Today we’re releasing another two chapters of the Compact Guide to Classical Inference. Today’s chapters lay much of the foundation for the compact approach. Chapter 2 describes briefly the organization of data and introduces two simple notions not usually found in traditional approaches: identifying a specific response variable and creating an indicator variable when the response is categorical. Simple as indicator variables are, using them enables problems involving proportions to be folded directly onto the settings for quantitative response variables. Just this simple step reduces the number of inferential settings by half! (Later, we’ll see how it also handles the situation usually, and unnecessarily, treated with chi-square.)
Chapter 3 is very short: measuring variation. As you’ll see, a central unifying theme of inference is measuring the amount of variation in the response variable and comparing that … well you’ll have to wait for Chapters 4 and 5 for that!
The variance is the star here. No longer relegated to being an intermediate step in calculating a standard deviation, the variance shines on its own.
The textbook method for computing the variance involves subtracting the mean from each data value. As an innovation, Chapter 3 shows the variance solely in terms of comparing pairs of values. This little added insight into a familiar statistical quantity alone justifies reading the chapter.