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Guidebook for Conducting Airport User Surveys (2009)

Chapter: Chapter 3 - Statistical Concepts

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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Suggested Citation:"Chapter 3 - Statistical Concepts." National Academies of Sciences, Engineering, and Medicine. 2009. Guidebook for Conducting Airport User Surveys. Washington, DC: The National Academies Press. doi: 10.17226/14333.
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Statistical Concepts C H A P T E R 3 Overview of Basic Concepts Distribution In any set of data, each item in the dataset has a particular value. The distribution of the data in the dataset refers to the proportion of the items that take each of the possible values in the dataset. With discrete data (e.g., the number of people in a travel party), each possible value (1, 2, 3, etc.) will occur for some proportion of the total number of items in the dataset. For continuous data (e.g., the time taken to drive to the airport), there are effectively an unlimited (or at least very large) number of possible values. Therefore, the distribution is defined in terms of a functional relationship, typically plotted as a graph or expressed as an equation. The relationship can be used to determine the proportion of values within a given range. Average The average value of a set of data (also referred to as the mean of the distribution) is defined as the sum of the values of each item in the dataset divided by the number of items. This corresponds to the common usage of the term “average.” Usual usage is to refer to the average of a set of data and the mean of a distribution, although the concepts are identical. Variance The variance of a dataset or a distribution measures the spread of the values about the average or mean value. It can be thought of as the average of the squared difference between each value and the mean of the distribution. The differences are squared so that larger differences have greater importance than smaller differences and negative and positive differences do not offset each other. Standard The standard deviation of a dataset or distribution is defined as the square root of the variance. Deviation This expresses the spread of the values around the average or mean of the dataset or distribu- tion in the same units as the data. More details can be found in textbooks on general statistics, such as those listed at the end of this guidebook. 27 An understanding of the underlying concepts of sampling and statistical accuracy is funda- mental to an understanding of such issues as the size of the sample to be used and the accuracy of the resulting findings. This chapter is primarily intended for readers who are not familiar with these concepts or those who are interested in a review of the basic statistical principles.

3.1 Concepts of Census and Sample Surveys In general, a survey will collect information from a sample of individuals from the target pop- ulation (see Section 1.3 for a discussion of survey terminology). In some cases, it may be appro- priate to survey the entire population, in which case the survey is termed a census survey. A census survey is generally appropriate for collecting information on small populations when a very high level of accuracy is required and when there are no significant constraints due to budget, survey resources, or the time period when individuals are available to be surveyed. A census survey might be appropriate, for example, for a survey of tenants at the airport, but not for a survey of air passengers. For a sample survey, a sample of respondents is selected from the target population in such a way that the characteristics of the population can be inferred from the corresponding character- istics of the sample. The way this is done and the implications for the accuracy of the resulting estimates of the characteristics of the population are discussed in more detail below. 3.2 Statistical Accuracy and Confidence Intervals The characteristics of interest of the population being surveyed, such as the mode of travel to the airport, will vary across the members of the population. Aggregate measures of the popula- tion, such as the proportion of air passengers accessing the airport by taxi, can be estimated from the corresponding values for the sample. However, when drawing a sample from a population, the distribution of the characteristics of interest across the members of the sample will generally be different from the corresponding dis- tribution across the population, and thus measures of this distribution, such as the average value, will also be different. This difference between the sample average and population mean is referred to as the error of the estimate. With very small samples relative to the size of the population, it is unlikely that the distribu- tion of the characteristics across the sample will correspond exactly to the distribution across the population as a whole, since the opportunity for the sample to include the full range of values that exist in the population is limited by the small sample size. As the size of the sample increases, it becomes more likely that the distribution of any given characteristic will correspond to that of the population. The degree to which the distribution of a given characteristic in a sample of a given size cor- responds to the distribution of the characteristic in the population as a whole depends on how variable the characteristic is in the population. In statistical terminology, this variability is termed the variance of the characteristic. In the extreme case in which every member of the population has the same value for a given characteristic, a sample of only one respondent would provide a completely accurate estimate of that value. At the other extreme, if every member of the popu- lation has a different value for a given characteristic, a sample of the entire population (a 100% sample) would be required in order to include every possible value of the characteristic occur- ring in the population. If a sample of a given size is drawn randomly from a population multiple times, a slightly different distribution would be expected of any given characteristic in each sample, except in the special case where every member of the population had the same value of the characteristic. The greater the variance of the characteristic in the population, the more variation there would be in the distribution of the characteristic across the different samples. Therefore, the average 28 Guidebook for Conducting Airport User Surveys

Statistical Concepts 29 2 The theory underlying this statement can be found in any statistics textbook. 3 Under the Central Limit Theorem, the probability distribution of the sample average will approach the Normal distribution as the sample size approaches infinity. Error (standard deviations) Pr ob ab ili ty D en si ty 95 % -3 -2 -1 0 1 2 3 Note: Probability of error being between two values is given by the area under the probability density curve between those values. Figure 3-1. Example of the probability distribution of the expected error. value of a given characteristic in a sample of a given size, although it is a specific value for any particular sample, will vary across the different samples. This results in the following funda- mental point: The average value of any given characteristic in a sample drawn randomly from a given population has an expected variance that depends on the variance of the characteristic in the population, as well as the size of the sample relative to the size of the population. Because of this variance, there will be an expected error between the average value of a partic- ular characteristic given by a single sample and the true average (or mean) value of the charac- teristic in the population. Because the value of the population mean is not known (the survey is being performed to estimate this), the actual error is not known. However, the expected distri- bution of the error can be determined from statistical principles and an estimate made of the likely range of the error.2 The standard deviation of the estimated average value of any particular characteristic deter- mined from a sample is termed the standard error of the estimate (SEE) and is a measure of the accuracy of an estimate. For large enough samples, the error will approximate a Normal distribution with an expected (mean) error of zero, as illustrated in Figure 3-1.3 This exhibit shows the probability of a sample giving an error of any particular size, measured in terms of the number of standard deviations from the mean value, with the area under the curve between any two values representing the probability of the actual value lying in that range of values. As the range gets larger, measured in terms of the number of standard deviations from the mean, so the probability of the actual value lying in the range approaches 100%. The greater that the variance of the sample estimate of the mean is (i.e., the larger the standard deviation of the sample estimate), the fewer standard devi- ations from the mean an error of any particular value will be. Figure 3-1 also illustrates an important related aspect of sample error. As the standard devia- tion of the sample estimate of the mean increases, so the range of values covered by any given number of standard deviations also increases. Because an error of any particular absolute value

