Guidebook for Conducting Airport User Surveys (2009) / Chapter Skim
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Appendix B - Sample Sizes, Sample Estimates, and Confidence Intervals
Appendix B - Sample Sizes, Sample Estimates, and Confidence Intervals
Pages 161-177
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From page 161... ...
σ X x ni= ∑ ( ) 1 A P P E N D I X B Sample Sizes, Sample Estimates, and Confidence Intervals
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From page 162... ...
For a 99% confidence interval, the constant should be 2.58, and for a 90% confidence interval, use 1.65. If the sample size is to be chosen so that the sample mean is within w of the population mean, μ, with a probability of 0.95, then the 95% confidence interval is given by: This can be solved to give the sample size, n: In the survey planning stage when trying to determine the sample size, the standard deviation of the variable X, σX, will be unknown and must be estimated based on data from previous surveys, other similar airports, or knowledge of the airport.
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From page 163... ...
Sequential Sampling Sequential sampling is equivalent to random sampling if the order of the sample with respect to the characteristics of interest is essentially random. In this case, sample sizes and estimates of standard deviation and confidence intervals are determined in the same way as outlined above for random sampling.
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From page 164... ...
: which can be solved to give the sample size, n, as: If separate estimates for each stratum cannot be obtained in the planning stage, an approximate estimate of the standard deviation of X over the total population could be used to provide a conservative estimate of the sample size, n. For proportional stratified samples, the sample size for each stratum, ni, is then found by: n nWi i= n W w W i i Xi i i Xi = ( )
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From page 165... ...
The sample mean for each stratum and overall sample mean can be found using Equations 4 and 5, respectively. The sample sizes, ni , are chosen so that a confidence interval of width 2w is given by the relationship: In this case, many different combinations of ni could be chosen to produce a confidence interval width of 2w.
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From page 166... ...
Where the clusters to be sampled are drawn randomly from the population of all clusters, and a sample of individuals are drawn randomly from each cluster, the variance of the sample mean, X – , includes two components of variation, the between and within cluster components, and for a categorical variable is estimated by: where p is the proportion of the total population in the category of interest pk is the proportion of individuals in cluster k in the category of interest σc is the variance of the cluster means around the population mean and can be estimated by: if all individuals in each selected cluster are sampled, mk = Mk, and the variance is given by the "between cluster component" term only. Clusters could be selected using stratified sampling to reduce the variance between clusters within a given stratum and thus improve the accuracy of the estimate.
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From page 167... ...
It should be noted, however, that cluster sampling is less efficient that random, sequential, and stratified sampling and larger sample sizes will be required to obtain the same levels of accuracy. Use of the expressions applicable for random sampling will underestimate the true standard errors of estimated population characteristics and the associated confidence intervals.
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From page 168... ...
The ratio of the variances: σX–C 2 / σX–R 2 is often referred to as the design effect, DE, and is given by: The effective sample size is given by: mav n / DE. Examples of Calculation of Sample Sizes Small Population Size -- Using Random or Sequential Sampling for Categorical Variables In this example, the sample size is required for a survey of a relatively small population, such as an employee or tenant survey, using random sampling.
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From page 169... ...
: What is the percentage of passengers dropped off at the curb outside departures check-in? It was decided to determine the sample sizes for each of the different sampling types and chose the most cost-effective method.
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From page 170... ...
Sample sizes for random sampling of passengers for 95% confidence interval widths 2%, 3%, and 4%. 32 The denominator in the equation in Section 3.4.1 is a2 where the width of the 95% confidence interval is ± a where a is expressed in percentage points.
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From page 171... ...
Sample sizes for stratified sampling of passengers by sector of flight for 95% confidence interval widths 2%, 3%, and 4%. Sample Size for C.I.
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From page 172... ...
Sample sizes for stratified sampling of passengers by day of week for 95% confidence interval widths 2%, 3%, and 4%. Stratified Sampling of Passengers -- Stratified by Day of Week Now consider the case where the passengers are stratified by the day of the week.
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From page 173... ...
Sample sizes for each day for stratified sampling of passengers by day of week for 95% confidence interval widths 2%, 3%, and 4%. For Flight Sector, i Total Quantity Symbol Short-Haul Domestic Long-Haul Domestic International Symbol Value No.
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From page 174... ...
Sample sizes for cluster sampling with random sampling flights for 95% confidence interval widths 2%, 3%, and 4%. 33 Note that if there was no difference between sectors, so that the mean percentage of passengers dropped off at the curb was 58.9% for all flights, the standard deviation in the percentage between flights, σci, would equal the standard deviation of the mean for each flight.
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From page 175... ...
Sample sizes by sector for cluster sampling with flights stratified by sector and all passengers on selected flights surveyed for 95% confidence interval widths 2%, 3%, and 4%.
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From page 176... ...
. The flight sample size is determined for a given confidence interval X – ± w by solving the following relationships for n: w = 1.96 σX– 2 where σX– 2 is given by the equation above.
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From page 177... ...
2.00% 3.40% 117 3.00% 5.09% 47 4.00% 6.79% 26 Table B-18. Sample sizes by sector for cluster sampling with flights stratified by sector and a 50% sample of passengers on selected flights surveyed for 95% confidence interval widths 2%, 3%, and 4%.
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