## Saturday, March 3, 2012

### Confidence Interval

(To our junior colleagues and students)

Confidence interval is a statistical term frequently encountered in papers describing various kinds of medical research. It is one of the terms that postgraduate medical students need to know.
The following examples serve to explain it.
If you want to find the mean weight of a group of 30 men, you measure the weight of each one, add the figures and divide by 30. The result is the mean weight of the group.
If you want to find the mean body weight of men residents of a big city, it is not practical to do the same because of the large number involved. Statisticians get around this by taking a random sample of the men in question. They calculate the mean weight of the men in the sample and consider it a satisfactory representation of the required mean of the total. They may take e.g. a thousand men, chosen randomly from various districts of the city, measure the weight of each and then add and divide to find the mean. They consider this representative of the mean body weight of the men of that city. Now imagine yourself to be the person who requested that mean because you wanted to assess the nutrition status of the people in the city and you asked a statistician to do it for you. Imagine also that the mean weight of the thousand men was 60 kg. You may then have the following dialogue with the statistician:
·         Are you sure the figure you gave me is exactly the same as the figure you would have obtained had you taken all the men in the city?
·         No, most probably it is not, but it is very near that figure and is sufficient for your purpose.
·         How near is it? How much is the difference?
·       I cannot tell you the exact difference because I do not know the true figure of all the men in the city. We statisticians usually deal with probabilities. I can tell you the probability of the difference being of a certain magnitude. I can work out from the data of the thousand men a figure we call the Standard Error (SE). In fact I have already done that and found the standard error of the mean of the sample to be 2. We know from statistics laws and rules that the probability of the difference being not more than one standard error (1SE) is approximately 67% and being not more than 2SE approximately 95%. In other words I can tell you that I am practically 95% confident that the true figure of the mean weight of all men in the city is within 2SE above and below the figure of 60 i.e. between 56 and 64 kg. That is what I mean when I say the mean body weight of the sample of men is 60 kg. and its 95% Confidence Interval (CI) is 56 - 64.
The 95% probability (or confidence) becomes approximately 67% if you choose 1SE above and below the mean as the limits of your confidence interval and approximately 99% if you choose 2.5 SE. The 95% (i.e. mean ± 2SE) is commonly used and if the percentage is not written it usually means 95%.
I used the mean as an example to explain the confidence interval. The same applies to other parameters like proportions when samples are used instead of the total.