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Confidence Intervals

I would guess that by now you have come across the term “confidence interval” while reading a clinical trial or another kind of paper. This is a critically important concept for clinicians and academics in healthcare to grasp. CIs are typically used when, instead of wanting the mean value of a sample, we instead want a range likely to contain the true population variable. Now, the idea of a “true value” is really something that remains theoretical, but it refers to the mean value we would find if we could gather data for the entire population from which our sample is drawn.

Statisticians can calculate a range (or an interval, if you will) in which they (and therefore us) can be pretty sure (confident) that the “true value” lies within. For example, we might be interested in pain reduction with spinal adjusting. From a sample of research participants, we can work out the mean reduction in pain as measured on, say, a Numerical Rating Scale. However, this will only be the mean for our specific sample. If we gathered a second group of research participants, we would not get, nor expect to get, the exact same mean value. There are any number of reasons for this: chance, biological variation, etc. The CI gives the range in which the true value is likely to lie, if we could repeat this an infinite number of times.

Example: the average pain score prior to adjusting in study A was 7/10 in a group of 80 low back pain patients. After adjusting, the mean pain score dropped by 3 points. If the 95% CI is 1-5, we can be 95% confident that the true effect of treatment is to lower pain by 1-5 points. If in study B, using a different chiropractic technique, and also reducing their mean pain score by 3 points, there is a wider 95% CI of -1-5. This CI includes 0 (it runs from -1 to +5) and the inclusion of 0 (no change) means there is more than a 5% chance that there was no true change in pain, and the treatment was actually ineffective. (This is, you may note, similar to saying that p>.05, but the CI is much easier to intuitively understand).

A point to remember is that the size of the CI is related to the sample size of the study. Larger studies will almost always have narrower CIs.

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