Sampling Procedures Y520. Strategies for Educational Inquiry. Robert S Michael

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1 Sampling Procedures Y520 Strategies for Educational Inquiry Robert S Michael RSMichael 2-1 Terms Population (or universe) The group to which inferences are made based on a sample drawn from the population. Sample A representative subset of the population from which generalizations are made about the population. RSMichael 2-2 1

made based on a sample drawn from the population.

2 Why Sample? All members of a population may not be available. Cheaper Less time consuming RSMichael 2-3 Sampling Procedures Probability samples Randomness is the bases for sample selection and insures that the sample is representative of the population. Non-probability samples Randomness is not the basis for selecting the sample. RSMichael 2-4 2

Randomness is the bases for sample selection and insures that the sample is

3 Sampling Procedures ( continued) Probability samples Generalizations from sample to population are possible because sample is representative of the population. Non-probability samples Generalization is not possible because the sample is not representative of population. RSMichael 2-5 Probability Sampling is: Equal and independent Every member of a population has an equal chance of being selected. Selection of one individual has no influence on the selection of the next individual. Humans cannot generate random numbers; a mechanism (such as a random number table) must be used. RSMichael 2-6 3

RSMichael 2-5 Probability Sampling is: Equal and independent Every member of a population has an equal chance of being selected.

4 Probability Sampling Procedures Simple random sampling Stratified sampling Cluster sampling Systematic sampling RSMichael 2-7 Simple Random Sampling The preferred method probability is highest that sample is representative of population than for any other sampling method. Every member of a population has an equal chance of being selected. Least chance of sample bias RSMichael 2-8 4

highest that sample is representative of population than for any other sampling method.

5 Proportional Stratified Sampling Proportion of subgroups in sample represent proportion of subgroups (strata) in population. Every member within the subgroup has an equal chance of being selected. Used when size of population subgroups is discrepant. RSMichael 2-9 Cluster Sampling Conceptually similar to simple random sampling except: Unit of analysis is a group (aka, cluster), not an individual. Examples: classrooms, schools, districts, families, census tract. RSMichael

Used when size of population subgroups is discrepant.

6 Systematic Sampling Example: Select every tenth student from a randomly ordered school roster. Principle of independence is violated, for selection of first student determines selection all others. RSMichael 2-11 Remember Random procedures do not guarantee that the sample is representative, but they do increase the probability. Sampling variation Random differences between sample and population. Decreased by increasing sample size. Sampling bias Non-random difference due to flawed procedures. RSMichael

RSMichael 2-11 Remember Random procedures do not guarantee that the sample is representative, but they do increase the

7 The Big Question: How large should the sample be? Too small a sample increases the likelihood of sampling error. Too large a sample reduces efficiency. RSMichael 2-13 For Comparison Groups & Correlations: Use power analysis where power is the probability of detecting differences when, indeed, a true difference exists. Power analysis uses: power, alpha, and the directionality of the statistical test. RSMichael

RSMichael 2-13 For Comparison Groups & Correlations: Use power analysis where power is the probability

8 For Comparison (continued): Knowledge of these three facts was well as desired effect size enables us to compute the sample size. For multiple regression sample should include at least 10 for each group; 20 per variable is preferred ( rule of thumb). RSMichael 2-15 Caution: What can happen with improper sampling? Incorrect conclusions can be drawn, such as... RSMichael

For multiple regression sample should include at least 10 for each group; 20 per variable is

9 Caution: (continued) 1936 Presidential election. Literary Digest poll incorrectly predicted Alf Landon the winner because the sample (people with telephones) was not representative of voters. An example of sampling bias. RSMichael 2-17 Caution: (continued) 1936 Presidential election, Literary Digest poll: An additional problem was voters for one candidate were more likely to express their preference. This is an example of response bias; i.e., non-responders had a differing opinion. RSMichael

representative of voters. An example of sampling bias.

10 Caution: (continued) 1948 Presidential election. Newspapers used quota sampling and erroneously predicted Dewey to defeat Truman. From this point on, random sampling became the preferred procedure. RSMichael 2-19 Caution: (continued) 1970 Lottery Selection for military service based on drawing names from a hat. Names were not randomized. Too many draftees were born in December. RSMichael

From this point on, random sampling became the preferred procedure.

11 Caution: (continued) Terman s study of gifted students: Teachers nominated students whom they felt met criteria for genius. RSMichael 2-21 Caution: (continued) Kohlberg s study of moral development: Concluded that girls lag behind in moral thinking. All his studies were conducted only with boys (it was later reported). RSMichael

RSMichael 2-21 Caution: (continued) Kohlberg s study of moral development: Concluded

12 Rule: If you wish to make inferences to the population from which the sample was drawn, a random sampling procedure must be used. RSMichael 2-23 Statistics to Describe Samples: Measures of central tendency: Mean Median Mode RSMichael

13 Statistics to Describe Samples: Measures of variability: Range Standard deviation Quartile deviation RSMichael 2-25 Statistics to Describe Samples: Use of effect size: Calculation Difference = (Mt Mc) / sd c RSMichael

2-25 Statistics to Describe Samples: Use of effect size:

14 Statistics to Describe Samples: Useofeffectsize: Interpretation: Describes the difference between treatment and comparison group means expressed as standard deviation units. Convert to a percentile shift using the z- distribution for normal curve. RSMichael 2-27 Non-Random Sampling Limitation: Cannot generalize from sample to population because: Each member of population did not have equal chance of being selected Independence principle violated No random process used. Sample is biased in unknown ways. RSMichael

RSMichael 2-27 Non-Random Sampling Limitation: Cannot generalize from sample to population because: Each member of population did

15 Non-Random Sampling Procedures Convenience sampling (aka, accidental, haphazard) Purposive / judgment sampling Quota sampling Note: All of these procedures violate the principles of equal and independent No randomness mechanism Generalization not logically defensible. RSMichael 2-29 Non-Random Sampling Procedures Convenience samples Consists of individuals readily available (e.g., students in a classroom). Purposive sample Inquirer substitutes judgment for randomness Sample nonrepresentativeness virtually guaranteed Quota Equal & independent principle violated. RSMichael

RSMichael 2-29 Non-Random Sampling Procedures Convenience samples Consists of individuals readily available (e.g., students in a classroom).

16 Non-Random Sampling Procedures Convenience sampling (aka, accidental, haphazard) Purposive / judgment sampling Quota sampling RSMichael 2-31 Samples in Qualitative Studies Qualitative sampling procedures are based on non-random processes. Qualitative samples are typically small. These are the conditions that maximize the likelihood of sampling variation and sampling bias. Drawing inferences about a population from such samples is not logically defensible. RSMichael

processes. Qualitative samples are typically small.

17 Qualitative Sampling Procedures Intensity sampling Homogeneous sampling Criterion sampling Snowball sampling Random purposive sampling RSMichael

Chapter 8: Quantitative Sampling

Chapter 8: Quantitative Sampling I. Introduction to Sampling a. The primary goal of sampling is to get a representative sample, or a small collection of units or cases from a much larger collection or