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104 A Guidebook for Using American Community Survey Data for Transportation Planning 6.2 Benefits and Limitations of ACS for Trend Analysis This section summarizes the perceived benefits and limitations of using ACS data for trend analysis. In our discussions with transportation planners, the following potential benefits of ACS were identified: The availability of regularly updated ACS data may allow for more data points for trend analysis, especially to identify a steady trend or a sudden jump or drop in a trend variable like trip distribution by time. Another application identified by users is to use the more frequently reported data to validate and enhance demographic projections for use in travel demand models.53 Given the lower sample sizes in ACS and the need to examine corresponding confidence inter- vals, however, users need to be wary of the following new issues: ACS data come with a lot of variability and standard errors for each yearly estimate. Because several potential data releases are possible for a particular year, (e.g.: one-year estimate, three- and five-year average), planners must pay more attention and may need to examine several numbers instead of one.54 This issue is further illustrated in the case study included in this section. The time-series component of ACS may help improve the relationship between means and medians of key trend variables and the percentages of households falling into different categories. The following ACS issues were identified as potential problems for trend analysis: ACS estimates will need to be based on moving averages of the trend variables. It can be problematic to evaluate year-to-year changes by using multiyear moving average estimates because some of the data are from overlapping time periods and are consequently identical. In comparing these overlapping estimates, the variances of the estimates of change will be underestimated incor- rectly. Moving averages also present similar problems when used as dependent variables in statis- tical models (such as time-series models) and regression models, since the statistical properties of the data (such as autocorrelations) would be affected by the overlaps in the moving averages. The potential advantage of ACS possibly providing insights into seasonality issues will not be realized, because information by month and quarter will not be provided. In addition, the weighting of estimates to the July 1 reference date in the annual population estimates will make the analysis of data for areas with highly seasonal populations more difficult to interpret. 6.3 Trend Analysis Case Study This section presents a case study that demonstrates how ACS estimates might be used for performing trend analyses. It shows how to analyze the change in a characteristic over recent years and whether the estimates indicate that a meaningful change has taken place. Section 3 of this guidebook has detailed instructions on downloading ACS data. Assume that you are a transportation analyst working in a hypothetical MPO in the autumn of 2007. Your manager has asked you to examine how the percentage of workers in the central county of your region (called Central County) that use public transportation (bus or trolley bus, streetcar or trolley car, subway or elevated, railroad) to work has been changing over the period 1996-2006. 53 C. Alexander, 2002, "A Discussion of the Quality of Estimates from the American Community Survey for Small Population Groups," Personal correspondence with Caliper Corporation, David Hartgen, and Vermont Agency of Transportation. 54 See, for example, C. Taeuber, 2004, "The American Community Survey: Challenges and Opportunities." See http://rnyi.cornell.edu/Overview%205-14-04.ppt.

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Trend Analyses Using ACS Data 105 Although aggregate ridership data are available, transit on-board survey data that provide infor- mation on riders' trip purposes and other details are only available for snapshots in time over the past decade, so it is difficult to make conclusions about how commuter ridership has changed. This section describes some options for presenting the analysis results to policymakers. A use- ful way to analyze trends is to plot the indicator of interest versus time. This helps in visualizing the magnitude and direction of change in the indicator of interest, helps identify outliers, and provides insight into subsequent analysis strategies that could be used. Presentation options for two types of analysis are described. First, the trend at the county level is analyzed. Second, the county-level trend is compared to the city-level trend. Figure 6.3 shows the percentage of workers in Central County using public transportation to work, using the annual estimates. For each year, the lower bound, upper bound, and midpoint of the 90 percent confidence interval are shown. The following conclusions can be drawn from this analysis: There is no real noticeable trend in the percentage of workers using public transportation to work over the years 1996-2006; and The change is statistically not significant except for the change between 1996-1997, 1997-1998, and 1999-2000 (see "Analysis Steps" section). One can alternatively show the actual percentages for each year, the difference in percentages, the confidence interval of the difference, and whether the difference is statistically significant (see, for example, Table 6.7). Figure 6.4 shows a comparison of the trends for Central County and a smaller city in the county, called Fairview City, using the five-year moving average data for both geographies to maintain consistency of comparison. The following conclusions can be drawn from this analysis: The confidence intervals at the city level are larger than at the county level, as expected, because of smaller sample sizes at smaller geographies; and Overall, the percentage of workers using public transportation to work is smaller in Fairview City than in Central County as a whole. 6.3.1 Available Data For areas with population over 65,000, the Census Bureau will release annual ACS estimates as well as three- and five-year moving averages. Since the total population of the county in Percent 14 12 10 8 6 4 2 0 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Figure 6.3. Percentage of workers in Central County using public transportation to work, using annual ACS estimates.

