Torrance Transit System Sampling Method Analysis presented by Paul M. Yun
description
Transcript of Torrance Transit System Sampling Method Analysis presented by Paul M. Yun
![Page 1: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/1.jpg)
Torrance Transit System Sampling Method Analysis
presented by Paul M. Yun
![Page 2: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/2.jpg)
Contents
• Background
• Understanding Question
• Approach
• Writing
![Page 3: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/3.jpg)
Background
• Letter from Torrance Transit System to Dr. Drew.
![Page 4: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/4.jpg)
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?
![Page 5: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/5.jpg)
What????
![Page 6: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/6.jpg)
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)
![Page 7: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/7.jpg)
Finding what to do
![Page 8: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/8.jpg)
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.
![Page 9: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/9.jpg)
Close examination
![Page 10: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/10.jpg)
Idea!!
![Page 11: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/11.jpg)
Initial thought
• Correlation between the average travel mileage in Westbound & the average travel mileage in Eastbound
![Page 12: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/12.jpg)
Confirmation
![Page 13: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/13.jpg)
I got you!!
![Page 14: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/14.jpg)
Meeting with folks in Torrance Transit System
![Page 15: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/15.jpg)
Homework Assignment to Torrance Transit System folks
• Collect a sample of 13 round trips.
![Page 16: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/16.jpg)
Magic number
.3188
![Page 17: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/17.jpg)
• 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
![Page 18: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/18.jpg)
• 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.
![Page 19: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/19.jpg)
0.536
• Estoy mucha triste!!
![Page 20: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/20.jpg)
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
![Page 21: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/21.jpg)
Conclusion
• Torrance Transit System needs to make 60 more round-trips (= 422 – 362) or 120 more one-way trips (= 60 X 2).
![Page 22: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/22.jpg)
Torrance Transit System is HAPPY!!
![Page 23: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/23.jpg)
• We saved over $7,000!!
![Page 24: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/24.jpg)
Me??
![Page 25: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/25.jpg)
Lots of work!!
![Page 26: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/26.jpg)
Lots of money!!
![Page 27: Torrance Transit System Sampling Method Analysis presented by Paul M. Yun](https://reader036.fdocuments.us/reader036/viewer/2022062520/56815720550346895dc4bfc0/html5/thumbnails/27.jpg)
Lots of Learning!!