(in the units of the variable) will be fewer standard devia- tions from the mean, this reduces the probability of getting an error no greater than that value, and hence increases the corresponding probability of getting an error greater than that particular value. Thus as the variance (and hence the standard deviation) of the sample estimate increases, so the probability of getting an error greater than any particular value also increases. This leads to the second fundamental aspect of sampling accuracy: Although the actual error of a sample estimate of the mean value of any characteristic of the population is unknown, the probability of this error being less than any given value can be estimated. This second aspect has the important implication that any estimate of the expected error has two attributes: the magni- tude of the error being considered and the probability that the actual error is less than this value (referred to as the con- fidence level). Because the error distribution is symmetrical, as shown in Figure 3-1, it is common to express the expected error range, sometimes termed the margin of error, as plus or minus a specified amount (for a continuous variable) or number of percentage points4 (for a categorical variable, where the value is one of a defined list of values). For exam- ple, the results of an opinion poll might be reported as being accurate to within plus or minus 3% with 95% confidence. In this case, the probability of the estimate being within a margin of error of plus or minus 3 percentage points is 0.95, or 95%, and the results could also be described as having a 95% confidence interval of plus or minus 3%, where the term confidence interval refers to the margin of error for a spec- ified confidence level. As shown in Figure 3-1, as the confidence level increases (i.e., there is a greater probability that the actual error lies within the interval being considered), the size of the associ- ated error range also increases. For a given confidence level, the size of the corresponding error range depends only on the variance (and hence the standard deviation) of the expected error. As illustrated by Figure 3-1, a given confidence interval spans a fixed number of standard deviations either side of the mean. For a 95% confidence interval, this range is plus or minus about 2 (strictly 1.96) standard deviations. For a 90% confidence interval, this range is plus or minus about 1.65 (strictly 1.645) standard deviations. Thus if the variance of the estimated mean of some characteristic in a given sample is 0.0004 (i.e., the standard deviation is 0.02 or 2%), for a confidence interval of 95%, the margin of error would be plus or minus 4% (2 times the standard deviation). For a confidence interval of only 90%, the margin of error would be plus or minus 3.3% (1.65 times the standard deviation). 30 Guidebook for Conducting Airport User Surveys 4 The term “percentage points” is used to refer to the absolute change in a variable that is expressed as a percentage. For example, a range of 50% ± 5 percentage points is equivalent to the range 45% to 55%. Expressing the Accuracy of Variables Expressed as a Percentage For categorical variables, results are often expressed as a percentage of the sample, for example, the percentage of air passengers who use transit to access the airport. In such cases, expressing the accuracy of the estimate of the proportion of the sample in a given subgroup as a percentage can have two different meanings: • A percentage of the sample size (e.g., ±5% of the sample), or • A percentage of the subgroup mean (e.g., ±5% of the proportion in the subgroup). The first meaning is often referred to as “percentage points” to distinguish it from the latter. The two are very different. For example, if it is esti- mated that 10% of passengers take transit, then an accuracy of ±5 percentage points at the 95% confi- dence level corresponds to the interval from 5% to 15%. This range corresponds to plus or minus 50% of the proportion of transit passengers in the survey (i.e., 5/10 = 50%). However, an accuracy of ±5% of the estimated proportion of passengers taking tran- sit corresponds to the interval from 9.5% to 10.5%, equivalent to an accuracy of ±0.5 percentage points. To avoid confusion, care must be taken when expressing the accuracy of variables expressed as a percentage. When interpreting such values, care must be taken to be clear whether the accuracy is a percentage of the entire sample or of the subgroup in question. It may be helpful to make a distinction between percentage and percentage points in dis- cussing accuracy. Failure to be clear in this distinc- tion when reporting survey results can result in a situation where the reader cannot determine which way to interpret the stated accuracy.

In practice, in addition to the sample size and variation in the attributes being estimated, the accuracy of the estimated population attributes also depends on the sampling method, the level of non-response, and the characteristics of the non-respondents. Unfortunately, the character- istics of the non-respondents are generally unknown and must be estimated in some way. In the absence of any information about the characteristics of the non-respondents (the usual case), they are generally assumed to be the same as the characteristics of the respondents. The appropriate level of confidence to be used in expressing the margin of error in the results of a sample depends on the costs associated with making an error. The higher the costs of an error, the greater the confidence that is required that the true value is within the confidence interval. The width of the confidence interval can be reduced by increasing the sample size or, possibly, improving the sample design. Generally 95% confidence intervals are used for most purposes, but 99% confidence intervals may be used for some critical variables, while in other cases 90% confidence intervals may be adequate. Accuracy is discussed further in Section 3.4. Information on the calculation of the SEE using the different sampling methods is provided in Appendix B. 3.3 Sampling Methods For a sample survey, the sample of respondents should be selected from the population in such a way that the probability of any individual respondent being selected can be estimated. This method allows generalizations to be made about the entire population from the character- istics of the sample and estimates to be made of the likely accuracy of the estimated characteris- tics of the population based on the size of the sample. The most straightforward approach to obtaining a representative sample from a population is to select the members of the sample ran- domly from among the members of the population. However, in practice this is often difficult to achieve, particularly in an airport environment. Furthermore, it has the disadvantage that the sample will include relatively few members of particular subgroups of the population that com- pose only a small proportion of the total population. To address these concerns, other common sampling methods may be used. These methods are summarized in Table 3-1 and discussed in more detail in the following subsections. The choice of the appropriate sampling method is partly a question of how best to achieve the desired accuracy of the survey results and partly a consequence of the practicalities of perform- ing the survey. For example, it is common to perform air passenger surveys in departure lounges, because passengers are more willing to be interviewed or fill out a survey form when they are no longer anxious about whether they will make their flight and they are sitting down. However, this locale constrains the sample to those passengers on a set of flights, and does not provide a truly random sample of all passengers using the airport. On the other hand, a mail-back survey sent to the home address of airport employees can sample employees randomly from a list of all employees at the airport. The sampling method selected will depend on the type of survey, data collection method, and characteristics of the population. Random and sequential sampling are the simplest methods to implement but require large sample sizes to obtain an adequate number of responses from small subgroups of the population, while stratified and cluster sampling can be used, with a limited budget, to improve the accuracy of survey results for different subgroups. Often multi-stage sam- pling is appropriate. For example, cluster sampling may be used with flights selected using strat- ified sampling, and passengers on those flights are selected using sequential sampling. A controlled sample attempts to design the sampling approach so that the composition of the sample corresponds to the underlying distribution of the population characteristics. This Statistical Concepts 31

