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 oneway 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!!