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