On the estimation of the expected number of accidents

We show that similar entities (drivers, intersections, bus companies, rail crossings) which in one period recorded "x" accidents do not have, on the average, "x" accidents in the subsequent period. The difference is large and systematic. This leads us to conclude that in circumstances in which only the safety estimates in these two periods matter, use of "x" to estimate the expected number of accidents has definite shortcomings. Better estimators are suggested, explored and their use is illustrated. We note that the suggested estimators are similar to what is used when estimation is based on a "treatment-control" type experimental design. It is hoped that the suggested estimators will alleviate some practical problems in the structuring of controlled experiments in safety research, eliminate bias-by-selection from uncontrolled studies and in general enhance the accuracy of safety estimates.