objective is generally satisfied with a truly random sample, provided the sample size is large enough. In practice achieving a truly random sample with airport user surveys is often difficult, as discussed in Section 3.3.1. In the case of other sampling methods, it is necessary to adjust the sampling rate or define the strata or clusters so that, where the characteristics of the population vary across different subgroups or time periods, those subgroups or time periods are represented in the sample in proportion to their occurrence in the population. A controlled sample is thus an attribute of a particular sample design rather than a differ- ent type of sampling method. If the sample is not controlled so that its composition reflects the underlying distribution of the population characteristics, then the survey results need to be weighted to properly reflect the characteristics of the population. A cluster sample in which sampled flights are chosen to reflect the proportions of flights in markets that are believed to have different passenger characteristics (e.g., international, domestic short-haul, domestic long-haul, etc.) and passengers are sampled for each flight in proportion to the passengers on the flight would represent a controlled sample. Thus a self-completed air passenger survey in which flights are selected in proportion to the number of flights in broadly defined markets and survey forms are given to every adult passenger on those sampled flights would qualify as a con- trolled sample. Because variation in the characteristics of the population over time or across different sub- groups will not in general be known until the survey results are obtained, designing a controlled sample means making assumptions about subsets of the population with different characteris- tics and ensuring that each subset is sampled in proportion to its occurrence in the population. If it turns out that two subsets of the population that were expected to have different character- istics in fact have similar characteristics, the results for the two subsets can be combined. How- ever, if two subsets that in fact have different characteristics are assumed to be similar and are not sampled in proportion to their occurrence in the population, the results will be biased. Weighting of the subgroups will be required to remove this bias. 32 Guidebook for Conducting Airport User Surveys Type Method Comment Random Respondents are selected randomly from the target population. Often difficult to do in airport environment. Need to use some randomizing technique (e.g., use of random number tables). Selection by interviewers can lead to biases if not well trained. Sequential (Systematic) Every nth individual is selected when potential respondents are arranged in some order. First respondent should be selected randomly from among the first n individuals. Good practical technique for airport surveys. Sample characteristics will be equivalent to a random sample if the order of potential respondents is not related to the variables of interest. Stratified Respondents are grouped into homogeneous groups (e.g., different categories of employee). Sampling occurs within each group separately. Used to obtain a more representative sample of different groups, particularly if the groups vary in size, or to obtain a specific accuracy in estimates for each group. Cluster Respondents are sampled from naturally occurring groups (e.g., flights). A sample of flights are selected, then all or a sample of passengers on those flights are selected. Suitable for large surveys where a wide range of flights can be sampled. Can use stratified sampling of flights to obtain a more representative sample. Non- probability Respondents are selected on the basis of some criterion that does not allow the probability of sampling any given member of the population to be determined. May be useful for gathering information on the range of possible responses, where the frequency with which those responses occur in a defined population is not required. Table 3-1. Summary of sampling methods.

Analysis of the results of previous surveys at the airport in question or of surveys conducted at other airports with similar traffic patterns can help identify subsets of the population that are likely to have different characteristics. The design of the controlled sample then attempts to ensure that those subsets are sampled in proportion to their occurrence in the population. 3.3.1 Random Sampling With random sampling, each individual must have an equal (or at least known) chance of being selected. An example of random sampling would be a tenant survey where a list of all airport ten- ants is assembled and a table of random numbers is used to select individual tenants from the list. The sampling approach will generally ensure that no individual can be in the sample more than once. For air passenger surveys, the sample size is typically so small relative to the population and the methodology is such that there is very little likelihood of surveying the same person twice.5 For most other airport user surveys, the methodology precludes sampling the same respondent twice. Obtaining a truly random sample is often difficult, particularly for airport surveys. For exam- ple, identifying each member of the population to include in the sampling process, then applying a method for randomly selecting them can be difficult, if not impossible, in an airport departure lounge. There are also problems associated with having surveyors select passengers to survey; this introduces a human element and invariably leads to biases. To avoid this, random numbers or sequential sampling, discussed in the following subsection, should be used for selecting individ- uals to survey. Interviews at groundside locations such as curb areas and parking lots, where the next available passenger is surveyed once an interview has been completed, are equivalent to random sample sur- veys as long as the ratio of interviews to passengers is fairly constant. However, such an approach will clearly change the sampling rate as the passenger flow changes. During periods of very low flow, every passenger might be interviewed, while during periods of high flow only a small proportion of passengers would be interviewed, and this should be taken into account in analyzing the results. 3.3.2 Sequential Sampling Sequential sampling is generally a good form of sampling for use in airport surveys. With sequential sampling, also referred to as systematic sampling, the population is arranged in some logical order and every nth individual is selected, starting with a randomly selected individual from the first n individuals. An example of sequential sampling is to survey every fourth passen- ger in a check-in queue. Sequential sampling is usually easier to apply than random sampling and will yield a random sample if the order of individuals in the list is essentially random with respect to the characteristics being measured in the survey.6 For example, there is no reason to think that the order in which people sit in a departure lounge has any systematic relationship to the characteristics being measured (such as their trip purpose or how they got to the airport), and therefore selecting every nth person is in effect a random sample. Of course, depending on the layout of the lounge, early arriving passengers or those with difficulty walking may sit closer to the boarding point, while later arriving passengers may have to use seats further away. How- ever, as long as all passengers in the lounge are included in the sampling strategy, where they sit will not affect their chance of being sampled. Statistical Concepts 33 5 If an individual gets surveyed twice on two different trips, that is not the same thing as surveying the same traveler twice on the same trip. The former should be valid as the sample being drawn is really of passenger trips, not of passengers, and a single passenger may make more than one trip during the survey period. 6 Serious biases can occur if a characteristic of interest occurs in a cyclic order in the population list and the length of each cycle corresponds to the sampling fraction, but this phenomenon would be rare in airport surveys.

