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VI. Sampling: (Nov. 2, 4) Frankfort-Nachmias & Nachmias (Chapter 8 – Sampling and Sample Designs) Frankfort-Nachmias & Nachmias (Chapter 8 – Sampling and Sample Designs) King, Keohane and Verba (Chapter 4) King, Keohane and Verba (Chapter 4) Barbara Geddes How the Cases You Choose Affect the Answers You Get: Selection Bias in Comparative Politics. Political Analysis, 2:1, Barbara Geddes How the Cases You Choose Affect the Answers You Get: Selection Bias in Comparative Politics. Political Analysis, 2:1, How the Cases You Choose Affect the Answers You Get: Selection Bias in Comparative Politics.How the Cases You Choose Affect the Answers You Get: Selection Bias in Comparative Politics.Applications William Reed, A Unified Statistical Model of Conflict Onset and Escalation. American Journal of Political Science, Vol. 44, No. 1 (Jan., 2000), pp William Reed, A Unified Statistical Model of Conflict Onset and Escalation. American Journal of Political Science, Vol. 44, No. 1 (Jan., 2000), pp A Unified Statistical Model of Conflict Onset and EscalationA Unified Statistical Model of Conflict Onset and Escalation Richard Timpone Structure, Behavior and Voter Turnout in the United States. American Political Science Review, Vol. 92 (1): Richard Timpone Structure, Behavior and Voter Turnout in the United States. American Political Science Review, Vol. 92 (1): Structure, Behavior and Voter Turnout in the United StatesStructure, Behavior and Voter Turnout in the United States

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Sampling Population – any well-defined set of units of analysis; the group to which our theories apply Population – any well-defined set of units of analysis; the group to which our theories apply Sample – any subset of units collected in some manner from the population; the data we use to test our theories Sample – any subset of units collected in some manner from the population; the data we use to test our theories Parameter vs. Statistic Parameter vs. Statistic

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Types of Samples Probability sample – each element of the population has a known probability of being included in the sample Probability sample – each element of the population has a known probability of being included in the sample Nonprobability sample - each element of the population has an unknown probability of being included in the sample Nonprobability sample - each element of the population has an unknown probability of being included in the sample

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Types of Nonprobability Samples Convenience sample Convenience sample Purposive sample Purposive sample Problem – may not be representative of the population to which we want to generalize Problem – may not be representative of the population to which we want to generalize

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Famous Example of Convenience Sampling Literary Digest – used automobile registration lists and telephone directories as sampling frame for presidential polls Literary Digest – used automobile registration lists and telephone directories as sampling frame for presidential polls million postcards to accurately predict outcome of 1928 election (Hoover-R) million postcards to accurately predict outcome of 1928 election (Hoover-R) 1932: 20 million postcards to accurately predict 1932 election (Roosevelt-D) 1932: 20 million postcards to accurately predict 1932 election (Roosevelt-D)

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Famous Example of Convenience Sampling Literary Digest – used automobile registration lists and telephone directories as sampling frame for presidential polls Literary Digest – used automobile registration lists and telephone directories as sampling frame for presidential polls predicted Hoover-R predicted Hoover-R 1932: predicted Roosevelt-D 1932: predicted Roosevelt-D 1936: predicted Landon (R) 57% 1936: predicted Landon (R) 57% What happened? What happened?

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Famous Example of Convenience Sampling Before 1936 Before 1936 Upper class/Working Class – more or less representative partisan distribution Upper class/Working Class – more or less representative partisan distribution

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Famous Example of Convenience Sampling Before 1936 Before 1936 Upper class/Working Class – more or less representative partisan distribution Upper class/Working Class – more or less representative partisan distribution 1936 and beyond 1936 and beyond Upper class disproportionately Republican Upper class disproportionately Republican Working class disproportionately Democrat Working class disproportionately Democrat

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Types of Nonprobability Samples Quota samples – elements are chosen based on selected characteristics and the representation of these characteristics in the population Quota samples – elements are chosen based on selected characteristics and the representation of these characteristics in the population Insures accurate representation of selected characteristics Insures accurate representation of selected characteristics Elements with selected characteristics chosen in convenience fashion Elements with selected characteristics chosen in convenience fashion

