StATS: Missing values (June 22, 2004).

Someone here at the hospital asked me how to do a reliability analysis on a 20 item measure where a large number of participants left a single item blank. There are several approaches that work, but you need to exercise a bit of caution.

The simplest thing is to analyze only those participants who completed all 20 items. This is known as listwise deletion. You can lose a lot of precision with this approach because your sample size will often be a lot smaller. You also have to assume that the patients who left one or more items blank do not differ substantially from other patients.

You could also replace the missing items by the average score of the remaining items. This is known as mean imputation. You have to assume that patients who left one or more items blank do not differ from other patients and that items left blank do not have different responses from items that were filled out. Even if these criteria are satisfied, mean imputation will tend to understate the variability because the mean values that you substitute for the missing values will artificially reduce the variation in your data.

You can also conduct a simulation by randomly replacing the missing values from a probability distribution that reflects your best understanding about the process that generated missing values. The is known as multiple imputation. It is a tricky process and it is only as good as the probability distribution that you choose. A nice introduction to multiple imputation is on the web at http://web.inter.nl.net/users/S.van.Buuren/mi/hmtl/whatis.htm.

Multiple imputation is far better than listwise deletion or mean imputation, as long as you have the time and energy to do it well. I have not read it yet, but the classic reference on missing data is

Statistical Analysis with Missing Data, Second Edition by Roderick J.A. Little and Donald B. Rubin. [BookFinder4U link]

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Statistical theory.