Where the population list is ordered by a relevant characteristic, the use of sequential sam- pling will often result in a sample with a more representative range of characteristics than using random sampling. For example, in selecting flights to survey, if all flights during the survey period are listed in order of flight stage length, the resulting sample would likely better reflect passenger characteristics such as destination city or region than a random sample, as sequential sampling ensures a more even spread of flights by stage length and thus over destinations and regions. With random sampling, some subgroups of the population (flights with a particular stage length in the above example) may be missed completely and others may be over-sampled. One common application of sequential sampling in air passenger surveys is to list flights by departure time (and destination to resolve flights with the same departure time) and select every nth flight to survey. A variation on this approach is to list the number of seats on each flight and calculate the cumulative total number of seats for each flight (the total number of seats on previous flights on the list plus the number on the current flight). Flights are then selected by identifying the flight that corresponds to every mth seat on the cumulative list. This ensures that the probability of a given flight being sampled is proportional to the size of the aircraft, which approximates a random sample of air passengers if the same number of passengers is interviewed for each flight.7 3.3.3 Stratified Sampling In stratified sampling, the population is divided into mutually exclusive groups (strata) and individuals within each group are randomly sampled. Groups should be selected so that they are homogeneous with respect to the variables being studied (there is low variation within the groups), but so that the variation in the relevant variables is large between groups. For example, in a survey to determine passenger spending at airport concessions, passengers taking short-haul domestic flights are likely to spend much less than passengers taking long-haul international flights. The variation in spending among short-haul domestic passengers and among long-haul international passengers is likely to be less than the variation in spending between the two groups. If the criterion for stratification is highly correlated to the variable being studied, such as in this example, the gain in accuracy can be significant. Examples of stratified sampling include dividing flights into groups—such as international and domestic short and long haul, or by region—and dividing passengers to be sampled into groups based on day of the week, time period during the day, and airport terminal used. The variable used for stratifying the population must be known for all individuals in the pop- ulation. Once the survey population has been stratified into groups, simple random or sequen- tial sampling is used to select individuals from each group. With proportional stratified sampling, the proportions of individuals surveyed in each group are equal. This form of sampling is often used to assure a more representative sample than sim- ple random or sequential sampling. In non-proportional stratified sampling, different sampling fractions are used to improve the accuracy of estimates for a given overall sample size. Situations where non-proportional sam- pling is desirable include the following: • Where the variation in the variables being studied differs greatly between groups. The non- homogeneous groups (with a high variation in the variables of interest) should have a larger sample than the homogeneous groups. For example, consider a survey conducted to determine the average number of check-in bags per passenger where a stratified sample is to be drawn with flights grouped into long- and short-haul domestic and international flights. If it is known that 34 Guidebook for Conducting Airport User Surveys 7 This method assumes that the load factor (the ratio of passengers to seats) does not vary significantly across flights. Where this is not the case, and some classes of flight have a higher average load factor than others, an adjustment to the number of passen- gers interviewed on each flight may be required to approximate a random sample.

the variation in the number of check-in bags is greater for passengers on long-haul international flights than short-haul domestic flights, the sampling fraction would be higher for the long-haul international flights. • Where comparisons of distinct subgroups of the population are required, for example com- parisons between domestic and international passengers. • Where the cost of collecting the data differs greatly between groups. Here, overall accuracy for a given cost can be improved by having a lower sampling fraction for the groups with high data collection costs. However, while this may lead to a higher overall accuracy for the pooled data, when the characteristics of subgroups need to be considered, as is almost always the case in airport surveys, it can lead to very different accuracy for the various subgroups. Thus the approach of reducing the sampling fraction for groups with higher data collection costs is not generally recommended for airport surveys. Expanding the sample results of non-proportional stratified sampling to determine estimates for the population is not as straightforward as with proportional stratified sampling, and is dis- cussed in Appendix B. If non-proportional stratified sampling is appropriate, it is suggested that the planning team either become knowledgeable on the subject (refer to the Bibliography for appropriate guidance) or consider using external expertise. 3.3.4 Cluster Sampling With cluster sampling, the population is distributed in a large number of naturally occurring groups, for example passengers on flights. The groups, or clusters, are sampled, thus not all clus- ters are included in the sample. This is the primary difference from stratified sampling where individuals are sampled from every group. In the simplest form, all individuals within a cluster are sampled. When clusters are homogeneous, it is more efficient to sample only a fraction of the individuals within a cluster, and to sample more clusters. Cluster sampling is used to make sam- pling easier and less costly by limiting the survey to well-defined groups, such as passengers on specific flights, and works well when the characteristics of interest have low variability between clusters and high variability within clusters. For example, although the household income of pas- sengers on a given flight will span a wide range, the average household income of passengers on different flights will show much less variability. The accuracy of estimates made using cluster sampling will almost always be lower than if a ran- dom sample is used with the same sample size, because the selected clusters may not be fully rep- resentative of the target population as a whole, and can be significantly lower if variability between clusters is high and/or a small number of clusters are selected. It is important that the consequences of the design of the cluster sample (often referred to as the design effect) are incorporated into the analysis when evaluating the accuracy of estimates and required sample sizes. Details of how to calculate sample sizes and confidence intervals for cluster samples are included in Appendix B. A common example of cluster sampling in airport surveys is the use of individual flights as clusters, with the flights to be surveyed being selected using random, sequential or stratified sampling. Then either all passengers on each selected flight or a sample of passengers on those flights are surveyed. 3.3.5 Non-Probability Sampling Non-probability (or uncontrolled) sampling is where the probability of an individual’s selec- tion cannot be determined. Examples of non-probability sampling include the following: • Surveys of passengers who ask for help at an airport information booth, where no record is kept of the number of passengers seeking help at the booth. • Voluntary Web-based surveys where all visitors to the site are invited to complete a survey. Statistical Concepts 35

