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Trend Analyses Using ACS Data 111 Table 6.8. Difference in percentages of workers using public transportation to work using annual ACS data. Percentage of Workers Using Public Transportation to Work Year Estimate SE (Estimate) Difference SE (Diff) ME (Diff) LB (Diff) UB (Diff) Significant? 1996 10.51 0.21 1997 12.42 0.43 1.91 0.48 0.79 1.12 2.70 Yes 1998 10.84 0.47 -1.58 0.64 1.05 -2.63 -0.53 Yes 1999 10.75 0.44 -0.09 0.64 1.06 -1.14 0.97 No 2000 11.88 0.42 1.12 0.61 1.00 0.12 2.12 Yes 2001 11.71 0.42 -0.17 0.59 0.98 -1.15 0.80 No 2002 11.37 0.61 -0.33 0.74 1.21 -1.55 0.88 No 2003 11.39 0.58 0.02 0.84 1.38 -1.36 1.41 No 2004 11.20 0.59 -0.19 0.83 1.37 -1.56 1.17 No 2005 11.07 0.61 -0.13 0.85 1.40 -1.53 1.27 No 2006 10.84 0.61 -0.23 0.86 1.42 -1.65 1.19 No UB ( DIFF1996-1997 ) = 1.91 + 0.79 = 2.70% Finally, the statistical significance of the difference in percentages is determined according to the rules described in Section 5. For example, since both the lower and upper bounds of the 90 percent confidence interval of the difference in percentage of workers who used public transportation to work between 1996 and 1997 are positive, it can be concluded with 90 percent certainty that this difference is statistically significant. Similar computed values for the years 1996 through 2006 are shown in Table 6.8. 6.4 Conclusions from the Case Study As described, one can plot the trend versus time. Figures 6.5 and 6.6 show these plots for the three- and five-year moving average data. Similar to the conclusions drawn from the analysis of annual estimates, Figures 6.5 and 6.6 indicate that the change in the percentage of workers using public transportation to work was minimal; the plots of the three- and five-year moving averages are almost flat. This also illustrates that estimates based on the moving averages tend to smooth out any sudden changes in the indi- cator of interest. For example, even though there is a significant increase (around 2 percent) in the percentage of workers using public transportation to work between years 1996 and 1997 in the annual data plot, the increase occurs at a slower rate using the three- and five-year moving average data analysis. The drop in the rate in 1998 dampens the effect of the one-year variation. Even if there were a more pronounced increase from one year to the next, the multiyear esti- mates would have shown the increase at a slower rate. The dampening is desirable in the case of year-to-year minor fluctuations (noise), but means that trends that occur for smaller geographic areas will not be detectable for some time. The confidence intervals become narrower (i.e., more stable estimates) for the three-year moving average data than for the annual data, and narrower for the five-year moving average data than for the three-year moving average data. This reflects the larger sample sizes, but the seemingly increased precision comes at the cost of the more difficult interpretation of the multiyear averages. For the second analysis comparing the trends at the county level and at the city level for Fairview City, only five-year moving average data would be available for Fairview City, a small
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112 A Guidebook for Using American Community Survey Data for Transportation Planning Percent 14 12 10 8 6 4 2 0 1996-1998 1997-1999 1998-2000 1999-2001 2000-2002 2001-2003 2002-2004 2003-2005 2004-2006 Figure 6.5. Percentage of workers in Central County using public transportation to work, using three-year moving average data. area with population less than 20,000. Therefore, for comparison purposes, since only the five- year data are available for the small area, the five-year average estimates for the county also should be used. The confidence intervals at each of the two geographic levels can then be plot- ted, as was shown in Figure 6.4. The confidence intervals at the city level are larger than at the county level, as expected, because of smaller sample sizes at smaller geographies. For any given time period, one can then compare the two moving average estimates (county and city levels) using the difference calculations described in Sections 4 and 5. Often, when the confidence intervals for the areas being compared are significantly different and not overlapping, an analyst will know that the difference is statisti- cally significant without calculating the standard errors of the differences. For example, the confi- dence interval at the city level corresponding to the 2001-2005 moving average does not overlap with the confidence interval at the county level. The upper bound of the confidence interval at the city level is smaller than the lower bound of the confidence interval at the county level. Therefore, one can be pretty certain that the percentage of workers using public transportation to work is smaller in Fairview City than in Central County as a whole. To determine the statistical significance of the difference, an analyst could apply the differences analysis described in Section 5. Percent 14 12 10 8 6 4 2 0 1996-2000 1997-2001 1998-2002 1999-2003 2000-2004 2001-2005 2002-2006 Figure 6.6. Percentage of workers in Central County using public transportation to work, using five-year moving average data.
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Trend Analyses Using ACS Data 113 This case study has shown how some elements of trend analysis can be accomplished using ACS data. Some of the issues that data users should be aware of when analyzing ACS data for the purpose of trend analysis are summarized below. 6.4.1 When to Use Each Type of Estimate When more than one type of estimate is available (either in the form of annual and moving average estimates or in the form of moving average estimates of different lengths), as in the case of geographic areas with 65,000+ population, the choice of estimate to use depends on the pur- pose of the analysis. Consistency If the characteristics of two populations in areas of similar geographic scales (e.g., populations of two counties or two states) are compared over time, it is important to use the same type of estimate to ensure consistency. For example, if County A has a 65,000+ popu- lation and County B has a population less than 65,000, then it is recommended to use the moving average estimate from County A (rather than the single-year estimate, which is available) to compare it to the moving average estimate from County B (where annual estimates are unavailable). Reduction in Lag Time If the timeliness of the data is important for the analysis, and if the single-year estimates are deemed reliable (e.g., with reasonable standard errors and without too many fluctuations), the analyst could use the single-year estimates rather than the moving aver- age estimates to reduce the lag time between the analysis year and data collection year. Reliability If the trend analysis focuses on a certain sub-population for whom three- and five-year moving averages are available, and if greater reliability is desired, the five-year moving averages would be more stable to use. Reducing Correlations As was discussed in the example above, moving averages that include overlapping years are correlated. Therefore, when modeling a trend using ordinary least squares regression or Poisson regression (see below), or testing for the significance of an annual rate of change, it is recommended that annual estimates be used rather than moving average esti- mates that include overlapping years. 6.4.2 Correlation between Moving Average Data When three- or five-year moving average data are used for computing differences in estimates between different years, users should be aware of the correlation between these estimates. For example, annual estimates of change cannot be computed from the difference of two mov- ing averages if the two moving averages are based on data from overlapping years (e.g., a mov- ing average of years 1996-1998 and a moving average of years 1997-1999). This is because when standard statistical procedures are used to test for significant differences between estimates over time, it is assumed that the two estimates are drawn from independent samples, an assumption that is violated in the case of two consecutive moving averages. One can, for example, compare a moving average of data from years 1996-1998 with a moving average of data from years 1999 and beyond, because these two intervals do not include overlapping years. 6.4.3 Modeling the Trend In addition to visually observing the pattern of change in the percentage of workers using pub- lic transportation to work and computing differences in percent distributions, statistical meth-