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106 A Guidebook for Using American Community Survey Data for Transportation Planning Percent 14 Central County Fairview City 12 10 8 6 4 2 0 1996-2000 1997-2001 1998-2002 1999-2003 2000-2004 2001-2005 2002-2006 Figure 6.4. Percentage of workers in Central County and Fairview City using public transportation to work, using the five-year moving average ACS estimates. question is greater than 65,000 in each of the years 1996-2006, all three types of ACS data are available for use. Table 6.1 shows the number of workers using public transportation to work and the total number of workers in Central County. This table uses annual ACS data for the years 1996 through 2006. You can find the annual ACS data at the county level available online at the Census Bureau ACS website. Every estimate is associated with a lower bound and an upper bound cor- responding to the 90 percent confidence interval. The 90 percent confidence interval means that 90 times out of 100 the true value of the characteristic for that area falls between the lower and upper bounds of an estimate derived from a sample like the one taken. Tables 6.2 and 6.3 show the three-year and five-year moving averages, respectively, of the number of workers using public transportation and the total number of workers. Since the first Table 6.1. Annual ACS data for Central County,1996-2006. Total Lower Upper Workers by Lower Upper Year Workers Bound Bound Public Transportation Bound Bound 1996 305,713 303,259 308,167 32,133 31,052 33,214 1997 309,411 303,548 315,274 38,427 36,119 40,735 1998 312,609 305,785 319,433 33,883 31,365 36,401 1999 316,423 312,417 320,429 34,027 31,691 36,363 2000 330,828 327,614 334,042 39,289 36,977 41,601 2001 326,542 323,206 329,878 38,222 35,934 40,510 2002 319,537 313,896 325,178 36,333 33,076 39,590 2003 318,607 313,050 324,164 36,297 33,179 39,415 2004 318,000 312,423 323,577 35,616 32,453 38,779 2005 318,500 312,940 324,060 35,258 32,017 38,499 2006 319,000 313,407 324,593 34,580 31,314 37,845

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Trend Analyses Using ACS Data 107 Table 6.2. Three-year moving average data for Central County, 1996-2006. Total Lower Upper Workers by Public Lower Upper Year Workers Bound Bound Transportation Bound Bound 1996-1998 309,244 306,136 312,353 34,814 33,620 36,009 1997-1999 312,814 309,532 316,097 35,446 34,066 36,825 1998-2000 319,953 317,106 322,800 35,733 34,353 37,113 1999-2001 324,598 322,556 326,639 37,179 35,844 38,514 2000-2002 325,636 323,203 328,069 37,948 36,414 39,482 2001-2003 321,562 318,698 324,426 36,951 35,265 38,636 2002-2004 318,715 315,486 321,943 36,082 34,246 37,918 2003-2005 318,369 315,156 321,582 35,724 33,891 37,556 2004-2006 318,500 315,280 321,720 35,151 33,290 37,012 Table 6.3. Five-Year moving average data for Central County, 1996-2006. Total Lower Upper Workers by Public Lower Upper Year Workers Bound Bound Transportation Bound Bound 1996-2000 314,997 312,868 317,126 35,552 34,579 36,524 1997-2001 319,163 316,986 321,339 36,770 35,717 37,822 1998-2002 321,188 319,035 323,341 36,351 35,202 37,499 1999-2003 322,387 320,385 324,389 36,834 35,627 38,040 2000-2004 322,703 320,556 324,850 37,151 35,872 38,431 2001-2005 320,237 317,906 322,568 36,345 34,988 37,703 2002-2006 318,729 316,231 321,227 35,617 34,181 37,052 year of data collection is 1996, the first three-year moving average is available in 1999. Initially, the Census Bureau calculated the three-year average estimates as (1996 Estimate + 1997 Estimate + 1998 Estimate)/3 However, for the full ACS data release beginning with 2005 data, the three-year averages will be calculated as the weighted averages of the data collected over the three-year period. Thus, the three-year average estimates are calculated in the same way as the single-year estimates, but over the course of three years. The same method is employed for five-year estimates. Since the 1996 to 2003 data are based on the ACS demonstration phase, the three- and five- year moving average estimates and their lower and upper bounds would not be available online. Therefore, these estimates have been synthesized for this case study. All computation methods are described in the next section. 