Psychology 395 Exam Four: Sampling

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History of Sampling
Alf Lanen-1936

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Used polls to correctly predict outcomes of pres elections in 1924, 1928, and 1932. 1936, Literary Digest sent 10 mil ballots to people in telephone books, received 2 mil responses, predicted victory by alf Landen over FDR, Literary Digest went out of business in 1938...compared to today's typical poll of 3000

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History of Sampling
George Gallup

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Used quota sample to predict FDR vicotry, also 1940&1944...Then used quota sample to predict Dewy over Truman in 1948, quota changed after WWII demographic switch, old quota no longer good.

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Quota Sample

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Subset of a population in which the proportions match those of the population in selected, demographic categories (e.g. male-female; rural-urban; high-medium-low income) [note: requires accurate population information]

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Sampling Bias

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Systematic difference between sample and population on one or more characteristics, such as proportion of rural or high-income voters.

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Sample

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Deliberately selected subset of a population intended as representative of that population. Ex. 400 students selected from all currently registered UTK students.

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Population

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Entire collection of all units of study, but also requires...
1)Operational definition of units of study, ex. "americans" would need further definition, like "legal citizens"
2)May not be completely specified in the sampling frame

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Sampling Frame

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List of members of a population actually used in a research

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Probability Sample

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Selected subset in which each element of the population has a known probability (usually equal) of inclusion in the sample. Best example: simple random sample, chosen from a numbered list via planned use of random numbers table...random selection is not the same as random assignment, different uses of "random"

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Non-probability Sample

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Subset of a population in which elements have unknown probability of selection. Example: Gallup's quota sample of 1936 voters

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Problems with Non-probability samels

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1)Likely to have a sampling bias:researchers have discretion in selecting respondents in each demographic category. Ex. Gallup's door2door interviewers might have avoided run down looking houses., leading to underrepresentation.
2)Cannot calculate sampling error in non-probability sample

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Sampling Error

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Extent of deviation of sample characteristics from population characteristics. Ex. margin of error for % yes in Gallup poll with n=1,000 is +or- 3%

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Sampling Error Characteristics

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1)Sampling error is a function of sample size - not population size, not proportion sampled. [standard error for percent in 2 categories =sqrt (PQ/n]
2)In a population with 50% men a sample of 400 give a margin of error +or- 5% with a confidence of .95 (We expect all but 5% of samples of size 400 to have between 45% and 55% men, and only 5% of samples of that size have more than 55% or less than 45%.

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Simple Random Sample

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Selected from an identified population, using a list of the members of the population, in a way that makes any member equally likely to be selected (usually using a table of random numbers or fair drawing from a well-mixed container of marker).

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Example of Simple Random Sample

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Select a simple, random sample of 1000 UTK students (for example, a registration list with social security numbers).
Use a table of random numbers to select (e.g. choose 4 digits and select students with matching last 4 digits of SS#'s) at random from the list until 1,000 are selected. Could use a fair drawing from 26,000.
2)Gives representative samples as expected from sampling error, but requires list.

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Systematic Sample

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Convenient alternative to simple random sample, calls for selecting ever kth element of a listed population, where k=N/n, with a random start.

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Example of Systematic Sample

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1)To draw a systematic sample of all 26,000 UTK students, k is 26. Continue from that first selection to choose every 26th name on the list, should have selected 1,000.

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Problem with Systematic Sample

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1)Bias in lists with repeating or cyclincal patterns. Ex. One reserach project on military personnel used a systematic sample with k=10, and ended up selecting only squad leaders; list had the leader first for each squad of 10.

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Advantage of Systematic Sampling

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Lists may be ordered by demographic groups, such as a UTK list with freshmen, sophmores, juniors, seniors =>automatic stratification.

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Stratified Sample

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Drawn by randomly selecting randomly from within known segments or layers (strata) of the population, usually in proportion to the size of each segment, to assure representativeness on the variable(s) that define the segments.

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Example of Stratified Sample

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1)Select a sample of Knoxville residents stratified by family income
2)obtain a list of Knoxville residents
3)obtain access to informatin on family income
4)obtain accurate distribution of family income in knoxville population
5)randomly select form the list (checking income on each) intil the sample has the same proportions in the three categories.

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Advantage of Stratified Sample

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Lower margin of error than simple random sample, but much more demanding, requires data on statifying variable and on its distribution.
Best in a highly heterogeneous population where population categories differ.

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Cluster Sample

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Drawn by randomly selecting form natural clusters and using those clusters as either the sample or the basis for further sampling (in a multi-stage sample)

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Example of Cluster Sample

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Select a sample of Knoxville elementry schools (the clusters), say there are 35
Randomly select a subset, say 5, suing a random numbers table. Thats the sample.

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Multi-Stage Cluster Sample

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Select a sample of Knoxville elementrary school students
1)Within each school, instead of using the whole school ass the sample, select at random within the school a constant number (say100)
@)2 Stages or select a sample of homerooms (say 10) and then select 10 students from each (three stages)

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Advantage of Multi-stage Cluster Sample

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Least demanding, requires only a list of clusters to start, but has higher margin of error than simple random sample of same size.