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Torrance Transit System Sampling Method Analysis presented by Paul M. Yun

Torrance Transit System Sampling Method Analysis presented by Paul M. Yun. Contents. Background Understanding Question Approach Writing. Background. Letter from Torrance Transit System to Dr. Drew. Their Question.

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Torrance Transit System Sampling Method Analysis presented by Paul M. Yun

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  1. Torrance Transit System Sampling Method Analysispresented by Paul M. Yun

  2. Contents • Background • Understanding Question • Approach • Writing

  3. Background • Letter from Torrance Transit System to Dr. Drew.

  4. Their Question If we only do two round-trips per survey day (362 round-trips, or 724 one-way trips), would our data meet the 95% confidence , 10% accuracy FTA criteria? If not, would there be a way of adding a few extra surveys to meet the standard?

  5. What????

  6. Sampling Schemes • FTA(Federal Transportation Administration) Sampling scheme: Every 2nd day/ 3 one-way trips/ 549 one-way trips per year • Torrance Transit Sampling scheme: Every 2nd day/ 2 round trips/ 362 round trips (724 one-way trips)

  7. Finding what to do

  8. Things to do • Read US Department Transportation Booklet for Sampling Procedure. • Contact with David Banks, statistician of US Department of Transportation. • Read relevant documents from Torrance Transit System.

  9. Close examination

  10. Idea!!

  11. Initial thought • Correlation between the average travel mileage in Westbound & the average travel mileage in Eastbound

  12. Confirmation

  13. I got you!!

  14. Meeting with folks in Torrance Transit System

  15. Homework Assignment to Torrance Transit System folks • Collect a sample of 13 round trips.

  16. Magic number.3188

  17. Var[ m ] = • n-2 ( Σi Var[ Xi ] + Σ i≠j Cov[ Xi, Xj]) • = n-2 ( n σ2 + nc ) • = (σ2 + c )/n = σ2 (1 + ρ )/n

  18. Let’s find the correlation coefficient for which the proposed sampling scheme provides information equivalent to the FTA sampling scheme. • σ2/549 = σ2 (1 + ρ )/724 • ρ=.3188.

  19. 0.536 • Estoy mucha triste!!

  20. Find the sample size (n) required to meet the federally defined criteria. • ρ = 0.536 • σ2/549 = σ2 (1 + ρ )/n • σ2/549 = σ2 (1 + 0.536 )/n • n = 1.536 X 549 • n = 844 one-way trips or 422 round trips

  21. Conclusion • Torrance Transit System needs to make 60 more round-trips (= 422 – 362) or 120 more one-way trips (= 60 X 2).

  22. Torrance Transit System is HAPPY!!

  23. We saved over $7,000!!

  24. Me??

  25. Lots of work!!

  26. Lots of money!!

  27. Lots of Learning!!

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