Sample Size Determination to Evaluate the Impact of Highway Improvements

This paper was prepared for the Department of Transport, as a support document to a main report on the feasibility of measuring responses to highway improvements. The paper discusses the statistical issues involved, particularly as regards the determination of suitable sample sizes. Worked examples are provided, using such data on ambient variability and adjustment factors as were available to us. Some of the data is included as an appendix where it was felt to be otherwise not easily available.

The note asks two sort of questions. Firstly, what is the minimum sample size to take to be a certain percent confident that a given quantity lies in a range of a given width. Secondly, what sample sizes should be taken in Before and After studies so as to be a certain percent confident that a change in a quantity by a given amount will be detected as a statistically significant difference at some chosen significance level.

Three sorts of quantities are discussed:

- total flows past a point, which may be counted by loops, tubes or manually;

- partial flows, such as a particular 0-D flow, which require roadside interviews;

- journey times over particular links.