Question

how do I find the confidence interval for the median of a population?

Answer 1

The confidence limits are given by actual values in the sample. We choose which values using the following formulae:

For example:

If there are 20 values in the sample:

The median is between the 10th and 11th highest ordered measurements

The 95% confidence interval for the median is given by the values ranked:

10-4.38 = 5.62 and 1+10+4.38 =15.38

Of course, there are no 5.62 and 15.38 ranked values, so we choose the nearest ranks to these and have an APPROXIMATE 95% confidence interval for the median. For the 20 values this will be the 6th to the 15th ranked values.

Example:

Consider the differences in temperature between the start and end of surgery for the 12 patients undergoing percutaneous surgery.

The median difference is halfway between the 6th and 7th largest values i.e., between -0.9 and -0.7 = -0.8

There are 12 values and hence:

So an approximate 95% confidence interval is given by the 3rd and 10th ranked values (-3.2, -0.2).