Airport Passenger-Related Processing Rates Guidebook (2009)

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84 A P P E N D I X B B.1 Data Analysis: Introduction Researchers analyze data for a number of reasons: • To describe, summarizing data in accordance with previously defined requirements. • To explore, searching for unanticipated findings, and a “story” the data might be revealing. • To examine relationships or potential correlations. • To compare groups. • To develop and use prediction models. • To test for hypothesized relations among the data. Regardless of the reasons for analysis, a fundamental goal of data analysis is to reduce relatively large numbers of data values into a more succinct form, facilitating interpretation and reporting. Consider Exhibit B-1. The first exhibit (B-1a) contains a number of observations in the order in which they were collected. The second (B-1b) presents the same data, sorted in ascending order. The third exhibit (B-1c) presents the same data, grouped by range. Finally, the bar chart (B-1d), shows the number of observations per group. While transforming the data from an unsorted state to a sorted state helps somewhat in discerning meaning from the data, summarizing it in tabular and graphical format substantially helps. While a set of only seven observations, how- ever, may not gain much from such reduction, examine Exhibit B-8. In this instance, approxi- mately 23,400 data values have been summarized. Summarizing the data using a frequency table (Exhibit B-2) permits one to see quite quickly that the region most represented is the North Central (35.9 percent), and that the regions with the lowest representation are New England and Pacific, at 2.1 and 2.2 percent, respectively. The same data are shown graphically in Exhibit B-3. Tables and graphics can effectively help translate raw data into usable information by virtue of condensing and summarizing data. As common to most tools, however, there is a potential risk: the use of tables and graphs also makes it easy for researchers to unintentionally bias results, and for those of ethically questionably character, to intentionally misrepresent. The remainder of this chapter presents select recommendations for how to be effective in communicating results, and how to become more critical in evaluating what is presented to you. B.2 Frequency Distributions Data that are collected using a nominal level of measurement can be represented in frequency tables using the same categories in which the data were collected. For example, Exhibit B-4 summarizes gender data coded as male or female. Analyzing and Reporting Data

Appendix B: Analyzing and Reporting Data 85 Unsorted Sorted 15 15 53 19 19 22 22 31 46 38 31 46 38 53 Queue Time 0 1 20.5 1.5 2.5 0 - 19 20 - 29 30 - 39 40 - 49 50 - 59 In te rv al s (se co nd s) n of observations B-1a B-1b B-1c B-1d Range Freq. Pct. Cum. Pct. 0-19 2 28.6 28.6 20-29 1 14.3 42.9 30-39 2 28.6 71.4 40-49 1 14.3 85.7 50-59 1 14.3 100 Exhibit B-1. Data ordering and presentation. Region 1513 6.5 6.5 4510 19.3 25.7 502 2.1 27.9 8399 35.9 63.8 519 2.2 66.0 4377 18.7 84.7 3578 15.3 100.0 23398 100.0 Middle Atlantic Mountain New England North Central Pacific South Atlantic South Central Total Frequency Valid Percent Cumulative Percent Exhibit B-2. Frequency and percent of observations by region. Exhibit B-5, however, presents a different situation. Here, data were collected at a scale level of measurement, i.e., a stopwatch was used, and a recording of the time, rounded to the nearest second, was made. Whereas in Exhibit B-4 any given datum could reasonably only assume one of two states—male or female—the approximately 14,500 data points reflected in Exhibit B-5 could be organized in any number of ways. As represented here, less than 4 percent of the times were recorded to be less than 50 sec. In contrast, nearly 62 percent of the recorded times took between 51 sec and a minute. Consider now the same data, categorized differently, shown in Exhibit B-6. With question- able ethics, a researcher presenting the data in this manner could legitimately assert some- thing to the effect of: “Approximately 66 percent of all wait times were one minute or less.” The moral is to maintain a healthy skepticism about the scheme the researcher chose for aggregating data. A common abuse occurs when data from rating scales are presented (e.g., satisfaction, quality). Responses labeled as “very satisfied” and “satisfied” are sometimes col- lapsed to obscure that relatively few respondents might have reported that they were indeed very satisfied.

