In Brief: Statistics in Brief: Confidence Intervals: What is the Real Result in the Target Population?

Abstract

Background Authors of a recent article [1] indicated there was a difference (p = 0.015) in compliance at 6 months between the percentage of patients with osteoarthritis receiving insoles (71%; 32 of 45) versus the patients receiving braces (45%; 21 of 46). The small p value along with randomization of the patients provided strong evidence that the percent compliance in the target population (ie, all patients with osteoarthritis being treated by these methods) really is different. However, the p value alone does not provide us with much information concerning the magnitude of the difference in compliance in the target population. For that, we need to consider the estimated difference of 26% (71%-45%) and appropriate confidence interval. Question What is a confidence interval and how should it be used? Discussion The confidence interval provides us with a range of values that we believe, with a given level of confidence, contains the true value of the statistical parameter (difference of percentages in this case) in the target population. The estimated parameter value of 26% difference in this small sample is the best point estimate we can make. However, we can be fairly certain this point estimate is not equal to the targeted true value as a very small sample rarely would give the exact estimate of the true proportion in the target population. Thus an interval estimate is needed to show the reliability of this point estimate. This is given by a confidence interval. To form a c…