Language, confidence intervals and beliefs
People often speak and write about values of treatment effects outside their confidence intervals as being “excluded.” For example; “the risk ratio for major morbidity was 0.98 (95% CI 0.91, 1.06), which excluded any clinically important effects.” I just made that up but you often see and hear similar statements. What understanding do people take from it? There are two possible interpretations.
First, the straightforward meaning that clinically important values are outside the confidence interval. This is using “exclude” just as the opposite of “include” to make a statement about what is and isn’t inside the confidence interval.
But there is another interpretation, or another layer of interpretation, which I suspect is very common, and results from the meaning of “exclude” as something a bit stronger. Dictionary definitions give things like “to keep out, reject or not consider, shut or keep out,” which have a sense that excluding something is actively rejecting it. Using that word may therefore give the impression that the values outside the confidence interval can be discounted or ruled out. That is too strong a conclusion. Those values may be less compatible with the data, but that alone doesn’t make them unlikely or implausible.
I guess this is a similar issue to the use of “significant” and “confidence”; the word brings extra connotations.