1. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Sampling Chapter Six

2. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-HillSampling Chapter Six

3. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill What is a Sample? Sampling is the process of selecting a number of individuals from a population, preferably in a way that the individuals are representative of the larger group from which they were selected. Sampling is the process of selecting a number of individuals from a population, preferably in a way that the individuals are representative of the larger group from which they were selected. A sample is any group on which information is obtained. A sample is any group on which information is obtained.

4. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Defining the Population A population refers to all the members of a particular group. A population refers to all the members of a particular group. The first task in selecting a sample is to define the population of interest. The first task in selecting a sample is to define the population of interest. In Educational Research, the population of interest is a group of persons who possess certain characteristics. In Educational Research, the population of interest is a group of persons who possess certain characteristics. A target population is the actual population that the researcher would like to generalize. A target population is the actual population that the researcher would like to generalize. Considered rarely available Considered rarely available The accessible population would be the group that is available (realistic choice) The accessible population would be the group that is available (realistic choice)

5. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Representative vs. Non-representative Samples (Fig. 6.1)

6. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Two Main Types of Sampling Sampling may be either random or non-random Sampling may be either random or non-random Random sampling is a method of selecting subjects from a population by chance, so that biases do not alter the sample. Random sampling is a method of selecting subjects from a population by chance, so that biases do not alter the sample. The 3 most common ways of obtaining this type of sample are: The 3 most common ways of obtaining this type of sample are: Simple Random Sampling Simple Random Sampling Stratified Random Sampling Stratified Random Sampling Cluster Sampling Cluster Sampling

7. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Part of a Table of Random Numbers (Table 6.1) 011723223456222167032762062281565451 912334379156233989109238934128987678 086401016265411148251287602345659080 059397022334080675454555011563237873 666278106590879809899030909876198905 051965004571036900037700500098046660 063045786326098000510379024358145678 560132345678356789033460050521342021 727009344870889567324588400567989657 000037121191258700088909015460223350 667899234345076567090076345121121348 042397045645030032657112675897079326 987650568799070070143188198789097451 091126021557102322209312909036342045

8. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Simple Random Sampling A Simple Random Sampling is a sample selected from a population in such a manner that all members have an equal chance of being selected A Simple Random Sampling is a sample selected from a population in such a manner that all members have an equal chance of being selected If the sample is large, it is the best method to obtain a sample representative of the population from which it has been selected If the sample is large, it is the best method to obtain a sample representative of the population from which it has been selected The larger the sample size, the more it is likely to represent the population The larger the sample size, the more it is likely to represent the population Any differences that occur are the result of chance rather than bias on the part of the researcher Any differences that occur are the result of chance rather than bias on the part of the researcher Disadvantages of this method are: 1) the difficulty of performing the sampling and, 2) this method does not ensure that subgroups are present in the sampling in the same proportion as they are in a population Disadvantages of this method are: 1) the difficulty of performing the sampling and, 2) this method does not ensure that subgroups are present in the sampling in the same proportion as they are in a population

9. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Stratified Random Sampling A Stratified Random Sampling is a sample selected so that certain characteristics are represented in the sample in the same proportion as they occur in the population A Stratified Random Sampling is a sample selected so that certain characteristics are represented in the sample in the same proportion as they occur in the population The term strata refers to sub-groups The term strata refers to sub-groups The advantage of stratified random sampling is that it increases the likelihood of representation, especially if the sample size is small The advantage of stratified random sampling is that it increases the likelihood of representation, especially if the sample size is small It virtually ensures that any key characteristics of individuals in the population are included in the same proportions in the sample size It virtually ensures that any key characteristics of individuals in the population are included in the same proportions in the sample size The disadvantage is that it requires still more effort on the part of the researcher The disadvantage is that it requires still more effort on the part of the researcher

10. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Selecting a Stratified Sample (Figure 6.2)

11. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Cluster Random Sampling A Cluster Random Sampling is a sample obtained by using groups as the sampling unit (cluster), rather than individuals A Cluster Random Sampling is a sample obtained by using groups as the sampling unit (cluster), rather than individuals There are instances where it is not possible to select a sample of individuals from a population There are instances where it is not possible to select a sample of individuals from a population This is considered more effective with large numbers of clusters This is considered more effective with large numbers of clusters Advantages include more efficient and easier to implement in schools Advantages include more efficient and easier to implement in schools Its disadvantage is that there is a great chance of selecting a sample that is not representative of the population Its disadvantage is that there is a great chance of selecting a sample that is not representative of the population

12. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Random Sampling Methods (Figure 6.3)

13. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Two-Stage Random Sampling This method selects groups randomly and then chooses individuals randomly from these groups. This method selects groups randomly and then chooses individuals randomly from these groups. This becomes a combination of a cluster random sampling with individual random sampling. This becomes a combination of a cluster random sampling with individual random sampling. Considered less time consuming but allows for a good representation of the groups at random. Considered less time consuming but allows for a good representation of the groups at random.

14. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Nonrandom Sampling Methods There are 3 main types of nonrandom sampling methods used in Educational Research There are 3 main types of nonrandom sampling methods used in Educational Research A Systematic Sample is a sample obtained by selecting every nth name in a population A Systematic Sample is a sample obtained by selecting every nth name in a population A Convenience Sample is any group of individuals that is conveniently available to be studied A Convenience Sample is any group of individuals that is conveniently available to be studied Are not considered representative of the population and should be avoided, if possible Are not considered representative of the population and should be avoided, if possible A Purposive Sample is a sample selected because the individuals have special qualifications of some sort, or because of prior evidence of representation A Purposive Sample is a sample selected because the individuals have special qualifications of some sort, or because of prior evidence of representation Personal judgment is used for selection purposes Personal judgment is used for selection purposes A major disadvantage is that the researcher’s judgment could be in error A major disadvantage is that the researcher’s judgment could be in error

15. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Convenience Sampling (Figure 6.4)

16. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Nonrandom Sampling Method (Figure 6.5)

17. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Sample Size The question remains as to what constitutes an adequate sample size. The question remains as to what constitutes an adequate sample size. Samples should be as large as a researcher can obtain with a reasonable expenditure of time and energy. Samples should be as large as a researcher can obtain with a reasonable expenditure of time and energy. The recommended minimum number of subjects are as follows for the following types of studies: The recommended minimum number of subjects are as follows for the following types of studies: 100 for a Descriptive Study 100 for a Descriptive Study 50 for a Correlational Study 50 for a Correlational Study 30 in each group for Experimental and Causal-Comparative Study 30 in each group for Experimental and Causal-Comparative Study The use of 15 subjects per group should probably be replicated

18. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill External Validity, a.k.a. Generalizability The whole notion of science is built on generalizing. The whole notion of science is built on generalizing. External Validity refers to the extent that the results of a study can be generalized from a sample to a population. External Validity refers to the extent that the results of a study can be generalized from a sample to a population. Population generalizability is the degree to which a sample represents the population of interest. Population generalizability is the degree to which a sample represents the population of interest. Obtaining a representative sample becomes very important Obtaining a representative sample becomes very important Ecological generalizability refers to the extent to which the results of a study can be generalized to conditions or settings other than those that prevailed in the study. Ecological generalizability refers to the extent to which the results of a study can be generalized to conditions or settings other than those that prevailed in the study.

19. © 2006 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Population as Opposed to Ecological Generalizing (Figure 6.6)