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Confidence Intervals

Imagine that you want to take a measurement on a group of 100 people. Perhaps you are measuring their glucose level, as a conceptually easy measure to think about. In that group of 100 people, you find that the mean glucose level is 87. Now what if you were to find another group of 100 people. Would you expect their mean glucose level to also be exactly 87? Or would you expect to see it differ slightly? And if we did this again, what would you expect to see?

The idea of a confidence interval (CI) is designed to give you an idea of the approximate mean of a population. The interval is actually a range of values in which you are likely to find the parameter of interest. Most often the interval is constructed at a level of 95% confidence. The easiest way to think about this is look at it as if you did the study 100 times. If you did, the actual value would fall within that interval 95 out of the 100 times you determined the mean measurement. It is therefore a measurement of precision, if you will. It is a different way of looking at a p value, which at times can confuse people as they read down a chart of measures made in, for example, a clinical trial. Is p=0.66 significant or not? Hard to remember. But looking at the confidence interval can tell you how significant it is at a glance.

It is not important for you as a clinician to understand how a confidence interval is calculated. If you are interested, you can look it up, of course. But of course you are a busy clinician and you do not have the time to do so. Which is fine. All you need to know is how to interpret the 95% CI (please note that we can construct the CI at different levels, such as a 90% CI, etc., but 95% is most common in clinical research). And interpreting it is simple. Here is the key to understanding how to look at a 95% CI: if the interval runs from a negative number to a positive one- that is, if it crosses 0- it is not statistically significant. And the larger the population of a study, the smaller the 95% CI will be. This makes sense. Larger populations will come closer to representing the true mean. Consider a trial of 8000 versus a trial of 80. The mean in the smaller trial may vary a lot from the true mean, by chance alone, since the sample is small. This will create a large 95% CI. The more people in the study, the more likely you will see measures that approximate reality, and so you will see a smaller, more precise CI.

In case, this is all confusing, consider the following statement: “The mean measure for our factor of interest was 4.3 (95% CI 4.0, 4.7).” This tells you that the mean would fall within a range of 4.0 to 4.7 95 out of 100 times you might make the measurement. It is a significant finding. This is as opposed to a similar statement of “The mean measure for our factor of interest was 2.2 (95% CI -2.1, 4.4).” Seeing this cross the 0 line tells you that this was not a significant finding. It is equivalent to a p value of greater than .05.

A good explanation can be found on Wikipedia at http://en.wikipedia.org/wiki/Confidence_interval.

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