Approach to Median calculation
Hounslow feel that the median calculation is more suitable for larger data sets, whereas for small sample sizes the addition or removal of a single value can significantly impact the median. The method does not give weighting to relevant factors such as the actual number of clients supported by a provider – costs submitted by a provider supporting one Hounslow client would have an equal impact on the median calculation as a provider supporting 100 Hounslow clients. Additionally, the median calculation method diverges from current practice, whereby Hounslow uses a mean average calculation method to determine the iBCF rates.
As the median rate simply selects one value in the middle of the range of prices submitted by providers, this does not guarantee that a median rate will correspond with an accurate whole market rate. The median cost is derived from a sample of the care market that chose to provide data, so risks not being fully representative of the cost of care.
However, for the purposes on the exercise Hounslow considered 2 methods to calculate the median values.
- Medians calculated using end per hour costings from each submission
- Medians calculated at line level, summed at subtotals, then subtotals summed
Exclusions of the two outlier providers submissions for Hounslow made a significant difference to the end total cost median calculation, (this moved from £21.54 to £23.55), however their inclusion in the line level median cost had the inverse effect and reduced the median calculation from £21.77 to £21.64. Hounslow has determined that whilst their inclusion in a line level median cost may seem beneficial to the Council there can be more statistical confidence in the data which excludes them, whilst acknowledging the shortfalls of a median approach as outlined above.
Hounslow have selected option 2 (calculated at line level) as the basis to calculate the median. It was felt that the sample size was large enough to not be significantly distorted by remaining anomalies in the line data and that to use option1 (end per hour), the impact of end total cost per hour rate meant that this method gave an unrepresentative rate relative to the market.
The median calculation method produced results that do not reliably reflect market costs. Future modelling must include benchmarking and regional data as several providers work across Northwest London and reflect their regional costs in their submissions.
Home Care Draft LQ, Median and Upper Quartile figures excluding outliers*
Cost per Hour |
Lower Quartile |
Median |
Upper Quartile |
---|---|---|---|
Cost per hour (Calculated median at end total cost per hour level) |
£20.75 |
£21.54 |
£23.57 |
Cost per hour (Calculated line level median costs, then summed) |
£18.81 |
£21.77 |
£26.27 |
Home Care Draft LQ, Median and Upper Quartile figures including all data received.
Cost per Hour |
Lower Quartile |
Median |
Upper Quartile |
---|---|---|---|
Cost per hour (Calculated median at end total cost per hour level) |
£20.82 |
£23.55 |
£24.51 |
Cost per hour (Calculated line level median costs, then summed) |
£17.43 |
£21.64 |
£25.87 |