance of context
 Appreciation of participant’s perspectives
 Description of a single setting
 The need for alternative sampling strategies
Obj. 7.2

33. Qualitative Sampling
 Purposive techniques – relying on the
experience and insight of the
researcher to select participants
 Intensity – compare differences of two or
more levels of the topics

Students with extremely positive and extremely
negative attitudes

Effective and ineffective teachers
Obj. 7.3

34. Qualitative Sampling
 Purposive techniques (continued)
 Homogeneous – small groups of
participants who fit a narrow homogeneous
topic
 Criterion – all participants who meet a
defined criteria
 Snowball – initial participants lead to other
participants
Obj. 7.4, 7.5, & 7.6

35. Qualitative Sampling
 Purposive techniques (continued)
 Random purposive – given a pool of
participants, random selection of a small
sample
 Combinations of techniques
 Inherent concerns related to
generalizability and representation
Obj. 7.7 & 7.8

36. Qualitative Sampling
 Sample size
 Generally very small samples given the
nature of the data collection methods and
the data itself
 Two general guidelines

Redundancy of the information collected from
participants

Representation of the range of potential
participants in the setting
Obj. 7.9

37. Generalizability
 Probability sampling
 Begins with a population
and selects a sample
from it
 Generalizability to the
population is relatively
easy
 Non-probability and
purposive sampling
 Begins with a sample
that is NOT selected
from some larger
population
 Must consider the
population hypothetical
as it is based on the
characteristics of the
sample
 Generalizability is often
very limited Obj. 7.10