Statistical Inference

Now that we have the basics of examining data down, we turn to another issue that we can address with statistical analysis. Howe confident are we that the the results from the data represent the larger population from which the data are drawn? This issue only applies to cases where the data we use constitutes a sample from a larger population. However, many of the datasets that we work with in the social sciences are of this type, so this is typically an important issue. We don’t want to to reach an incorrect conclusion that \(x\) is associated with \(y\) in cases when that association in our sample is basically a result of random chance.

In many introductory statistics courses, statistical inference would take up the majority of the course and you would learn a variety of cookbook formulas for conducting “tests.” We won’t do much of that here. Instead I will focus on the logic of the two most common procedures in statistical inference: the confidence interval and the hypothesis test. Once you understand the logic behind these procedures, it turns out that all of the various “tests” are just iterations on the same basic theme. Nonetheless, we will have to use some formulas in this module with associated number crunching. This is the most math heavy module of the course, so be prepared.

Slides for this module can be found here.

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