5.10 Summarizing Where We Are

Let’s take a moment to think about how far you have already come in this class. As a result of your hard work and perseverance, you’ve gained knowledge of how data in the world can be organized, visualized, and summarized!

Up until this chapter, we used the DATA = MODEL + ERROR idea in a qualitative way. We built on this qualitative approach in this chapter to introduce our first statistical model—the simple (or empty) model, which we represented as DATA = MEAN + ERROR. As soon as we conceptualize a model as a number, then we can be more specific: we can be specific about which number we use for our model, and how to calculate it. And, we can be more specific about the meaning of error, defining it as the gap between our model prediction and an actual observed score (i.e., the residual).

But then we went and added a bunch of notation, which seems to complicate everything. In a sense, it does complicate everything. But in another sense, it simplifies everything, especially as we go forward. There are some key ideas we need to keep straight as we continue to work with models, and notation will help us do that.

Remember: our goal is to use a distribution of data to construct a statistical model of the population distribution.