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Length of stay in psychiatric hospitals

Priest et al. ( 1 ) recently published a strong argument for using the median instead of the mean when calculating a measure of the central tendency for length of stay in psychiatric hospitals. In particular, they demonstrate that the distribution of length of stay is heavily skewed and most similar to an exponential decay curve, not a normal distribution. Yet in fact there are several other strong arguments for using the median instead of the mean which should perhaps be considered. For example, the median is unaffected by the inability to obtain results at extreme ends of the distribution, unlike the mean, and this becomes important in the study of bed length of stay. Some patients who have still not been discharged at the time of the calculation of mean length of stay have not actually yet reached the end of their length of stay. Hence it is not possible to know what their final length of stay is going to be, and variations in their scores would dramatically affect the calculation of the mean, but not the median (2). Another important characteristic that statisticians often use to determine the goodness of a measure of central tendency is the degree to which it is close, in some sense, to the individual observations which it is supposed to represent. One mathematical measure of this goodness of an estimate of central tendency is if the sum of the deviations of the individual data points from that statistic is a minimum. This sum of the absolute deviations from the median is less than the sum of the absolute deviations from any other point, including the mean. However, one possible objection to the widespread use of the median, as opposed to the mean, as a summary statistic for length of stay is the inability to use medians for statistical comparison purposes in tests such as t-tests. It may be worth remembering that there is in fact a median test ( 3 ) , which is a procedure for testing whether two independent groups differ in central tendencies using the median as the measure of central tendency.