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SECTION 5.1 Designing Samples

Chapter Preview Exploratory data analysis seeks to discover and describe what data say by using graphs and numerical summaries.  Only applies to specific data that we examine What if we want to answer questions about a large group?

Chapter Preview To get valid answers, we need to produce data carefully.  Often we use samples to represent a larger population.  Once you have chosen a sample, you have a few ways to gather data.

Chapter Preview An observational study observes individuals and measures variables of interest but does not attempt to influence the responses. An experiment deliberately imposes some treatment on individuals in order to observe their responses.  If the goal is to understand cause and effect, experiments are the only source of fully convincing data.

Example 5.1, p. 270 Most adult recipients of welfare are mothers of young children. Observational studies of welfare mothers show that many are able to increase their earnings and leave the welfare system. Some take advantage of voluntary job-training programs to improve their skills. Should participation in job- training and job-search programs be required of all able- bodied welfare mothers? Observational studies cannot tell us what the effects of such a policy would be. Even if the mothers studied are a properly chosen sample of all welfare recipients, those who seek out training and find jobs may differ in many ways from those who do not. They are observed to have more education, for example, but they may also differ in values and motivation, things that cannot be observed.

To see if a required jobs program will help mothers escape welfare, such a program must actually be tried. Choose two similar groups of mothers when they apply for welfare. Require one group to participate in a job-training program, but do not offer the program to the other group. This is an experiment. Comparing the income and work record of the two groups after several years will show whether requiring training has the desired effect.

Confounding Explanatory variable – attempts to explain the observed outcome (p. 121) Lurking variable – a variable not among the explanatory variables, but still may influence the interpretation of relationships among those variables. (p. 226) Response variable – Measures an outcome of a study. (p. 121)

Vocabulary Population: The entire group of individuals that we want information about. Sample: The part of the population we actually look at to gather information.

Vocabulary Sampling: involves studying a part in order to gain information about the whole. Census: Attempts to contact every individual in the entire population.

Sample Designs Voluntary Response Samples  Ex. Call-in polls, text your vote, etc.  People choose themselves by responding.  People with strong opinions (especially negative) are more likely to respond. Problem: leads to bias!!!

Sample Designs Convenience Sampling  Ex. Sitting outside a mall or grocery store.  Choosing the individuals that are easiest to reach  Another source of bias: won’t represent the whole population.

Sample Designs Bias: The design of a study is biased if it systematically favors certain outcomes. SOLUTION: Let chance choose the sample. Essential principle of statistical sampling.

Sample Designs Simplest way: Put the whole population in a hat and draw out a handful of individuals for your sample.

Sample Designs A simple random sample (SRS) of size n contains n individuals from the population chosen so that every set of n individuals has an equal chance of being selected.

Homework p. 273, # 1 – 4 Please bring your books on block day.