Spatial sampling considerations involved in modelling speeds on rural single carriageway roads in Scotland

The paper illustrates the risk of bias in spatial sampling arising from spatial autocorrelation. With the aid of a road databank, a random sample of rural single carriageway Trunk roads was taken, stratified by width, hilliness and bendiness. Speeds and flows were measured by the University of Glasgow (‘GU’) in 1983 using the moving observer (‘MO’) method, at these 33 sites. During the same month, consultants measured speeds by the registration number (‘RN’) method on 96 road sections deliberately spatially clustered to form 17 contiguous groups of sites on 8 roads in 4 areas of Scotland, and to contain the full range of width, hilliness and bendiness. From the latter measurements they derived a formula for predicting speeds on other road sections from their physical and traffic characteristics. As a check on the validity of the MO method GU also measured speeds at the consultants’ sites, and found there was no significant difference between the methods. When the speeds measured at the GU sites were compared with the predictions made by the formula there was a strong tendency (R-squared of 77%) for speeds observed on fast roads to be higher than predicted. This might have been due to bias in the MO measurements, or it might have been because the consultants’ sites were clustered in areas not typical of Scotland e.g. having an exceptionally high proportion of drivers who were admiring the scenery.