6.3.2 Analysis Steps For this case study, two types of analyses are conducted. First, the percentage of workers using public transportation to work and its 90 percent confidence interval is computed for all three types of estimates: annual data, three-year moving average data, and five-year moving average data. Then, the difference in the percentage of workers using public transportation to work between any given two years and the statistical significance of the difference is computed. The formulas used in the analyses are based on documents released by the Census Bureau on the

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108 A Guidebook for Using American Community Survey Data for Transportation Planning accuracy of ACS data, the three-year averages, and the change profiles.55 The formulas are pre- sented in Section 4 of this guidebook, and also are used in the Section 5 case studies. Annual Data In any given year, you could compute an estimate of the proportion of work- ers who used public transportation to work, as given in Equation 5.1. For example, using the 1996 data, the proportion of workers who used public transportation to work is equal to ^1996 = 32,133 = 0.1051 = 10.51% P 305, 713 To compute the confidence interval of the percentage of workers who used public transporta- tion to work, you need to know its standard error. The steps needed to compute the standard error are similar to what is described in Sections 4 and 5. For example, using Equation 5.3, the standard error of the number of workers who used public transportation to work in 1996 is equal to ^ 1996 = 32,133 - 31, 052 = 657 ( SE X ) 1.645 Similarly, the standard error of the total number of workers in 1996 is equal to ^1996 = 305, 713 - 303, 259 = 1, 492 ( SE Y ) 1.645 Using Equation 5.4, the standard error of the proportion of workers who used public trans- portation to work in 1996 is equal to ( ) ^1996 = SE P 1 305, 713 [657 ]2 - 32,1332 305, 713 2 [1, 492]2 = 0.0021 = 0.21% Finally, using Equations 5.6, 5.7, and 5.8 (page81), the lower and upper bounds of the 90 per- cent confidence interval for the percentage of workers who used public transportation to work in 1996 are given by ( ) ^1996 = 0.1051 - 1.645 0.0021 = 0.1017 = 10.17% LB P ( ) ^1996 = 0.1051 + 1.645 0.0021 = 0.1085 = 10.85% UB P Similar computed values for all years from 1996-2006 are shown in Table 6.4. Three-Year Moving Average Data Given the lower and upper bounds of the confidence intervals for the three-year average total number of workers and the number of workers using public transportation to work, the other computations of the percentage of workers using pub- lic transportation to work and its confidence interval would be the same as those described for the annual data case. As mentioned earlier, the three-year moving average data were not avail- able for the 1996-2003 data and, therefore, are synthesized for this case study. The lower bounds and upper bounds of the 90 percent confidence interval for the three-year moving average estimates are derived in the same way as for the single-year estimates, and were shown in Table 6.2. The computed values are summarized in Table 6.5. 55 See "Change Estimates," at www.census.gov/acs/www/Downloads/ACS/accuracy2002change.pdf, "Accuracy of the Data (2003)," at www.census.gov/acs/www/Downloads/ACS/accuracy2003.pdf, and "Three-Year Aver- ages," at www.census.gov/acs/www/Downloads/ACS/ThreeYrAvg.pdf.

