Essentials

138 ESSENTIALS OF STATISTICSmean of a population. The solution was interval estimation—creating a confidenceinterval (CI) around our point estimate. In a similar fashion creating a CIaround an effect-size estimate (ESCI) adds a great deal of information.Admittedly, there are times when the CI for the difference of the populationmeans is more meaningful than the corresponding ESCI. For instance, if someherbal supplement claims to shorten the duration of the average cold, we wouldwant an estimate involving the number of hours or days we could expect to bespared the symptoms of a cold virus. Having a CI in units of time would be a greataid in deciding whether to use the product being tested. On the other hand, ifsome other supplement claims to improve memory and we test it with a list ofwords we just created, the CI will give us a range of how many additional wordswe are likely to remember after taking the supplement. But that is hardly meaningful,depending as it does on the number of words on the list, the commonnessof those words, study time, and many other factors. An ESCI would be moremeaningful. If the ESCI demonstrates that the effect size is likely to be large, atleast we would know that few people in the control condition can be expected toshow memory improvements as large as the average person taking the supplement.Unfortunately, ESCIs are rarely reported in the scientific literature, and this isundoubtedly due in large part to the fact that they are somewhat difficult to construct.The CIs we described in earlier chapters were based on critical values fromthe normal or the ordinary (i.e., central) t distribution. ESCIs, however, requirethe use of critical values from a noncentral distribution (e.g., for a given numberof degrees of freedom there are an infinite number of noncentral t distributionseach based on a different value for delta, the noncentrality parameter), and thesevalues are not available in standard tables. Only in recent years have major statisticalpackages (e.g., SPSS) included a procedure for obtaining these critical values,and even at the time of this writing there is no readily available computer programthat will construct such CIs for you. Steiger and Fouladi (1997) and Cumming andFinch (2001) explain how to construct CIs for effect-size measures, but we don’texpect to see their widespread use anytime soon.Meta-AnalysisA common misconception can occur when, say, a dozen researchers perform essentiallythe same experiment, and half obtain significant results in the expecteddirection, while the other half do not. It can look like the various results are contradictory,but it is possible that all 12 researchers are dealing with a situation inwhich power equals .5. Then we would expect only half of the results to be sig-