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Data Collection: Sample Design

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Terminology Observational Study – observes individuals and measures variables of interest but does not impose treatment on the individuals. Observational Study – observes individuals and measures variables of interest but does not impose treatment on the individuals. Experiment – deliberately imposes treatment on individuals and measures the responses Experiment – deliberately imposes treatment on individuals and measures the responses

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Observational vs. Experiment Observational studies often have confounding variables (variables are confounded when their effects on the response variable cannot be distinguished from each other). Observational studies often have confounding variables (variables are confounded when their effects on the response variable cannot be distinguished from each other). Well-designed experiments, on the other hand, try to reduce confounding variables. Well-designed experiments, on the other hand, try to reduce confounding variables.

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More terminology Population – the entire group of individuals that we want information about Population – the entire group of individuals that we want information about Sample – a part of the population that we actually examine in order to gather information Sample – a part of the population that we actually examine in order to gather information Census – attempts to contact every individual in the entire population Census – attempts to contact every individual in the entire population

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Sample Design Sample design is the method used to select the sample from the population. Sample design is the method used to select the sample from the population. Some poor examples of sample design are as follows: Some poor examples of sample design are as follows:

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Voluntary Response Sample What it is: people who choose themselves by responding to a general appeal. What it is: people who choose themselves by responding to a general appeal. Why it’s bad: people with strong opinions, especially negative opinions, are more likely to respond. Therefore, the sample is not likely to be representative of the whole population. Why it’s bad: people with strong opinions, especially negative opinions, are more likely to respond. Therefore, the sample is not likely to be representative of the whole population.

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Convenience Sampling What it is: a sample chosen because the individuals are the easiest to reach What it is: a sample chosen because the individuals are the easiest to reach Why it’s bad: It’s not likely to be representative of the entire population. Why it’s bad: It’s not likely to be representative of the entire population. –Example: Mall surveys… People at the mall tend to be wealthier. Also, those people who are attracted by mall surveys tend to be teens or the elderly.

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Common Thread Sample designs are bad when they are not representative of the whole population. Sample designs are bad when they are not representative of the whole population. –Sample designs are called BIASED if they systematically favor certain outcomes (in one direction). Some Other Problems: Undercoverage: Who did we leave out? Undercoverage: Who did we leave out? Non-response: Can’t be contacted; refuses to participate. Non-response: Can’t be contacted; refuses to participate.

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Good Sample Designs Probability Sample (any sample chosen by chance). We must know what samples are possible and what probability each sample has of being chosen. Probability Sample (any sample chosen by chance). We must know what samples are possible and what probability each sample has of being chosen. –Choosing a sample by chance allows neither favoritism by the sampler nor self-selection by respondents.

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Examples of Probability Samples SRS (Simple Random Sample) SRS (Simple Random Sample) –The simplest way to use chance to select a sample –Analogous to putting names in a hat (the population) and drawing out a handful (the sample). –Each individual has an equal chance of being chosen and each sample is equally likely.

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How to Choose an SRS 1.Label Assign a number to each individual in the population. They must all have the same number of digits. 2.Decide if you will throw out extras. 3.Random Selection: TableTable Use Table B to select numbers at random. OR CalculatorOR Calculator Use calculator to find random digits

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Random Digits from Table B Each digit 0-9 is equally as likely. Each digit 0-9 is equally as likely. If you need to have 1-9 individuals, look at numbers 1-9 (one digit). Have 1-99 individuals use numbers 01-99 (two digits). Have 1-999 individuals, numbers 001-999 (three digits) and so forth. If you need to have 1-9 individuals, look at numbers 1-9 (one digit). Have 1-99 individuals use numbers 01-99 (two digits). Have 1-999 individuals, numbers 001-999 (three digits) and so forth. Choose a row in your table to start with (if you use this method on the AP exam you should state which row you start with. Choose a row in your table to start with (if you use this method on the AP exam you should state which row you start with. Follow the row and choose individuals. Follow the row and choose individuals.

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Let’s perform our own SRS We will choose 5 students from the class at random. First, lets use Table B. How will we label? We will choose 5 students from the class at random. First, lets use Table B. How will we label?

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Random Digits in Calculator Go to Math Go to Math PRB PRB RandInt(1 st #, last #, how many numbers) RandInt(1 st #, last #, how many numbers)

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Let’s perform our own SRS We will choose 5 students from the class at random. Now let’s try using our calculator. We will choose 5 students from the class at random. Now let’s try using our calculator.

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Another Probability Sample Stratified Random Sample Stratified Random Sample –Divide the population into groups of similar individuals, called strata. Then choose a separate SRS from each stratum and combine the SRSs to form a full sample. Example: Choose an SRS from each class – freshmen, sophomores, juniors, and seniors. Example: Choose an SRS from each class – freshmen, sophomores, juniors, and seniors.

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Final Probability Sample Multi-stage Sample Multi-stage Sample –Chooses the sample in stages. Example: Take a random sample of the counties in NC. Then, divide the counties into sectors. Take a random sample of the sectors. Then divide each sector into blocks. Take a random sample of blocks. On each block, take a random sample of households. Example: Take a random sample of the counties in NC. Then, divide the counties into sectors. Take a random sample of the sectors. Then divide each sector into blocks. Take a random sample of blocks. On each block, take a random sample of households.

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CAUTIONS: Response Bias: Response Bias: People Lie! Especially with embarrassing or incriminating topics. Wording of questions can be misleading: Wording of questions can be misleading: Choose one: Yes, I would like my taxes to stay the same and not support the schools. No, I approve of passing the bond to fund new schools. Larger random samples give more accurate results than smaller samples. Larger random samples give more accurate results than smaller samples.

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