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