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Trend Analyses Using ACS Data 109 Table 6.4. Annual data computation worksheet for the percentage of workers who used public transportation to work with 90 percent confidence interval. Number of Workers by Percentage of Workers by Total Workers Public Transportation Public Transportation Year Estimate SE Estimate SE Estimate SE LB UB 1996 305,713 1,492 32,133 657 10.51 0.21 10.17 10.85 1997 309,411 3,564 38,427 1,403 12.42 0.43 11.71 13.13 1998 312,609 4,148 33,883 1,531 10.84 0.47 10.07 11.61 1999 316,423 2,435 34,027 1,420 10.75 0.44 10.03 11.48 2000 330,828 1,954 39,289 1,406 11.88 0.42 11.19 12.57 2001 326,542 2,028 38,222 1,391 11.71 0.42 11.01 12.40 2002 319,537 3,429 36,333 1,980 11.37 0.61 10.37 12.37 2003 318,607 3,378 36,297 1,895 11.39 0.58 10.43 12.35 2004 318,000 3,390 35,616 1,923 11.20 0.59 10.22 12.18 2005 318,500 3,380 35,258 1,970 11.07 0.61 10.07 12.07 2006 319,000 3,400 34,580 1,985 10.84 0.61 9.83 11.85 Five-Year Moving Average Data The computed values for the five-year moving average data are similar to those for the three-year moving average data, and are shown in Table 6.6. Computing Differences in Percentages The next step in the analysis is to compute the difference in the percentage of workers using public transportation to work between any two consecutive years and the statistical significance of the differences. It is important to note that statistically valid annual estimates of change cannot be computed from the difference of two moving averages if the two moving averages are based on overlapping data. Table 6.7 summarizes the three-year estimates that can be validly compared with each other. For the series involving data from 11 years (1996 to 2006), a maximum of three time peri- ods (assuming three-year moving averages) that do not include overlapping years should be sta- tistically compared to each other. For example, moving averages of 1996-1998, 1999-2001, and 2002-2004 can all be compared to each other without the effects of the overlapping data. Using five-year moving averages, a maximum of two time periods that do not include overlapping years can be compared to each other (e.g., moving averages of 1996-2000, 2001-2005). Table 6.5. Three-Year moving average data computation worksheet for the percentage of workers who used public transportation to work with 90 percent confidence interval. Number of Workers by Percentage of Workers by Total Workers Public Transportation Public Transportation Year Estimate SE Estimate SE Estimate SE LB UB 1996-1998 309,244 1,890 34,814 726 11.26 0.22 10.89 11.63 1997-1999 312,814 1,996 35,446 839 11.33 0.26 10.91 11.76 1998-2000 319,953 1,731 35,733 839 11.17 0.26 10.75 11.59 1999-2001 324,598 1,241 37,179 812 11.45 0.25 11.05 11.86 2000-2002 325,636 1,479 37,948 933 11.65 0.28 11.19 12.12 2001-2003 321,562 1,741 36,951 1,025 11.49 0.31 10.98 12.01 2002-2004 318,715 1,963 36,082 1,116 11.32 0.34 10.76 11.89 2003-2005 318,369 1,953 35,724 1,114 11.22 0.34 10.66 11.79 2004-2006 318,500 1,957 35,151 1,131 11.04 0.35 10.46 11.61

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110 A Guidebook for Using American Community Survey Data for Transportation Planning Table 6.6. Five-Year moving average data computation worksheet for the percentage of workers who used public transportation to work with 90 percent confidence interval. Number of Workers by Percentage of Workers by Total Workers Public Transportation Public Transportation Year Estimate SE Estimate SE Estimate SE LB UB 1996-2000 314,997 1,294 35,552 591 11.29 0.18 10.99 11.59 1997-2001 319,163 1,323 36,770 640 11.52 0.19 11.20 11.84 1998-2002 321,188 1,309 36,351 698 11.32 0.21 10.97 11.67 1999-2003 322,387 1,217 36,834 733 11.43 0.22 11.06 11.79 2000-2004 322,703 1,305 37,151 778 11.51 0.24 11.12 11.90 2001-2005 320,237 1,417 36,345 825 11.35 0.25 10.93 11.77 2002-2006 318,729 1,519 35,617 872 11.17 0.27 10.73 11.62 The difference in the percentage of workers using public transportation to work between two years is given by Equation 5.2. For example, this difference between 1996 and 1997 is ( ) ^1996 = 100% ( 0.1242 - 0.1051) = 1.91% ^1997 - P DIFF1996-1997 = 100% P The steps needed to compute the statistical significance of this difference are similar to what was described in Section 5. The standard error of the difference in the percentage of workers who used public transportation to work between 1996 and 1997 is given by Equation 5.5 and is equal to SE ( DIFF1996-1997 ) = 100% ^ SE P1997 ( + ^ ) SE P1996 ( ) = 100% [0.0043]2 + [0.0021]2 = 0.48% The 90 percent margin of error of the difference in the percentage of workers who used public transportation to work between 1996 and 1997 is given by Equation 5.6 and is equal to: ME ( DIFF1996-1997 ) = 1.645 0.48 = 0.79% The lower and upper bounds of the 90 percent confidence interval of the 1996-1997 differ- ence in percentages are given by Equations 5.7 and 5.8, respectively, and are equal to LB ( DIFF1996-1997 ) = 1.91 - 0.79 = 1.12% Table 6.7. Valid comparisons of ACS three-year average estimates. Year 1996-1998 1997-1999 1998-2000 1999-2001 2000-2002 2001-2003 2002-2004 2003-2005 2004-2006 1996-1998 1997-1999 1998-2000 1999-2001 2000-2002 2001-2003 2002-2004 2003-2005 2004-2006