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Sample Design Section 5.1

Sample Design Section 5.1. Terminology. 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. Observational vs. Experiment.

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Sample Design Section 5.1

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  1. Sample DesignSection 5.1

  2. Terminology • 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

  3. Observational vs. Experiment • Observational studies often have confounding variables. • Well-designed experiments, on the other hand, try to reduce confounding variables.

  4. More terminology • 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 • Census – attempts to contact every individual in the entire population

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

  6. Voluntary Response Sample • 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.

  7. Convenience Sampling • 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. • 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.

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

  9. 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. • Choosing a sample by chance allows neither favoritism by the sampler nor self-selection by respondents.

  10. Examples of Probability Samples • 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.

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

  12. Random Digits from Table B • Each digit 0-9 is equally as likely. • If you need to have 1-10 individuals, look at numbers 0-9 (one digit). Have 1-100 individuals use numbers 00-99 (two digits). Have 1-1000 individuals, numbers 000-999 (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). • Follow the row and choose individuals.

  13. 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?

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

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

  16. Another Probability 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.

  17. And Another • Cluster Random Sample • When you have items (or people) grouped into clusters and you choose a random sample of the clusters and examine all in the cluster. • Ex. You choose an SRS of 2nd period classes (clusters) at NCHS and sample everyone in those classes

  18. Final Probability 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.

  19. CAUTIONS: • Response Bias: People Lie! Especially with embarrassing or incriminating topics. • 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.

  20. Homework Chapter 4 # 2, 3, 8, 9, 10

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