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Famous Examples of Quota Samples 1936 – George Gallup used quota sampling to accurately predict: The (inaccurate) Literary Digest prediction The (inaccurate) Literary Digest prediction The winner of the 1936 election The winner of the 1936 election

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Famous Examples of Quota Samples 1948 – quota sampling incorrectly predicts Dewey to defeat Truman 1948 – quota sampling incorrectly predicts Dewey to defeat Truman

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Types of Probability Samples Simple random sample – each element of the population has an equal chance of being selected Simple random sample – each element of the population has an equal chance of being selected Systematic sample – elements selected from a list at predetermined intervals Systematic sample – elements selected from a list at predetermined intervals

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Types of Probability Samples Stratified sample – elements in population are grouped into strata, and each strata is randomly sampled Stratified sample – elements in population are grouped into strata, and each strata is randomly sampled

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Example of Stratified Sampling Population: 75% white, 10% black, 10 Hispanic, 5% Asian Population: 75% white, 10% black, 10 Hispanic, 5% Asian Simple random sample of 1000: Approximately 750 white, 100 black, 100 Hispanic, 50 Asian Simple random sample of 1000: Approximately 750 white, 100 black, 100 Hispanic, 50 Asian Samples too small for group comparisons Samples too small for group comparisons Solution: Use stratified sampling to over-sample minority groups (disproportionate stratified sampling) Solution: Use stratified sampling to over-sample minority groups (disproportionate stratified sampling)

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Types of Probability Samples Cluster sample – elements are grouped into clusters, and sampling proceeds in two stages: Cluster sample – elements are grouped into clusters, and sampling proceeds in two stages: (1) A random sample of clusters is chosen(1) A random sample of clusters is chosen (2) Elements within selected clusters are then randomly selected and aggregated to form final sample(2) Elements within selected clusters are then randomly selected and aggregated to form final sample This is the sampling method used in many national surveys (e.g. clusters=metropolitan areas, zip codes, area codes)This is the sampling method used in many national surveys (e.g. clusters=metropolitan areas, zip codes, area codes)

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Sampling Distribution (of sample means) Population Draw Random Sample of Size n Calculate sample mean Repeat until all possible random samples of size n are exhausted The resulting collecting of sample means is the sampling distribution of sample means

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Sampling Distribution of Sample Means Def: A frequency distribution of all possible sample means taken from the same population for a given sample size (n) Def: A frequency distribution of all possible sample means taken from the same population for a given sample size (n)

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Sampling Distribution of Sample Means Def: A frequency distribution of all possible sample means taken from the same population for a given sample size (n) Def: A frequency distribution of all possible sample means taken from the same population for a given sample size (n) The mean of the sampling distribution will be equal to the population mean The mean of the sampling distribution will be equal to the population mean The sampling distribution will be normally distributed (regardless of population distribution if n>30) The sampling distribution will be normally distributed (regardless of population distribution if n>30)

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Standard Error How the sample means vary from sample to sample (i.e. within the sampling distribution) is expressed statistically by the value of the standard deviation of the sampling distribution. How the sample means vary from sample to sample (i.e. within the sampling distribution) is expressed statistically by the value of the standard deviation of the sampling distribution.

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Standard Error, cont. The standard error for a sample mean is calculated as: s / n The standard error for a sample mean is calculated as: s / n Where s = sample standard deviation Where s = sample standard deviation n = sample size n = sample size

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Simulating a Sampling Distribution (For a Sample Proportion) Dichotomous variable for which the true population value is set at.25 Dichotomous variable for which the true population value is set at.25 Randomly draw 1,000 samples of size n Randomly draw 1,000 samples of size n Repeat for different ns and compare Repeat for different ns and compare

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Simulation of a Sampling Distribution (n=10)

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Simulation of a Sampling Distribution (n=100)

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Sample Size and Sampling Error

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Sample Selection Bias What is it? What is it? What are the consequences of selecting on: What are the consequences of selecting on: The dependent variable? The dependent variable? The independent variable? The independent variable?

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