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Statistical Concepts 43 Therefore, determination of the required sample size should proceed by asking the following questions: · What are the critical characteristics of the target survey population that will drive decision making? · For what subgroups of the target survey population will these characteristics be required for decision making, and what proportion of the survey population do these subgroups compose? · What is the expected proportion of respondents with the critical characteristics in each of the subgroups? · For a range of different possible sample sizes, what is the expected accuracy of the estimated proportion of respondents with the critical characteristics in each of the subgroups? · What are the potential consequences if decisions are made on the basis of the estimated propor- tions of respondents with the critical characteristics and these estimates turn out to be wrong by the magnitude of the expected accuracy for each of the different possible sample sizes? The final decision on sample size will involve a tradeoff between establishing a reasonable sam- ple size (and associated budget) for the survey and the resulting accuracy that is achievable for the various critical characteristics for each of the subgroups of interest. This tradeoff may involve accepting a significant reduction in the level of accuracy that will be achieved for many of the characteristics and subgroups, particularly those accounting for a small proportion of the target survey population. 3.5 Weighting Most survey designs attempt to select a representative sample of individuals from the target population. However, in practice the resulting sample rarely corresponds exactly to the compo- sition of the population. Some groups are over-sampled and some are under-sampled, because of the sampling approach adopted or the inevitable variability in executing the planned sampling approach. The objective of assigning weights to the individual survey responses is to correct for these differences and improve the accuracy of the results. For random, sequential, and proportional stratified sampling, the number of sampled indi- viduals with a particular characteristic can be expanded to an estimate for the population by simply dividing by the sampling fraction. Thus, if 1% of passengers are surveyed, population estimates can be obtained by multiplying the sample number by 100. Each response is there- fore given a weight of 100 and it is these weighted values that are used in the analysis and prepa- ration of results. For non-proportional stratified sampling, sampled numbers within each stratum must be expanded separately by dividing the sampling fraction for that stratum, and then summed to obtain estimates for the population. Similarly, for cluster sampling, the sample numbers in each cluster must be expanded separately, dividing by the sampling fraction for that cluster (if not all individuals in the cluster were sampled), then the sample cluster numbers expanded to popula- tion estimates. If the clusters were selected using random, sequential, or proportional stratified sampling, the sampled numbers in each cluster are summed and divided by the fraction of clusters sampled. Weighting can also be used in surveys where the sampling proportion varies over the time of day. For example, if the same number of interviewers is used over the day, the proportion of pas- sengers surveyed in the busy periods will be much less than during the quiet periods, and peak period passengers will be under-represented in the sample. This issue can be addressed by apply- ing higher weighting to surveys collected in the peak period. The method for determining the