STATISTICS IN SUMMARY
Chapter Specifics
• To measure something means to assign a number to some property of an individual.
• When we measure many individuals, we have values of a variable that describes them.
• Variables are recorded in units.
• When you work with data or read about a statistical study, ask if the variables are valid as numerical measures of the concepts the study discusses.
• Often, a rate is a more valid measure than a count.
• Validity is simple for measurements of physical properties such as length, weight, and time. When we want to measure human personality and other vague properties, predictive validity is the most useful way to say whether our measures are valid.
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• Also ask if there are errors in measurement that reduce the value of the data. You can think about errors in measurement like this:
measured value = true value + bias + random error
• Some ways of measuring are biased, or systematically wrong in the same direction.
• To reduce bias, you must use a better instrument to make the measurements.
• Other measuring processes lack reliability, so that measuring the same individuals again would give quite different results due to random error.
• A reliable measuring process will have a small variance of the measurements. You can improve the reliability of a measurement by repeating it several times and using the average result.
In reasoning from data to a conclusion, we start with the data. In statistics, data are ultimately represented by numbers. The planning of the production of data through a sample or experiment does not by itself produce these numbers. The extent to which these numbers represent the characteristics we wish to study affects the quality and relevance of our conclusions. When you work with data or read about a statistical study, ask exactly how the variables are defined and whether they leave out some things you want to know. This chapter presents several ideas to think about in assessing the variables measured and hence the conclusions based on these measurements.
CASE STUDY EVALUATED The Case Study that opened the chapter is motivated by research conducted in 1991 by Willerman, Schultz, Rutledge, and Bigler. Read about this study in the EESEE story “Brain Size and Intelligence,” and use what you have learned in this chapter to answer the following questions.
1. How did the researchers measure brain size? Is this a valid measure of brain size? Is it reliable? Is it biased?
2. How did the researchers measure intelligence? Is this a valid measure of intelligence?
3. The researchers found some evidence that brain size and intelligence are related. However, the study described in Example 8 did not. Discuss the differences in the two studies.
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Online Resources
• LearningCurve has good questions to check your understanding of the concepts.