86 Airport Passenger-Related Processing Rates Guidebook Gender 8821 60.6 60.6 60.6 5729 39.4 39.4 100.0 14550 100.0 100.0 Female Male Total Frequency Percent Valid Percent Cumulative Percent Exhibit B-4. Gender data. Frequency Percent Cumulative Percent 30 seconds or less 20 0.1% 0.1% 31 - 40 seconds 180 1.2% 1.4% 41 - 50 seconds 350 2.4% 3.8% 51 - 60 seconds 9000 61.9% 65.6% 61 - 75 seconds 1500 10.3% 75.9% > 75 seconds 3500 24.1% 100.0% Total 14550 100.0% Exhibit B-5. Restroom observations arranged by 10-second time groups. Frequency Percent Cumulative Percent 60 seconds or less 9550 65.6% 65.6% 61 - 75 seconds 1500 10.3% 75.9% > 75 seconds 3500 24.1% 100.0% Total 14550 100.0% Exhibit B-6. Restroom observations arranged by irregular time groups. South CentralSouth AtlanticPacificNorth CentralNew EnglandMountainMiddle Atlantic Pe rc en t 40 30 20 10 0 Region Exhibit B-3. Percent of observations by region.

B.3 Averages and Medians Exhibit B-7 presents fictitious data reflecting the annual salaries of 13 persons employed at a hypothetical company. Let’s assume that during the course of interviewing a prospective employee, an unscrupulous interviewer, when asked about the average salary of persons employed by the company, responds “On average our employees earn more than $120,000 annually.” Technically, this is an accurate response. Ethically however it has some problems. The reason the average salary is calculated to be in excess of $121,000 is that the average, or mean, is sensitive to extreme values, and the salaries of the CEO, the president, and the VP are extreme relative to the salaries of all other employees. If every employee earned $121,307.69, the average salary would be $121,307.69. If one reports only an average value the person to whom it is reported has no way of assessing how well that value reflects all the other values for which it stands. To be useful, at least two values need to be reported: the mean and standard deviation. As addressed in Chapter 5, the standard deviation is a measure of how much values, on average, are dispersed around the mean. The standard deviation of $128,199.59 shown in Exhibit B-7 suggests that, on average, salaries vary around the mean on average of plus or minus about $121,000. A more accurate reflection of salary in the company is the median, which is the value midway between the highest and the lowest values. Whenever a distribution is markedly skewed, that is, lacking symmetry by leaning to the right or the left, the median provides a better summary sta- tistic for how the data values cluster together. So, if you want to consider yourself wealthy, attend a meeting at which Bill Gates is present, and estimate the average salary of those attending the meeting. On average, the average salary of those in the group, including your own, will likely exceed $1 million. Voila: now you are a multimillionaire. B.4 Correlation Correlation was referred to in the sampling section of the Guidebook. It is a way of quantify- ing two aspects of the relationship between variables: the strength of their association, and the directionality of the relationship. While methods have been developed for looking at relation- ships between variables at different levels of measurement, the Guidebook will limit considera- tion to the most commonly known statistic, r, sometimes referred to as Pearson’s r, or Pearson’s Appendix B: Analyzing and Reporting Data 87 CEO 400,000.00$ President 350,000.00$ VP 300,000.00$ Worker 1 0,000.008$ Worker 2 0,000.008$ Worker 3 5,000.007$ Worker 4 0,000.007$ Worker 5 5,000.005$ Worker 6 0,000.005$ Worker 7 0,000.004$ Worker 8 0,000.003$ Worker 9 5,000.002$ Worker 10 22,000.00$ Average 121,307.69$ Standard Deviation 128,199.59$ Median 70,000.00$ Exhibit B-7. Annual employee salaries.

