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Hospital Performance: Time patients spent in emergency departments in 2011–12

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Appendix 2: Approach for calculating deciles

The Authority used multiple methods to identify hospitals that were performing higher or lower than most facilities.

Highest and lowest 10% of hospitals in peer groups for percentage of patients departing ED within four hours of arrival

The highest and lowest 10% of hospitals in each peer group were identified using deciles. Deciles are a statistical measure of distribution across an indicator. The Authority reported hospitals in the highest and lowest deciles, by peer group, for each of the following indicators:

  • Percentage of all patients departing ED within four hours of arrival—National Emergency Access Target (NEAT)
  • Percentage of admitted patients departing ED within four hours of arrival
  • Percentage of discharged patients departing ED within four hours of arrival.

For this report, a decile of 1 represents the highest-performing 10% of hospitals against NEAT while a decile of 10 represents the lowest-performing 10% of hospitals for NEAT.

For example, a hospital with the decile being 1 for the percentage of presentations within four hours means that if hospitals in the peer group are sorted by the descending percentage of presentations within four hours, this hospital is in the top 10%.

The Authority uses the data for each hospital and the mean of the corresponding rank for tied data values to assign the decile in SAS®9. The decile was calculated using the following formula:

The following image is the equation to calculate decile. This formula is: decile = FLOOR((rank * 10) / (n + 1))Equation to calculate decile

where

FLOOR(x) returns the largest integer that is less than or equal to x;

rank is the value’s order rank based on the descending percentage of presentations within four hours (and the mean of the corresponding rank for tied data values);

n is the number of hospitals in the peer group.

9. SAS Institute Inc. 2009. Base SAS® 9.2 Procedures Guide: Statistical Procedures, Third Edition, Carey, NC: SAS Institute Inc.