STATISTICS IN SUMMARY
Chapter specifics
• Any statistical study records data about some individuals (people, animals, or things) by giving the value of one or more variables for each individual.
• Some variables, such as age and income, take numerical values. Others, such as occupation and sex, do not. Be sure the variables in a study really do tell you what you want to know.
• The most important fact about any statistical study is how the data were produced. Observational studies try to gather information without disturbing the scene they are observing.
• Sample surveys are an important kind of observational study. A sample survey chooses a sample from a specific population and uses the sample to get information about the entire population.
• A census attempts to measure every individual in a population.
• Experiments actually do something to individuals in order to see how they respond. The goal of an experiment is usually to learn whether some treatment actually causes a certain response.
LINK IT
In reasoning from data to a conclusion, we start with the data. Where the data come from is the first step in the argument. The nature and validity of the conclusion are affected by this first step.
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Two sources of data are observational studies and experiments. Observational studies are best suited for a conclusion that involves describing some group or situation without disturbing the scene we observe. Sample surveys are a type of observational study in which we draw conclusions about a population by observing only a part of the population (the sample). Experiments are best suited for a conclusion that involves determining if a treatment causes a change in a response.
[Design Element Start: Inserted From IPS9e]
Example 1.44
Eligibility for aid and practice.
What proportion of all students who take the SAT would be eligible to receive athletic scholarships and to practice with the team but would not be eligible to compete in the eyes of the NCAA? That is, what proportion of students have SAT scores between 620 and 800? First, sketch the areas, exactly as in Example 1.41. We again use X as shorthand for an SAT score.
1. Standardize.
2. Use the table.
As in Example 1.41, about 13% of students would be eligible to receive athletic scholarships and to practice with the team.
[Design Element End]
In the next several chapters, we discuss these sources of data in more detail. We will see what makes for a good observational study and for a good experiment. And we will see how a bad observational study or experiment undermines the validity of the conclusions we wish to make.
CASE STUDY EVALUATED Use what you have learned in this chapter to answer some basic questions about the data collected in the MLive poll described in the Case Study that opened the chapter. To participate in the poll, you had to go online to the MLive website and click on one of the possible responses.
1. Is the poll a sample survey, census, or experiment?
2.What is the population of interest?
3.What are the individuals in the poll?
4.For each individual, what variable is measured?
5.Does this variable take numerical values?
Online Resources
• The Snapshot Video, Introduction to Statistics, describes real-world situations for which knowledge of statistical ideas are important.
• The Snapshot Video, Types of Studies, provides a nice introduction to the ideas of this section.