3tatistics in road transport index numbers
Page 63
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WERAGES, which we analysed last week, hould not be regarded as a panacea for olving all problems of summarizing inforaation. In some circumstances their use even with selection of the most appropriate riethod) is not very meaningful and other levices have to be employed.
Road casualties is a subject in which here are frequent statistical conclusions_ kveraging out of casualties for groups of rears produces figures which give little idea )1. the real picture. In "longhand" the infornation that in 1928, 170,976 were killed md injured on the roads of Great Britain, l67,922 in 1955 and 369, 978 in 1967 does lot really convey a great deal.
A much more vivid and clearer way of iresenting this information is to say that if he 1928 figure is taken as 100, road casualies rose to 157 in 1955 and 216 in 1967. rhis presentation by index number shows iy the variation the magnitude—in this case t can be seen at a glance that casualties are nore than double in comparing 1967 with l928. Where figures are presented for a eries of years (a "time series" in the Ian;nage of the statistician) the clearness of the nethod becomes even more apparent in passing it is interesting to note a slight casualty decline in 1967 as the index figures for 1965 and 1966 were 233 and 230.
The year which is taken as 100 is called the base year. In the example with 1928 as the base year, all that is required is to divide the figure for all subsequent years by 170,976 and multiply by 100. Care needs to be taken, however, that there should be nothing untypical or freakish about the year chosen for the base. It would be statistically useless, for example, to take one of the war years as a base for road accidents. Petrol rationing and many other restrictions drastically reduced the level of traffic while blackout and bombing produced further abnormalities (1941 recorded the highest ever figure of deaths and 1944 the lowest total casualty figures of any year from 1928 to 1967).
A further factor also needs considering—the problem of "weighting". The casualties mentioned for 1928 and 1967 are divided into two groups—killed and injured. In 1928 there were 6,138 killed and 164,838 injured while in 1967 7,319 died and 362,659 were injured. It is obviously important to separate the killed from the injured to indicate the special seriousness of fatality compared with an injury.
This can be done by giving a weight of say 100 to the killed as compared with the injured (that is counting each death as of 100 times the importance of each injury). Thus the rise in casualties over the period of 39 years is (with 1928 as 100): 100 (7,319 x 100) + 362,659 (6,138 x 100) + 4,164,838 The "weighting" index figure for 1967 is about 150. This figure is much lower than in the absence of weighting, as the numbers killed in the period have risen much less proportionately than those injured. Whatever the cause of this changing trend
— better medical care could be one reason
— it is clear that there has been an improvement since 1928 when the volume of traffic was very light.
An index number based on "equality" between deaths and injuries thus obscures the improvement and can lead to decisions based on incorrect premises. The "weighting" method does give this serious problem a much clearer perspective.