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GATHERING DATA Chapter 4

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4.1 Experiment or Observe?

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Population and Samples Population: Subjects of interest Sample: Subset for whom we have data Often want answers about large group but can’t measure all, so a subset is chosen Use statistical techniques to infer conclusions

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Observational Study Merely observe values of response and explanatory variables without doing anything to the subjects Ex. Cell Phone Study 1 (Page 155) Cell Phone Study 2 (Page 155)

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Sample Survey Select sample and interview Observational study Census is survey of entire population

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Experiment Assign subjects to certain experimental conditions and observe outcomes of the response variable The experimental conditions, which correspond to assigned values of the explanatory variable are called treatments Ex. Cell Phone Study 3 (Page 155)

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Experiments and Observational Studies Experiment reduces lurking variables and thus outside influences Experiments establish cause and effect, unlike observational studies Some experiments impractical because of ethics, time, money, etc. Exs. # 4.2, 4.8 Page 162

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4.2 What are Good and Poor Ways to Sample?

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Sampling Frame & Sampling Design Sampling frame – list of subjects in (hopefully total) population Sampling design determines how sample is selected

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Simple Random Sampling Random Sampling – best way to get representative sample Simple Random Sample – each possible sample of set size n has equal chance of being selected Ex. 4 Page 164 Simulate with Calculator/CD

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Choosing Random Numbers Pg. A6 of text 1. Number subjects from 1 to n 2. Select numbers from random number table or random number generator (calculator or computer) 3. Include subjects with random numbers selected

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Margin of Error for Population Percentages Margin of Error – how well sample predicts population For a random sample with n subjects, the margin of error is approximately Ex. A survey result states: “The margin of error is plus or minus 3 percentage points”

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Convenience Samples: Poor Ways to Sample Convenience Sample: survey sample that’s easy to get Unlikely to represent population Often severe biases Results apply only to observed subjects

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Convenience Samples: Poor Ways to Sample Volunteer Sample: most common convenience sample where subjects volunteer – not representative

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Types of Bias in Sample Surveys Bias: Favoring parts of population 1. Sampling Bias: from sampling method (e.g., nonrandom samples) 2. Nonresponse bias: some subjects cannot be reached or decline 3. Response bias: subject gives incorrect response or question is misleading Exs. # 4.24, 4.29

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Chapter 1: Introduction to Statistics

Chapter 1: Introduction to Statistics

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