product moment correlation coefficient. It is named for the British statistician, Karl Pearson in the early years of the 20th century.1 Pearson’s r can assume any value between −1 and +1. A graphical representation of the relationship between two variables, MPG and weight in pounds, of automobiles manufac- tured in the 1970s is shown as Exhibit B-82. Not surprisingly, there is a negative relationship between a vehicle’s weight and the average gas mileage it achieves. The r value for these data is −0.83, a relatively strong, albeit negative cor- relation: as automobile weight increases, gas mileage decreases. B.4.1 Correlation and Causation A colleague relayed the following, likely apocryphal, story. She was teaching an introductory statistics course at a small university in Ohio. While addressing the topic of correlation one of her students reported on an interesting finding. He had discovered a surprising relationship between annual pig iron production in the birth rate of pigs raised in the state. This story is sim- ilar to that related by Duckworth (2004) concerning a statistically significant correlation between the number of births in a town and the number of stork nests. In the birth-rate story, one might infer some meaningful relationship in so far as the larger the town is, the higher the birth rate, and, in turn, the greater the number of chimney stacks. Such sites also are an apparently desir- able location for storks to build their nests. Simply, be wary about drawing causal linkages. As the popular asserts, “correlation does not imply causation.” B.5 Misleading Graphical Displays Exhibits B-9 and B-10 represent two line graphs. The data used to construct the graphs are the same. There is, however, one difference. Note that the scale in Exhibit B-9 ranges from 64 to 84, whereas the scale in Exhibit B-10 ranges from 0 to 100. 88 Airport Passenger-Related Processing Rates Guidebook 1 Clapham, C. & Nicholson, J. (2005). Concise dictionary of mathematics, 3rd edition. New York: Oxford University Press, 2 Adapted from SPSS V. 15. 1000 2000 3000 4000 Vehicle Weight (lbs.) 15 20 25 30 35 M ile s pe r G al lo n Exhibit B-8. Plot of miles per gallon and vehicle weight.

While we have eliminated identifying information, Exhibit B-9 is a facsimile of what was pro- vided to a client by a consultant who had been secured to measure the performance of the Company’s website. The scale employed by the consultant was 100 points, yet interestingly the consultant chose to plot the data using a somewhat compressed scale. Exhibit B-10 plots the same data using a 100 point scale. You’ll notice that the lines in Exhibit B-10 are essentially straight, indicating no change in average performance across time. Whether Exhibit B-9 was created in ignorance or with intent to misrepresent, is not clear. The lesson, however, is hopefully clear. A related issue is incorrectly inferring meaningful variation when indeed the variation is simply random or “noise.” Tracking changes in the Dow Jones industrial index on an hourly basis may be interesting, but the vantage is so close that it obscures the proverbial forest for the trees. For example, a decrease in passenger waiting times based on data collected over a brief Appendix B: Analyzing and Reporting Data 89 64 69 74 79 84 1st quarter 2nd quarter 3rd quarter 4th quarter Sc or e Recommend Return Exhibit B-9. Data graphed using inappropriate scale. 0 20 40 60 80 100 1st quarter 2nd quarter 3rd quarter 4th quarter Sc or e Recommend Return Exhibit B-10. Data graphed using appropriate scale.

and statistically inadequate sample might result in an unjustifiable conclusion that a process is genuinely improving. Exhibit B-11 comes from the January 9, 2009, Washington Post. The height of each stack of money is intended to represent the debt, in billions, associated with five geographic areas. The pie chart is intended to represent the proportion of debt for the five geographical regions as well as all other holders of debt. The same data are presented in Exhibit B-12. While decidedly less embellished than Exhibit B-11, the graphical representation is more straightforward, and, in turn, less suspect to misinterpretation. 90 Airport Passenger-Related Processing Rates Guidebook Source: The Washington Post Exhibit B-11. Example of complex chart. U.S. Treasury Securities - Foreign Holders $- $100.0 $200.0 $300.0 $400.0 $500.0 $600.0 $700.0 B ill io ns 0.00% 0.05% 0.10% 0.15% 0.20% 0.25% % o f A LL D eb t H el d Amount $652.9 $585.5 $360.2 $219.5 $187.7 Percent 0.21% 0.19% 0.12% 0.07% 0.06% China Japan Britain Caribbean Oil Exporters Exhibit B-12. Simplified presentation of data.

