Measuring the Effectiveness of Public Involvement in Transportation Planning and Project Development (2019)

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P-1 A P P E N D I X P Calculating the Geometric Mean There are multiple ways to find the average (or “mean”) of a series of numbers. The mean varies depending on which method is used. With an arithmetic mean, poor performance on some measures can be compensated for by sufficiently high values on other measures. Compare the following two examples as an illustration. Example 1 Eight people respond to a measure with each of them choosing a different response from the others, representing a wide range of views on this topic. The geometric mean is lower than the arithmetic mean, because it is less influenced by the high scores. The two means are calculated as follows: Arithmetic Mean Geometric Mean • Sum N response scores for total score • Exclude “Don’t Know” responses • Divide total score by # of responses • Multiply N response scores for total score • Exclude “Don’t Know” responses • Take Nth square root of total score Step 1 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 Step 2 28 ÷ 7 = 4 Step 1 1 × 2 × 3 × 4 × 5 × 6 × 7 = 5,040 Step 2 7√5,040 = 3.4

P-2 Measuring the Effectiveness of Public Involvement in Transportation Planning and Project Development Arithmetic Mean Geometric Mean • Sum N response scores for total score • Exclude “Don’t Know” responses • Divide total score by # of responses • Multiple N response scores for total score • Exclude “Don’t Know” responses • Take Nth square root of total score Step 1 7 + 7 + 7 + 7 + 5 + 5 + 4 + 0 = 42 Step 2 42 ÷ 7 = 6 Step 1 7 × 7 × 7 × 7 × 5 × 5 × 4 = 240,100 Step 2 7√240,100 = 5.9 Example 2 Eight people respond to the same measure, but in this case four choose “strongly agree,” two choose “somewhat agree,” one chooses “neither agree nor disagree,” and one chooses “Don’t know.” There is more agreement among respondents than in the previous example. The geometric mean is again lower than the arithmetic mean, but the difference between the two means is smaller, because the responses are closer together. In this scenario, the two means are calculated as follows:

Abbreviations and acronyms used without definitions in TRB publications: A4A Airlines for America AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACI–NA Airports Council International–North America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FAST Fixing America’s Surface Transportation Act (2015) FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers MAP-21 Moving Ahead for Progress in the 21st Century Act (2012) NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TDC Transit Development Corporation TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S. DOT United States Department of Transportation

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