Effectiveness of Median

New to this board and hoping this question is something easy to describe. I am working on a project that look at median cycle times of emergency department patients length of stay. Across a quarter, the sample size is fairly large (n=5000). However, some of the patients (<10% of the sample) have elongated length of stay times since they are technically being held in the emergency department even though they have been admitted to the hospital. Technically, these patients are supposed to have their cycle times calculated with an endpoint of when they have been placed into this status and not when they leave the department (which is not data that we have available).

Some are arguing that this will unfairly increase the true median time being measured since we cannot make the above calculation due to data limitations. My feeling is that since we are using median and this only impacts less than 10% of the sample, that the results of including them in the population are nominal and may not be significant.

I would welcome the opinions any other proof statistically to support this argument

• What timescales will the median be calculated on? If you're computing it every week, for example, any week where over half of the patients are in the elongated condition will cause trouble, even if it won't cause trouble in the quarterly statistics. – Matthew Graves Oct 29 '15 at 19:04
• How are you modeling this? Are you using a Cox model or some other non- / semi- parametric model? – gung - Reinstate Monica Oct 29 '15 at 19:09
• Sorry, I'm a bit of a non-statistical guy and don't know about Cox models or others but we are measuring the median on a patient level basis. So that is about 55 samples per day and we will then aggregate a quarters worth of patients and perform the above. Again, no more than 500 patients per quarter follow the different process whose cycle time is elongated and I am trying to determine if this would sway the median as it is only 10% or so of the entire sample. My thought is no, but some feel like it does make a significant impact. Any way to statistically prove them wrong? :) – Eric B Oct 30 '15 at 22:42