Foundations for inference

So far we have been talking about describing data and looking for possible relationships between things we measure. We began with the problem of having too many numbers and discussed how they could be summarized with descriptive statistics, and communicated in graphs. We also looked at the idea of relationships between things. If one thing causes change in another thing, then if we measure how one thing goes up and down we should find that other thing goes up and down, or does something systematically following the first thing. At the end of the chapter on correlation, we showed how correlations, which imply a relationship between two things, are very difficult to interpret. Why? Because an observed correlation can be caused by a hidden third variable, or could be a spurious finding “caused” by random chance. In the last chapter, we talked about sampling from distributions, and we saw how samples can be different because of random error introduced by the sampling process.

Now we begin our journey into inferential statistics. These are tools used to make inferences about where our data came from, and to make inferences about what causes what.

In this chapter we provide some foundational ideas. We will stay mostly at a conceptual level, and use lots of simulations like we did in the last chapters. In the remaining chapters we formalize the intuitions built here to explain how some common inferential statistics work.

Adapted from Answering Questions with Data: Introductory Statistics for Psychology Students, by Matthew J. C. Crump (Brooklyn College of CUNY), crumplab.com/statistics, licensed under CC BY-SA 4.0. Portions adapt Danielle Navarro's Learning Statistics with R (CC BY-SA). Changes were made; this adaptation is distributed under the same license. License: CC-BY-SA-4.0.