With non-probability sampling, it is not possible to calculate the sample size required to achieve a given level of accuracy or to make generalizations about the population. These types of surveys are usually of limited value in ascertaining properties of the population but can be use- ful for obtaining ideas and user feedback. 3.4 Sample Size A critical issue in planning any survey is determining the appropriate sample size, which is influenced by such considerations as the following: • Survey purpose. • Analysis of subgroups of interest. • Required precision of the survey results. • Credibility of results among decision makers and data users. • Available resources (including budget, personnel, and equipment). The survey purpose influences the required sample size in three ways: (1) by determining the key characteristics of the air travel party and the precision to which they need to be known, (2) by establishing the level of disaggregation to which the results need to be expressed, and (3) by identifying the value to be gained from improved precision. For any desired degree of pre- cision in the survey results, the need to consider subgroups of interest—such as air passengers with ground origins in a particular area or visitors on business trips—will increase the required sample size of the overall survey in order to ensure a large enough number of respondents in the subgroup(s) of interest. The required precision and the credibility of results influence the size of confidence interval and the acceptable margin of error. Larger samples are required to reduce the margin of error and/or increase the confidence level for a given margin of error. Although the target sample size for a survey should ideally be determined by the purpose and objectives of the survey and the uses to which the results will be put, in reality the financial resources available to fund the survey often constrain the sample size, particularly where bud- gets have been established before the detailed planning of the survey has begun. Time constraints can also influence the sample size if information is required on short notice. Other factors affecting the required sample size include the following: • The proportion of the population with the attributes being measured. An airport seeking pas- sengers’ opinions of the retail concessions, for example, must design a survey that takes into account the fact that only a small proportion of passengers will have actually visited the retail concessions. The passengers visiting the retail concessions are a subgroup of all passengers, and so the required sample size is found in a similar way to that described previously for a subgroup. • The variability of attributes being measured. If the variability is high, a larger sample size will be required. • The sample design used. For example, a good stratified sample can permit a smaller sample size than a random sample for a given level of accuracy, while cluster sampling will usually necessitate a larger sample size (as discussed in Sections 3.3.3 and 3.3.4). In the following discussion, sample size refers to the number of completed responses; the number of people approached to participate in the survey may be significantly higher depend- ing on the rates of refusal and incomplete responses. These refusals and incomplete responses will generally take some time to survey and process, which could be significant in some surveys 36 Guidebook for Conducting Airport User Surveys

(e.g., where follow-up phone calls are made) and should be allowed for in determining resource requirements. To estimate the total number of individuals to approach, divide the desired sam- ple size of completed surveys by an estimate of the completed survey response rate, expressed as a proportion. For example, if a sample size of 1,000 is required and the response rate is 70%, then 1,429 [= 1,000/0.7] individuals would need to be approached. 3.4.1 Sample Size with Random Sampling Calculation of the sample size required to obtain a specified accuracy differs depending on whether the required accuracy is for a question with categorical or numerical responses (ques- tion types are discussed in Section 4.3.2).8 With a categorical response, the respondent must choose from a limited number of defined responses. For example, for a question on mode of travel to the airport, categories could be private vehicle, rented vehicle, taxi/limousine, train, bus, airplane, or walk/bicycle. Determination of the sample size for each type of question using ran- dom sampling is considered in the following paragraphs. Categorical Response Questions When using categorical response questions and random sampling, the sample size required to give a specified level of accuracy is a function of the population size and the proportion of the population in the category of interest (e.g., proportion using a private vehicle as their mode of travel to the airport). This proportion is unknown and should be estimated in the survey planning stage from experience, previous surveys, or values from other airports. The largest sample size required occurs when half of the population has the characteristic of interest. Table 3-2 provides approximate 95% confidence intervals for a range of population and sam- ple sizes and two values of the proportion of the population in the category of interest (50% and 20%).9 The largest sample size is required for a proportion of 50%. Thus, for surveys with many questions with a range of mean proportions, it is appropriate to use the sample size based on the 50% proportion as this will provide at least the required accuracy for all cases. Table 3-3 gives the required sample size using random sampling, based on the 50% proportion, for var- ious confidence intervals and a range of population sizes. Alternatively, the sample size for an accuracy of ±a percentage points10 can be calculated for a 95% confidence level using the following expression:11 where n is the sample size, N is the population size, a is the width of the confidence, and p is the estimated proportion of the population in the category of interest. n p p a p p N = −( ) ( ) + −( ) 1 96 1 100 1 96 1 2 2 2 . . Statistical Concepts 37 8 With a categorical response, the variance can be expressed in terms of the proportion of the population in the category of interest. Thus an initial estimate of this proportion, rather than the variance, is required. 9 For proportions (p) greater than 0.5, the required sample size is the same as for the proportion 1 – p. For example, for a pro- portion p = 0.75, the required sample size is the same as for p = 0.25. 10 If accuracy is expressed as a percentage of the mean, say b%, then the percentage points, a = b • mean. For example, a con- fidence interval width of ±25% of the mean with a mean of 40% corresponds to a confidence interval width of a = 25 • 0.4 = 10 percentage points. 11 For other confidence levels, replace 1.96 with the appropriate value from the standard Normal distribution for the confi- dence level required.

