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GEH statistic
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<h2 id="applications">Applications</h2> <p>The GEH formula is useful in situations such as the following:<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> </p> <ul><li>Comparing a set of traffic volumes from manual traffic counts with a set of volumes done at the same locations using automation (e.g. a pneumatic tube <a href="/facts/Traffic_counter/T2Vgb6gf">traffic counter</a> is used to check the total entering volumes at an intersection to affirm the work done by technicians doing a manual count of the turn volumes).</li> <li>Comparing the traffic volumes obtained from this year's traffic counts with a group of counts done at the same locations in a previous year.</li> <li>Comparing the traffic volumes obtained from a travel demand forecasting model (for the "base year" scenario) with the real-world traffic volumes.</li> <li>Adjusting traffic volume data collected at different times to create a mathematically consistent data set that can be used as input for travel demand forecasting models or traffic simulation models (as discussed in NCHRP 765).</li></ul> <h2 id="common-criticism-about-geh-statistic">Common criticism about GEH statistic</h2> <p>The GEH statistic depends on the magnitude of the values. Thus, the GEH statistic of two counts of different duration (e.g., daily vs. hourly values) cannot be directly compared. Therefore, GEH statistic is not suitable for evaluating other indicators, e.g., trip distance.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> </p><p>Deviations are evaluated differently upward or downward, so the calculation is not symmetrical.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> </p><p>Moreover, the GEH statistic is not without a unit, but has the unit v e h i c l e s h o u r {\textstyle {\sqrt {\frac {vehicles}{hour}}}} (<a href="/facts/Inverse_second/W0Iqf8EL">s−1/2</a> in <a href="/facts/SI_base_unit/M7PsTWg4">SI base units</a>).<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> </p><p>The GEH statistic does not fall within a range of values between 0 (no match) and 1 (perfect match).<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> Thus, the range of values can only be interpreted with sufficient experience (= non-intuitively). </p><p>Furthermore, it is criticized that the value does not have a well-founded statistical derivation.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> </p> <h2 id="development-of-the-sqv-statistic">Development of the SQV statistic</h2> <p>An alternative measure to the GEH statistic is the Scalable Quality Value (SQV), which solves the above-mentioned problems: It is applicable to various indicators, it is symmetric, it has no units, and it has a range of values between 0 and 1. Moreover, Friedrich et al.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> derive the relationship between GEH statistic and normal distribution, and thus the relationship between SQV statistic and normal distribution. The SQV statistic is calculated using an empirical formula with a scaling factor f {\textstyle f} :<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> S Q V = 1 1 + ( M − C ) 2 f ⋅ C {\displaystyle SQV={\frac {1}{1+{\sqrt {\frac {(M-C)^{2}}{f\cdot {C}}}}}}} </p> <h3>Fields of application</h3> <p>By introducing a scaling factor f {\textstyle f} , the SQV statistic can be used to evaluate other mobility indicators. The scaling factor f {\textstyle f} is based on the typical magnitude of the mobility indicator (taking into account the corresponding unit).<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> </p> <table><tbody><tr><th>Indicator</th><th>Order of<p>magnitude</p></th><th>Scaling factor f {\textstyle f} </th></tr><tr><td>Number of person trips per day (total, per mode, per purpose)</td><td>100</td><td>1</td></tr><tr><td>Mean trip distance in kilometers</td><td>101</td><td>10</td></tr><tr><td>Duration of all trips per person per day in minutes</td><td>102</td><td>100</td></tr><tr><td>Traffic volume per hour</td><td>103</td><td>1,000</td></tr><tr><td>Traffic volume per day</td><td>104</td><td>10,000</td></tr></tbody></table> <p>According to Friedrich et al.,<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> the SQV statistic value is suitable for assessing: </p> <ul><li>Traffic volumes (if necessary, differentiation can be made not only by time of day, but also by mode).</li> <li>Person-related mobility indicators: <ul><li>Number of trips per person (not differentiated or differentiated by mode and / or trip purpose, suggestion: f = 1 {\textstyle f=1} ),</li> <li>mean travel times per trip in minutes (not differentiated or differentiated by mode and / or trip purpose, proposal: f = 30 {\textstyle f=30} ),</li> <li>mean travel distances per trip in kilometers (not differentiated or differentiated by mode and / or trip purpose, suggestion: f = 10 {\textstyle f=10} ).</li></ul></li></ul> <p>However, the SQV statistic should not be used for the following indicators:<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> </p> <ul><li>Percentage of modal split or modal shares: here there is a fixed upper limit of 100% that cannot be exceeded. Instead, the number of trips per person per mode can be used for validation with the SQV statistic.