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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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