38 Guidebook for Conducting Airport User Surveys Table 3-2. Approximate 95% confidence intervals for a categorical variable for a range of population and sample sizes. 95% Confidence Interval for Proportion of Population in CategoryPopulation Size Sample Size Proportion of Population in Category Range Mean ±a Percentage Points, where a = Lower Limit Upper Limit 100 80 50% 4.9 pts 45% 55% 20% 3.9 pts 16% 24% 60 50% 8.0 pts 42% 58% 20% 6.4 pts 14% 26% 40 50% 12.0 pts 38% 62% 20% 9.6 pts 10% 30% 50,000 1,000 50% 3.1 pts 47% 53% or higher 20% 2.5 pts 18% 22% 400 50% 4.9 pts 45% 55% 20% 3.9 pts 16% 24% 100 50% 9.8 pts 40% 60% 20% 7.8 pts 12% 28% Note: SEE estimated using binomial distribution and sampling without replacement, Normal approximation used to determine confidence intervals. For further information, refer to statistical textbooks listed at the end of this guidebook. Table 3-3. Required sample size using random sampling for various sized confidence intervals and a range of population sizes.* Sample Size for 95% Confidence Interval: Sample Mean ±a Percentage Points, where a =Population Size 1 pt 2 pts 3 pts 4 pts 5 pts 6 pts 7 pts 8 pts 9 pts 10 pts 100 99 96 91 86 79 73 66 60 54 49 200 196 185 168 150 132 114 99 86 74 65 500 475 414 340 273 217 174 141 115 96 81 1,000 906 706 516 375 278 211 164 130 106 88 2,000 1,655 1,091 696 462 322 235 179 140 112 92 5,000 3,288 1,622 879 536 357 253 189 146 116 94 10,000 4,899 1,936 964 566 370 260 192 148 117 95 20,000 6,488 2,144 1,013 583 377 263 194 149 118 96 50,000 8,057 2,291 1,045 593 381 265 195 150 118 96 100,000 8,762 2,345 1,056 597 383 266 196 150 118 96 200,000 9,164 2,373 1,061 598 383 266 196 150 118 96 500,000 9,423 2,390 1,065 600 384 267 196 150 119 96 * Sample sizes where proportion of population in the category of interest is 50%. For large populations of over 50,000, the required sample size for a 95% confidence level is given approximately by: Thus if the proportion of some characteristic of the population is 5% (p = 0.05), say, and the desired accuracy of the estimate of this proportion is ±1 percentage point at a 95% confidence level, the required sample size to achieve this accuracy is 1,900. It should be noted that an error of 1 percentage point on an estimated proportion of only 5% is an error of ±20% of the esti- mated proportion. If it is desired to reduce this error to only 5% of the estimated proportion (±0.25 percentage points), the required sample size would increase to about 30,000. n p p a = −( )40 000 1 2 ,

If a subgroup composes S percent of the population and the estimate of the proportion of some characteristic of the subgroup is required to the same accuracy as the estimate of the pro- portion for the population as a whole, the sample will need to be larger by a factor of 100/S. Thus, to achieve the same accuracy for a subgroup that composes 20% of the population, the sample would need to be five times larger (100/20 = 5). If this level of accuracy is required for multiple subgroups, the required total sample size is given by the largest of the estimated total sample sizes calculated using the factor for each subgroup (100/Si where Si is the percentage of the popula- tion in subgroup i). For very small populations such as with airport tenant surveys, a high pro- portion of the population must be sampled to obtain estimates within 0.05 (i.e., 5 percentage points) of the proportion for the total population, but actual numbers of surveys required are small. For example, a sample size of 79 is required from a population of 100 to achieve an accu- racy of 5 percentage points. For large populations, a sample size approaching 400 is required to achieve a similar level of accuracy using random sampling. Numerical Response Questions For questions with a numerical response, such as the number of travelers in a group, expen- ditures at the concessions, or time spent at the airport, the sample size required for a specified level of accuracy is dependent on the variability (as measured by the standard deviation) in the numerical response. With random sampling, the population mean and standard deviation are estimated by the average and standard deviation (weighted if appropriate) of the responses in the sample. The required sample size for an accuracy of ±w can be calculated for a 95% confi- dence level using the following expression:12 where s is the standard deviation of the responses in the sample. The SEE can be found approximately by dividing the standard deviation of the sample values by the square root of the sample size of completed responses.13 The standard deviation of the vari- able of interest is unknown during the survey planning stage and an initial estimate is required to calculate the required sample size. This initial estimate could be obtained from previous surveys at the airport or from other airports, or estimated from knowledge of the typical range in values. Examples of the mean, standard deviation, SEE and accuracy of estimate (95% confidence interval), and required sample sizes for accuracy to within 10% of the mean for selected air pas- senger characteristics from some airport surveys are given in Table 3-4. As can be seen by these examples, the accuracy and required sample sizes vary greatly depend- ing on the variable of interest. Expenditures at the airport vary greatly as many people do not spend any money and some spend a lot. Thus large sample sizes are required to produce esti- mates to within 10% of their expected value. In contrast, variability in the time passengers spend at the airport is much less, and small samples would give a similar accuracy (in percentage terms). 3.4.2 Sample Sizes with Stratified and Cluster Sampling The methods for determining the sample sizes with stratified and cluster sampling are more complex and are outlined in the following paragraphs with details provided in Appendix B. n s w= 1 962 2 2. Statistical Concepts 39 12 For other confidence levels, replace 1.96 with the appropriate z-value from the standard Normal distribution for the confi- dence level required. For small population sizes, use the expression: n = 1.962 s2/[w2 + 1.962 s2/N] where N is the population size. 13 A more accurate estimate is given by dividing by the square root of the sample size less one. This can become important for small samples.

