Talk:GEH statistic

GEH Formula
I notice that the GEH formula got changed incorrectly (the 2 in the numerator was changed to 0.5) and then corrected (the 0.5 was then moved to the denominator,) however 2 in the numerator is more simple and elegant than 0.5 in the denominator, so I've changed it back to that form. 58.168.241.42 02:30, 22 January 2007 (UTC)

The form as written may be "more simple and elegant" but I believe that it is less comprehensible and less memorable. The GEH statisitic is the square root of the difference between observed and modelled divided by the average of the observed and modelled, all square rooted. The 2 is therefore the denominator of the denominator. I can understand that it is difficult to write an equation in computer text format where there are multiple denominators. In this eventuality the 0.5 value in the denominator would be the more correct form. What is not clear (generally, not just the Wikipedia entry) is whether the GEH statistic should be used in terms of vehicles or pcu (passenger car units). The GEH statistic is used by traffic modellers, who would normally use pcus, so as to convert all traffic types into a common unit. So for example HGVs might have a pcu value of around 2 per vehicle. The value of GEH is affected by the magnitude of the flows, the lower the value the greater the variation allowed; in mathematical terms this is because it is goverened by a flow raised to the power 2 divided by a flow to the power 1. If the pcu value is 2, then converting from pcu to vehicles reduces the value by the square root of two, which could well be sufficient to affect the goodness of fit conclusion. The Design Manual for Roads and Bridges which quotes the GEH does not make the units clear. However as the use of pcu does not appear in DMRB generally it suggest that vehicles (which not surprisingly does appear in DMRB as a unit of measure) must be assumed. Yet traffic modellers would generally use pcu.Mr Pogle (talk) 14:31, 26 August 2008 (UTC)