chapter  13
26 Pages

Precision for Planning

Precision is indicated by the width of a CI. Actually it’s MOE, the halfwidth of the CI, or one arm of the CI that’s our measure of precision. Higher precision is signaled by a shorter CI, and short CIs are good news. Precision is a highly valuable idea, but not sufficiently recognized or used. It usually contributes to what in Chapter 12 I called the informativeness of an experiment. Most of this book so far has been about using CIs to report and inter-

pret results, and one valuable approach to interpreting a CI focuses on MOE as a measure of precision. This chapter considers a further use of precision-in the planning of experiments. To carry out a precision analysis for planning, we first select a target CI width, and then the analysis tells us what sample size is likely to give CIs no wider than that target. In general, researchers have not yet made precision a central part of their research planning. When they do, they’ll no longer need to use statistical power. Precision for planning has the great advantage that it uses, before the experiment, CI concepts and judgments that correspond closely with those we use after the experiment for interpretation. This contrasts strongly with power, which really only applies before the experiment. Here’s the agenda for this chapter:

• Precision as arm length • Precision for research planning, for three experimental designs • Precision for planning using ESCI • Precision with assurance: finding N so we can be reasonably assured

our CI won’t be wider than the target width we’ve chosen • Precision for planning using Cohen’s d • Ways to increase precision

Consider any of the HEAT (Hot Earth Awareness Test) experiments we discussed in Chapter 12. To report our main result we’d no doubt use a CI,

which we’d display as the graphic on the left in Figure 13.1. I’ve labeled the arms of the CI as MOE because my focus in this chapter is on precision, as pictured by arm length and measured by MOE. Whenever we include a CI

in a figure we’re using precision to report our results. Precision is also the basis for our third approach to interpreting a CI,

as we discussed in Chapter 3-see also Table 5.1. Precision indicates the maximum likely error of estimation, although, of course, larger errors are possible-our CI just may be red, meaning it does not capture μ, or whatever population parameter it’s estimating. Vary the level of confidence, C, and MOE and thus precision change. Our measure of precision therefore relates to a particular C, usually 95. Figure 13.1 shows on the left the CI on our sample mean M. This CI is

symmetric and so the lower and upper arms can both be labeled as MOE. On the right is X, the point estimate of a population ES, with a CI that is asymmetric, meaning its two arms differ in length. We’ve already encountered in Chapter 11 asymmetric CIs on Cohen’s d. In Chapter 14 we’ll find that CIs on correlations and proportions are also generally asymmetric. Figure 13.1 distinguishes the two arms of the asymmetric CI by labeling the upper and lower arms as MOEU and MOEL, respectively. For symmetric intervals I’ll use MOE for the length of either

arm. For asymmetric intervals we’ll need to label the arms differently, as in Figure 13.1. For asymmetric intervals our measure of precision is simply MOEav, the average length of the two arms, and so

MOEav = (MOEL + MOEU)/2

It may feel strange to say increased precision gives shorter CI arms, or a smaller MOE, but that’s what I will do. Watch out for possible ambiguities in what you read or write about precision. Wide CIs mean low precision, and small MOE means high precision. If necessary, add a few words to make what you mean totally clear.