Stratified Sampling The objective of stratified sampling is to reduce the size of the required sample to achieve a desired level of accuracy in situations where it is possible to define population strata within which the variance of the population characteristic of interest differs between the strata. For example, if the characteristic of interest is the duration of air passenger air trips (because trip duration affects the likely use of parking at the airport), the duration values are likely to differ consider- ably between international trips, long-haul domestic trips, and short-haul domestic trips. Because the variance of the air trip duration within each of these three strata will be much smaller than the variance for the population as a whole, it may be possible to estimate the average trip duration for all air passengers to the desired level of accuracy with fewer total responses divided between the three strata than by randomly sampling the entire population. To achieve a similar level of accuracy in the results for each stratum, it will be necessary to use non-proportional stratified sampling, with the sample size in each stratum inversely proportional to the variance of the characteristic within that stratum. Because the actual variance in the char- acteristic for each stratum will not be known until the survey has been performed, it will be nec- essary to make an initial assumption of the differences in the variance across the strata in order to determine the proportion of the survey responses to assign to each stratum. These assumptions can be based on the results of prior surveys or of surveys performed at similar airports. If σXi is the standard deviation of characteristic X in stratum i, then for a confidence interval for the sample mean of X across the population of 2w (i.e., ±w) at a 95% confidence level, w is given by: where Wi is the proportion of the total population in stratum i Ni is the population in stratum i ni is the sample size in stratum i A given confidence interval can be obtained for varying combinations of ni. However, if ni is selected to be inversely proportional to the variance of X within each stratum, i.e., ni = k /σXi 2 , then ni can be replaced by k /σXi 2 in the above equation, which can then be solved for k and hence w W n N ni Xi i i i i = −( )⎡⎣ ⎤⎦∑1 96 12 2. σ 40 Guidebook for Conducting Airport User Surveys Table 3-4. Examples of 95% confidence intervals and sample sizes for selected air passenger characteristics from some recent airport surveys. With Sample Size = 400 Variable Mean Standard Deviation 95% Confidence Interval* Sample Size for Confidence Interval ±10% of Mean Number in travel group 1.4 1.6 ±0.16 or ±11% 503 Expenditure at all concessions Airport 1 $6.20 $8.53 ±$0.84 or ±14% 728 Airport 2 $8.00 $19.00 ±$1.86 or ±23% 2,168 Time at airport (min) Large intern'l 160 60 ±6 min or ±4% 55 Domestic 106 43 ±4 min or ±4% 64 * Confidence interval expressed as difference from sample mean, also given as a percentage of the sample mean. Note: Sample mean will be approximately normally distributed for large sample sizes according to the Central Limit Theorem, even for variables such as expenditure at concessions that are not normally distributed. Source: Airport surveys conducted by Jacobs Consultancy in the United States and Canada.

ni calculated for each stratum. The expression for calculating the value of k and the sample sizes for each stratum is provided in Appendix B. The total sample size is obtained by summing ni across all the strata. Cluster Sampling Calculating an appropriate sample size with cluster sampling in considerably more compli- cated than with random or stratified sampling, because the composition and size of the clusters affect the variance of the resulting estimates of the population characteristics. The accuracy of a cluster sample depends on both the variance of the characteristic of inter- est within each cluster and the variance between clusters. If the variation in the sample mean between clusters is fairly small (i.e., the clusters are fairly homogeneous and have similar means) but the variance of the characteristic within each cluster is fairly large, then the cluster sample will give a similar accuracy to a random sample of the same overall sample size. One can think of this situation as a series of small random samples of the population as a whole. Conversely, if the variance between clusters is fairly high, then the overall variance of the population sample mean of the characteristic will be larger than for a random sample and in consequence a cluster sample will require a larger overall sample size to achieve the same level of accuracy. 3.4.3 Comparison of Sampling Methods An example of sample size calculations for different sampling methods is given in Appendix B. The example provides some insight into the efficiencies of each sampling method and is sum- marized in this section. In the example, a survey of passengers is to be undertaken to obtain infor- mation on airport access trips. A critical question to be answered may be: What is the percentage of departing passengers dropped off at the terminal curb? Random and stratified sampling of passengers—with stratification by flight sector (e.g., short-haul domestic, long-haul domestic, international) and day of the week—and one- and two-stage cluster sampling—with both ran- dom and stratified sampling of flights by sector—are examined. The flight schedule for the sur- vey period includes 610 flights per week, and the number of originating passengers per week is estimated at 48,300. Some 42% of passengers are on short-haul domestic flights, 34% on long- haul domestic flights, and 24% on international flights. From past experience, initial estimates of the percentages of passengers dropped off at the curb are 40% of short-haul domestic passen- gers, 60% of long-haul domestic passengers, and 90% of international passengers. In the exam- ple, the percentage of passengers to be dropped off at the curb is quite strongly related to the flight sector, but fairly weakly related to the day of the week. Table 3-5 summarizes the required sample sizes for an accuracy of ±2, 3, and 4 percentage points for a 95% confidence level using various sampling strategies. The following observations were made from this example: • Using random sampling, the required sample size approximately doubles as the accuracy improves from ±4 to ±3 and doubles again from ±3 to ±2 percentage points. • Stratified sampling by flights (which has a strong relationship with the variable of interest) reduces the sample size required by 15%, but stratified sampling by day of the week (which has a weak relationship with the variable of interest) has a negligible effect on the required sample size. • Cluster sampling with random sampling of flights and surveying of all passengers on those flights was found to be very inefficient, increasing the sample size required by a factor of 9 or more compared to random sampling. • Cluster sampling with stratified sampling of flights by sector greatly improves the efficiency of cluster sampling. – With all of the passengers on the selected flights surveyed, the sample size required is reduced to approximately 3 times that of random sampling. Statistical Concepts 41

