STATISTICS IN SUMMARY
Chapter Specifics
• Statistical studies often try to show that changing one variable (the explanatory variable) causes changes in another variable (the response variable).
• In an experiment, we actually set the explanatory variables ourselves rather than just observe them.
• Observational studies and one-track experiments that simply apply a single treatment often fail to produce useful data because confounding with lurking variables makes it impossible to say what the effect of the treatment was.
• In a randomized comparative experiment we compare two or more treatments, use chance to decide which subjects get each treatment, and use enough subjects so that the effects of chance are small.
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• Comparing two or more treatments controls lurking variables affecting all subjects, such as the placebo effect, because they act on all the treatment groups.
• Differences among the effects of the treatments so large that they would rarely happen just by chance are called statistically significant.
• Observational studies of cause-and-effect questions are more impressive if they compare matched groups and measure as many lurking variables as possible to allow statistical adjustment.
In Chapter 1 we saw that experiments are best suited for drawing conclusions about whether a treatment causes a change in a response. In this chapter, we learned that only well-designed experiments, in particular randomized comparative experiments, provide a sound basis for such conclusions. Statistically significant differences among the effects of treatments are the best available evidence that changing the explanatory variable really causes changes in the response.
When it is not possible to do an experiment, observational studies that measure as many lurking variables as possible and make statistical adjustments for their effects are sometimes used to answer cause-and-effect questions. However, they remain a weak second-best to well-designed experiments.
CASE STUDY EVALUATED Use what you have learned in this chapter to evaluate the Case Study that opened the chapter. Start by reviewing the information on page 93. Then answer each of the following questions in complete sentences. Be sure to communicate clearly enough for any of your classmates to understand what you are saying.
First, here are the results of the study. After one season, the biomass of plants in the plot receiving additional spring rain was approximately twice that in plots receiving the other treatments. This difference was statistically significant.
1. Is this study an experiment or an observational study?
2. Explain what the phrase “statistically significant” means.
3. What advantage is gained by randomly assigning the plots to the treatments?
Online Resources
• The Snapshots video Types of Studies and the StatClips video Types of Studies both review the differences between experiments and observational studies.
• The Snapshots video Introduction to Statistics describes real-world situations for which knowledge of statistical ideas is important.
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• The StatBoards video Factors and Treatments identifies subjects, factors, treatments, and response variables in additional experiments.
• The StatBoards video Outlining an Experiment provides additional examples of outlining an experiment using figures similar to those given in this chapter.