While there is admittedly disagreement among those who conduct research into the graphi- cal display of data,3 and, as such, no recommendation is without some controversy, the follow- ing are recommendations based on The Elements of Graphing Data.4 Based on a number of studies assessing people’s accuracy in discriminating proportions, Cleveland rank ordered per- ceptual factors in descending order of accuracy, as documented in Exhibit B-13. To illustrate, Exhibit B-14 is an example of data presented on a common scale. In this instance, the data are the same as for four of the geographic regions shown in Exhibit B-12. Note that the information can be captured by a single point aligned with the scale on the y axis. The same data are represented in Exhibit B-15. Here, however, the viewer is required to make a judgment about length. Exhibit B-16 depicts three pie-chart variations. To interpret a pie-chart, the viewer is tasked with judging variations in angle, a task prone to inaccuracy as suggested in Cleveland’s research. In the bottom left representation, only the labels are shown, not the percentages. The reader might consider how the accuracy of his or her estimate of the actual percentages for Britain and the Caribbean as shown in the top graphic. Appendix B: Analyzing and Reporting Data 91 3 Spense, I. (2005). No humble pie: The origins and usage of a statistical chart. Journal of Educational and Behavioral statistics, 40,4, 353–368. 4 Cleveland, W. S. (1985). The elements of graphing data. Pacific Grove, CA: Wadsworth. Accuracy Perceptual Feature Position along common scale Position along identical, non-aligned scales Length Slope Angle Area Volume Most Accurate Least Accurate Color hue; saturation; density Exhibit B-13. Relative accuracy of various graphic methods. $100 $600 $200 $300 $400 $500 Japan Britain Caribbean Oil Exporters Exhibit B-14. Data on a common scale.

92 Airport Passenger-Related Processing Rates Guidebook $585.5 $360.2 $219.5 $187.7 $100 $600 $200 $300 $400 $500 Japan Britain Caribbean Oil Exporters Exhibit B-15. Data on a fixed scale. Percent China Japan Britain Caribbean Oil Exporters Caribbean China Japan Britain Oil Exporters Percent China 33% Japan 29% Britain 18% Caribbean 11% Oil Exporters 9% Exhibit B-16. Pie chart examples.

Whereas the percentages do convey substantially more information than the pie-chart with- out values, one might reasonably ask what value the graphic itself adds to the information. The final pie-chart is presented as an egregiously poor graphic, providing the reader with a 3-dimensional rendering that interferes with information. B.6 Threats to Internal Validity Internal validity is a measure of the extent to which a given outcome can be ascribed to a par- ticular reason. Let’s assume that you are planning to evaluate the value of a leadership training program mar- keted by a vendor, the results of which will drive your decision whether or not to purchase the training for deployment to all of your employees. What factors, independent of the training itself, might impact the results? Let’s say that you decide to place your “best” employees into the pro- gram to really give it “a run for its money.” A problem arises, however, in that these employees may not be typical. As an alternative, you consider an open enrollment. Given a limited number of seats in the program, however, those who rush to enroll may also not be typical employees. In both situations something may be “getting in the way,” potentially moderating the outcome. When the stakes are high, for example when medications are prescribed to a patient, potential interactions are often emphasized. (Think about all those stickers adorning your prescription medicine the next time you go to your medicine cabinet.) What’s the bottom line? Be wary of people and organizations who tout universal solutions. They may not be telling you the whole story. While printed ads for weight loss products often contain a disclaimer, in very small print, noting that the loss of weight described in the accom- panying testimonials may not be typical results, we have not encountered any consultants or service companies that take a similar approach. Another lesson is to be very careful in analyzing data to not attribute some outcome to a particular cause. Appendix B: Analyzing and Reporting Data 93