CHAPTER PREVIEW

In the previous chapter we provided an overview of basic experimental designs that allow us to establish cause-and-effect relationships. One reason that we can claim a cause-and-effect relationship is that we use random assignment when conducting experimental studies. We also rely upon statistical assumptions when deriving statements of cause and effect. In this chapter we will discuss the statistical assumptions and applications that allow us to make statistical claims about cause and effect. In particular, we will discuss the theory of probability and how it applies to statistical hypothesis testing. We will also discuss effect sizes that we use to describe meaningful differences that occur as a result of an IV.

We begin with an explanation of probability as applied to individual circumstances. Probability, or the likelihood of a particular outcome, is present in our daily lives. We extend our explanation of individual probability to statistical samples, which provides us with the foundation for hypothesis testing. Using the theory of probability, we describe how to use samples to test hypotheses and generalize the results back to the larger population—in other words, we describe basic inferential techniques. In this chapter we also describe two inferential techniques, the single sample z test, and the single sample t test, and we provide examples of how they might be used with experimental designs. Finally, we provide instructions for using SPSS to conduct the statistical tests described in this chapter.

Probability

Almost every day we make decisions based on an implicit set of assumptions about the likelihood of an event's occurring. We might consider the possibility of winning the lottery, and we might even anticipate what we would do with all the money if we win.

What is the likelihood that you will win the lottery? The real likelihood of winning is based on the theory of probability. Although the likelihood of winning the megaball lottery is extremely remote (i.e., 1 in 175,711,536), many people continue to play the lottery each day in hope that they will be the lucky winner.