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

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?

What????

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)

Finding what to do

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.

Close examination

Idea!!

Initial thought

• Correlation between the average travel mileage in Westbound & the average travel mileage in Eastbound

Confirmation

I got you!!

Meeting with folks in Torrance Transit System

Homework Assignment to Torrance Transit System folks

• Collect a sample of 13 round trips.

Magic number

.3188

• 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

• 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.

0.536

• Estoy mucha triste!!

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

Conclusion

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

Torrance Transit System is HAPPY!!

• We saved over $7,000!!

Me??

Lots of work!!

Lots of money!!

Lots of Learning!!