– With a random sample of 50% of passengers on each flight surveyed, the sample size required is reduced by 30% to 2.1 times that required using random sampling. However, with only 50% of passengers surveyed on each flight, the number of flights surveyed increases. – Several other percentages of passengers to survey on each flight were examined, and both the 30% and 75% levels resulted in larger passenger sample sizes. The optimal balance between the number of flights and the proportion of passengers on those flights to survey depends on the variation in responses between and within flights, and on the relative costs of surveying passengers and flights, which vary from survey to survey. The results of this example reflect the assumptions regarding variation used in the example and will vary in other situations. Refer to Appendix B for more information on the example and the calculation of the sample sizes. In comparing the required sample sizes for different sampling methods, it should be borne in mind that true random sampling of air passengers is almost impossible to achieve, as discussed in Chapter 5. 3.4.4 Determining Desired Accuracy While the mathematics of calculating required sample size is generally fairly straightfor- ward, deciding on the appropriate desired level of accuracy is anything but, because it depends on the consequences of being wrong. Although it is common in statistical analysis to use a target accuracy of ±5% at a 95% confidence level, this is an entirely arbitrary choice and is typically not achievable or not accurate enough for many issues addressed by air pas- senger surveys. Consider the case where the characteristic of interest accounts for only a small proportion of respondents, say air passengers using transit to access the airport, which from past surveys is esti- mated to be approximately 5%. The proportion using transit is to be estimated for a subgroup that composes 20% of the population (e.g., air passengers from a particular part of the region). If the required accuracy for the estimated proportion of this subgroup is ±5% of the estimated proportion (i.e., ±0.25 percentage points) at a 95% confidence level, a random sample survey would require a sample size of 150,000 responses, a level of effort that is totally impractical. Even accepting an accuracy of ±20% of the estimated proportion (i.e., ±1 percentage point) at the same confidence level, the required sample size would still be 9,500—potentially achievable, but sig- nificantly larger than most air passenger surveys. 42 Guidebook for Conducting Airport User Surveys Table 3-5. Sample sizes in example survey for an accuracy of 2, 3 and 4 percentage points for a 95% confidence level using various sampling strategies. Mean ±a Percentage Points, a =Method UnitSampled 2 pts 3 pts 4 pts Comment Random Passengers 2,218 1,012 574 Random sampling of passengers (pax) Stratified Passengers 1,879 853 484 Stratified by sector of flight Passengers 2,215 1,011 574 Stratified by day of the week Cluster 1. Flights 252 146 92 Passengers 19,953 11,560 7,285 Random sampling of flights with all pax on each flight sampled 2. Flights 83 41 24 Passengers 6,560 3,280 1,910 Stratified sampling of flights by sector with all pax on each flight sampled 3. Flights 117 47 26 Passengers 4,615 1,860 1,040 Stratified sampling of flights by sector with 50% pax on each flight sampled

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 Statistical Concepts 43

weights will vary depending on the survey type. For example, for surveys of passengers exiting the security checkpoint, weights for surveys collected in a particular hour could be set equal to the total numbers of passengers going through security in that hour divided by the numbers of surveys collected in that hour. The numbers of passengers exiting the security in each hour of the survey could possibly be obtained from the security authority or counted manually. Rather than applying equal weights to all passengers, or to all passengers within a group, weights can be applied so that the sample is more representative of the population. For example, weights could be set so that the distribution of surveyed passengers by airline matched the actual distribution of passengers by airline during the survey period. If the actual numbers are not avail- able from the airlines, they could be estimated based on the seat capacity of departing flights and average load factors for each airline during that month. In some cases, different sets of weights may be required for analyzing different characteristics of the population. For example, in a survey of passengers, questions relating to their travel to the airport and air trip are relevant to the respondent’s companion or companions, as well as the respondent, but personal questions such as gender and age apply only to the respondent. By including questions on the number of travelers in the group and number of questionnaires com- pleted by others in the group, it is possible to define two sets of weights, one for the airport access and trip characteristics and the other for personal traveler characteristics. Although the air travel party and those traveling together to the airport are generally the same, this is not always the case, as discussed in Section 5.2. People who have been attending an event such as a business meeting or conference may travel together to the airport but then take differ- ent flights, while others may travel separately to the airport and meet there to travel together on the same flight. The latter situation is particularly common with large air travel parties such as school groups or sports teams. Therefore, it is desirable for passenger surveys to ask how many people are traveling together on the same flight as well as how many people traveled to the air- port together with the respondent. This specificity will allow separate weights to be calculated for the air travel party characteristics and the ground access travel characteristics. 3.6 Summary The goal of this chapter has been to provide the non-statistician with an understanding of the basic statistical principles behind sample design, the terminology involved, and the importance of considering how the sampling approach and the sample size interact to determine the statisti- cal accuracy of the resulting data. Although it is not unusual to present the results of airport user surveys without any real discussion of the likely accuracy of those results, it is not good practice. If the results are to be used for decision making, it is the responsibility of those managing the sur- vey process to decide how accurate the results need to be, design the survey accordingly, and ensure that decision makers using the survey results are aware of the likely accuracy of the results. One of the most fundamental questions in planning a survey is deciding how large a sample size is required, because this has a major influence on the cost of conducting the survey. As discussed in this chapter, the decision on sample size is in turn influenced by the sampling approach adopted, which also affects the cost of conducting the survey. An appreciation of the statistical basis for assessing the likely accuracy of the results of a particular survey approach and the sample size required to achieve a desired level of accuracy is therefore critical to effective survey planning. 44 Guidebook for Conducting Airport User Surveys

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TRB’s Airport Cooperative Research Program (ACRP) Report 26: Guidebook for Conducting Airport User Surveys explores the basic concepts of survey sampling and the steps involved in planning and implementing a survey. The guidebook also examines the different types of airport user surveys, and includes guidance on how to design a survey and analyze its results.

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