Soon we’ll sound the trumpets for the arrival of CIs, but we need to explore several other ideas first. Watch out for the dance of the means and the mean heap, then the margin of error. After that the trumpets won’t be far away. Here’s the plan for the chapter:
• The population and a random sample • Sampling: dance of the means and the mean heap • Errors of estimation, and the margin of error (MOE) • Confidence intervals at last • Reporting CIs • Interpreting CIs: the first three approaches
There are two parts to this chapter: The first covers the first four bullet points and the second covers the last two. The first part is my version of the story that starts with sampling and finishes with CIs. Numerous textbooks give a version of that story. The main novel aspect of my version is that it focuses on understanding the extent of sampling variability-which, unfortunately, some people often underestimate. I hope ESCI pictures and simulations can help you build accurate intuitions about sampling variability. Because those pictures and simulations are so central, in the first part of the chapter I integrate ESCI activities more closely into the discussion than in any other chapter. However, I include many figures, so I hope the discussion is useful even if you don’t work with ESCI as you read. The second part of the chapter comprises the sections Reporting CIs
and Interpreting CIs. These go beyond what many other textbooks say about CIs. I don’t need to integrate ESCI so closely into those sections.