</li> <li>Travel times for paths between 2 points in the network: This indicator does not depend on the path taken by a single person, but represents a sequence of distances along a route.</li></ul> <h3>Quality categories</h3> <p>Friedrich et al.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> recommend the following categories: </p> <table><tbody><tr><th>SQV statistic</th><th>GEH statistic<p>(with f = 1,000 and c = 1,000)</p></th><th>Evaluation</th></tr><tr><td>0.90</td><td>3.4 to 3.6</td><td>Very good match</td></tr><tr><td>0.85</td><td>5.4 to 5.8</td><td>Good match</td></tr><tr><td>0.80</td><td>7.5 to 8.5</td><td>Acceptable match</td></tr><tr><td></td><td><i>(Since the GEH statistic is not symmetrical,</i><p><i>the same absolute deviation of a</i></p><p><i>measured value upwards and downwards</i></p><p><i>are evaluated differently)</i></p></td><td></td></tr></tbody></table> <p>Depending on the indicator under comparison, different quality categories may be required. </p> <h3>Consideration of standard deviation and sample size</h3> <p>The survey of mobility indicators or traffic volumes is often conducted under non-ideal conditions, e.g. large standard deviations or small sample sizes. For these cases, a procedure was described by Friedrich et al.<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> that integrates these two cases into the calculation of the SQV statistic. </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Microsimulation/wa3WnKaP">Microsimulation</a></li> <li><a href="/facts/Traffic_counter/T2Vgb6gf">Traffic counter</a></li> <li><a href="/facts/Traffic_flow/uxRYw4EH">Traffic flow</a></li> <li><a href="/facts/Traffic_engineering_(transportation)/fWW0DgzW">Traffic engineering (transportation)</a></li> <li><a href="/facts/Transportation_planning/odR3qhs7">Transportation planning</a></li> <li><a href="/facts/Trip_generation/WMCpet7b">Trip generation</a></li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="https://web.archive.org/web/20051026234844/http://www.archive2.official-documents.co.uk/document/deps/ha/dmrb/index.htm">UK Highways Agency's Design Manual for Roads & Bridges (DMRB)</a></li> <li><a href="http://www.wisdot.info/microsimulation/index.php?title=Main_Page">Wisconsin Microsimulation Modeling Guidelines</a> <a href="https://web.archive.org/web/20180720125239/http://www.wisdot.info/microsimulation/index.php?title=Main_Page">Archived</a> 2018-07-20 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a></li> <li><a href="http://content.tfl.gov.uk/traffic-modelling-guidelines.pdf">Transport for London Traffic Modelling Guidelines</a></li> <li><a href="http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_765.pdf">National Cooperative Highway Research Program Report 765</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>UK Highways Agency, Design Manual for Roads and Bridges, Volume 12, Section 2, http://www.archive2.official-documents.co.uk/document/deps/ha/dmrb/index.htm Archived 2005-10-26 at the Wayback Machine <a href="http://www.archive2.official-documents.co.uk/document/deps/ha/dmrb/index.htm" target="_blank">http://www.archive2.official-documents.co.uk/document/deps/ha/dmrb/index.htm</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Wisconsin DOT Microsimulation Guidelines http://www.wisdot.info/microsimulation/index.php?title=Main_Page Archived 2018-07-20 at the Wayback Machine <a href="http://www.wisdot.info/microsimulation/index.php?title=Main_Page" target="_blank">http://www.wisdot.info/microsimulation/index.php?title=Main_Page</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Transport for London, Traffic Modeling Guidelines Version 3.0, http://content.tfl.gov.uk/traffic-modelling-guidelines.pdf, Retrieved 10-March-2016 <a href="http://content.tfl.gov.uk/traffic-modelling-guidelines.pdf" target="_blank">http://content.tfl.gov.uk/traffic-modelling-guidelines.pdf</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Shaw, et al (2014), Validation of Origin–Destination Data from Bluetooth Reidentification and Aerial Observation, Transportation Research Record #2430, pp 116–123 <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Van Vliet, D. (2015), SATURN Travel Demand Forecasting Software User's Manual Version 11.3, Section 15.6, http://www.saturnsoftware.co.uk/saturnmanual/pdfs/Section%2015.pdf Archived 2017-02-07 at the Wayback Machine, Accessed 10-March-2016 <a href="http://www.saturnsoftware.co.uk/saturnmanual/pdfs/Section%2015.pdf" target="_blank">http://www.saturnsoftware.co.uk/saturnmanual/pdfs/Section%2015.pdf</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>NCHRP 765: Analytical Travel Forecasting Approaches for Project-Level Planning and Design, http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_765.pdf, retrieved 10-March-2016 <a href="http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_765.pdf" target="_blank">http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_rpt_765.pdf</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>Markus Friedrich, Eric Pestel, Christian Schiller, Robert Simon: Scalable GEH: A Quality Measure for Comparing Observed and Modeled Single Values in a Travel Demand Model Validation. In: Transportation Research Record: Journal of the Transportation Research Board. Issue 2673, No 4, April 2019, ISSN 0361-1981, pages 722–732, doi:10.1177/0361198119838849 <a href="/wiki/ISSN_(identifier)" target="_blank">/wiki/ISSN_(identifier)</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> </ol>