Should statistics be taught longitudinally?

I’m working my way through my AP Statistics Candy Review activities and I really, really like them. And they are making me think about how this class is structured in my text and, I assume, most texts.

Here is the basic structure of MANY of the chapters of my text:

• Big Topic
  • A bit about it generally
  • How it applies to categorical data
  • How it applies to quantitative data

As specific examples, we have:

1. Chapter 1 – Exploring Data
   1. Analyzing categorical data
   2. Analyzing quantitative data
   3. Describing quantitative data
2. Chapter 7 – Sampling distributions
   1. What is it?
   2. Sample proportions
   3. Sample means
3. Chapter 8 – Confidence intervals
   1. The Basics
   2. Proportion intervals
   3. Mean intervals
4. Chapter 9 – Hypothesis tests
   1. Basics
   2. Proportions
   3. Means
5. Chapter 10 – two sample tests
   1. Comparing two proportions
   2. comparing two means

You get the picture.

I understand the appeal and purpose of setting things up this way; means and proportions are by far the most common things we do statistical studies and inference with, and the general process of, say, constructing a confidence interval is the same in both cases. But my students have struggled this entire semester with keeping straight the differences between them. This is partially my fault for failing to make the distinctions clear, but I have to wonder; would it be better to do everything to do with categorical data and proportions FIRST?

Here’s what I envision:

1. Designing studies (chapter 4 in my book). Crucial to any longitudinal, semi-project-based approach, since I will want the students to design our at least have input on the design of our longitudinal projects
2. A categorical data project. Not dissimilar from my Skittles activity but broken into pieces and interspersed with additional practice. This project, which will get touched on every single day, will require them to learn about:
   1.  Graphing and representing categorical data, including discussion of frequency tables, marginal distributions, conditional distributions, etc. (Chapter 1 in my book)
   2. Some aspects of Probability; using our sample data as the “true” value, imagine other future sampling options. (Chapter 5 in my book)
   3. Sampling distributions of proportions (Chapter 7 in my book) – this will be our first quantitative data, so…
   4. Displaying quantitative data with graphs (dotplots and histograms) and describing them with numbers (mean and standard deviation) (more chapter 1)
   5. Normal curves (Chapter 2)
   6. and now we have neough for… Confidence intervals and hypothesis tests with proportions (chapters 8 and 9)
   7. Comparing two proportions (chapter 10)
   8. chi-square goodness of fit and independence tests (Chapter 11)

Do you see how one giant, connected series of investigations involving exclusively categorical data and quantitative data about that categorical data, could lead to all of these ideas?

Once that project is finished, we start fresh and do data that was quantitative from the start. Two quantitative variables that can be connected, so we analyze each variable separately, do inference on each variable separately, then combine them for regression and regression inference.

Finally, fill in any gaps: probability ideas that never came up seem like the most obvious ones.

The chapters felt very disconnected this year. A significant part of that was teaching (I was basically relearning the curriculum myself as I went, after all), but a big part is structural as well, and I wonder if this sort of linear, longitudinal structure would be helpful. What would I lose by doing this?