Speed studies

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Speed studies

• Sept 2009

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Speed over link
2192 ft
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Speed over link
Spot speed at t 35 seconds 12 ft/sec (17.6 mph)
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Average Speed over link
Spot speed at t 70 seconds 27 ft/sec (39.6 mph)
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Average Speed Total time to traverse link 140
sec Distance 2192 feet Average speed _2192
feet 15.6 ft/sec (23.0 mph)
140 sec
2192 feet
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Spot Speed Studies
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Spot Speed Studies

• Speed Limit Effectiveness Studies
• Establish Trends
• Design Impacts (SSD)
• Traffic Control Placement and timing
• Collision Study with Speed Cause
• Investigate speed complaints

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Collection of spot speeds

• Collect during time period representative of
  desired outcome
• Usually cannot collect all vehicles
• Random sample

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Location Time

• Depends on purpose
• Time
• Depends on purpose
• Free-flow off-peak
• Time period corresponding to complaint

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Radar gun (uses Doppler principle)
Radar Meter
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Pneumatic Road Tubes
Set distance apart, measures time from when
wheels strike first tube to when wheels strike
second tube
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Data Analysis

• Transportation studies often require analysis of
  data
• Large datasets
• Only collecting a sample of a larger population
• Use of statistics to ensure
• Results are accurate and meaningful
• Correct sample size
• Accurate use of statistical tests
• Confidence in interpretation of results

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Random Variables

• Sampling population
• Too large to measure all
• Sample smaller number to represent
• Population should be sampled randomly to prevent
  bias
• Biased sampling sampling all red sports cars in
  a spot speed study
• Random sampling sampling every 5th vehicle

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Other Statistics

• Generally assume spot speeds are normally
  distributed
• Assume sufficient samples are collected
• Should be able to calculate mean, standard
  deviation, etc. based on assumption of normality

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Population Vs. Sample
63 mph
57 mph
62 mph
51 mph
59 mph
50 mph
55 mph
43 mph
43 mph
63 mph
53 mph
51mph
22 mph
55 mph
62 mph
47 mph
55 mph
42 mph
42 mph
47 mph
56 mph
36 mph
49 mph
53 mph
39 mph
41 mph
51 mph
70 mph
65 mph
Population
61 mph
Sample
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Normal Distribution
Bell shaped Symmetric about µ (mean) X
N(µ,s2) Completely described by mean and variance
Image source http//library.thinkquest.org/10030
/7ndndpnd.htm
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Dispersion

• Same mean
• Speeds 15 mph and 75 mph
• (15 75)/2 45 mph
• Speeds 44 and 46 mph
• (44 46)/2 45 mph
• But very different ranges of values
• Variance and standard deviation
• Magnitude of variation around mean

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STD
Standard deviation is square root of variance
Equation from Roess et al
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Standard deviation
s2 599.7 85.7 (7-1) s 85.70.5
9.25 mph Mean is 24.6 mph with std of 9.25 mph
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Confidence Intervals (normal dist)

• How confident are we in our estimate of a
  statistic? (i.e. mean)
• Resampling a population would give us a slightly
  different mean
• Standard error of the mean (E)
• µ X E, with 68.3 confidence
• µ X 1.96E, with 95 confidence
• µ X 3.0E, with 99.7 confidence

Equation from Roess et al
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Confidence Intervals (normal dist)

• Example Mean 45.5 mph, standard deviation
  4.5, what is the 95 confidence interval, N 67
• E _s_ ___4.5___ 0.55
• N0.5 (67)0.5

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Sample Size

• Selection of sample size depends on desired
  confidence level

N minimum sample size at selected confidence
level Z number of standard deviation for
confidence level (1.64 for 90, see table 4.1
page 88 of text) s standard deviation (mph) d
limit of acceptable error in average speed
estimate
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Example Sample Size

• An engineer wishes to determine whether vehicles
  are traveling at the posted speed limit for a
  school zone
• Desired standard deviation is 7 mph
• Limit of acceptable error 1.5 mph
• Desired confidence level is 90
• How many samples need to be collected?
• N (Zs)2 (1.647)2 58.57 vehicles 58
  vehicles
• ( d )2 ( 1.5 )

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Example Sample Size

• What if a confidence level of 99 is desired?
• N (Zs)2 (2.587)2 144.96 145
  vehicles
• ( d )2 ( 1.5 )

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Spot Speed Study Metrics

• Mean average
• Mode value that appears the most
• Pace 10 mile increment in which the highest
  percentage of drivers is observed
• 45 to 55 mph
• 85th Percentile speed
• 15th percentile speed

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Mean (Average Speed)

• Larger sample size greater probability that
  calculated mean is not significantly different
  from true mean

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Mean

• Speeds 22, 15, 11, 25, 31, 41, 27 (mph)
• Mean 22 15 11 25 31 41 27
• 7
• 24.6 mph

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Other Metrics

• Range highest and lowest value observed
• Minimum 5 mph
• Maximum 65 mph

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Spot Speed Study of 100 Vehicles
Data for 185 Vehicles by 5 mph range
Raw Data for 16 vehicles
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Modal Value that occurs the most frequently in
a sample of spot speeds
Mode is 53 mph
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Pace range in which most vehicles are found
(i.e. 10 mph hour range)
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92
104
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Distribution
10 vehicles from data collection were traveling
from 25 to lt 30 mph
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Fraction in 25 to lt 30 bin of vehicles in
bin/total of vehicles (80) __10__ 0.13
(13)
80
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This should 1.0 (100)
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If we plot it out, it should look somewhat like a
normal distribution (not even close here because
we just made the data up so the numbers were easy
to use)
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Shows fraction of vehicles in each speed bin
frequency distribution About 12 in speed bin 27.5
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Can also create a cumulative frequency
distribution
0 vehicles in group 15 to lt 20 0.06 of vehicles
in 20 to lt 25 0 0.06 in groups 15 to lt 25
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Group 15 to lt 35 has 0 0.06 0.13 0.19 0.38
or 38 of vehicles are found in those 4 bins or
38 of vehicles were traveling between 15 and lt
35 mph
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(No Transcript)
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ith percentile spot speed

• Spot speed below which i of vehicles are
  traveling
• 50th percentile 50 of vehicles are traveling
  at or below that speed (this is also the median
  speed)
• 85th Percentile 85 of vehicles traveling at or
  below that speed 15 traveling over that speed

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Cumulative Frequency Distribution
100 of vehicles are below 55 mph
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What is the 50th percentile speed?
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What is the 50th percentile speed? Would have
been easier if we had used smaller speed bins
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What is the 85th percentile speed? Would have
been easier if we had used smaller speed bins
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What is the 85th percentile speed? Would have
been easier if we had used smaller speed bins
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Data Quality Assurance

• Spot check data
• Simple tests (check average speed, min-max, etc)
• Know limitations of data collecting devices