1. Lec 7, Ch4, pp83-99: Spot Speed Studies (Objectives)
Know when you need to conduct a speed study and where you should do it
Learn how spot speed data can be collected (from the reading)
Know how to determine the sample size needed
Know how to reduce the collected data
Know how to compare mean speeds

2. What we cover in class today…
Use of spot speed studies and time and locations to choose
Methods for conducting spot speed studies
The formula to determine the sample size
How to compute descriptive statistics
How to compare two mean speeds

3. When are spot speed studies needed?
Spot speed studies are conducted to estimate the distribution of speeds of vehicles in a stream of traffic at a particular location on a highway.
Speed Limit 50
Used for:
Establish speed zones
Determine whether complaints about speeding are valid
Establish passing and no-passing zones
Design geometric alignment
Analyze accident data
Evaluate the effects of physical improvements, etc., etc.

4. Location, time of day, and duration…
The objective and scope of the study dictate these.
Basic data collection
Like deciding speed limits  Find locations where system characteristics change and TWTh
Speed trend analyses
Avoid external influences such as traffic lights, busy access roads; off-peak, TWTh  mid blocks of streets, straight,level sections of highways
Specific traffic engineering problems
All other specific purposes  Conduct it at the location of interest and time of day
At least 1 hour and at least 30 data (if you want to assume normal distribution)

5. Descriptive statistics of speed data
Once data are collected, the first thing you do is to compute several descriptive statistics to get some ideas about the distribution of the speed data. (Note that many statistical analyses used in traffic engineering assume data are normally distributed.  So, the goal is to check whether they are really normally distributed.
Typical descriptive statistics are:
Average speed
Variance and standard deviation
Median speed
Modal speed (or Modal speed range  Needs a histogram)
The ith-percentile spot speed
Pace  Usually a 10-mph interval that has the greatest number of observations.

6. Descriptive statistics (cont.)
Average speed
Speed data Grouped Not grouped
Standard deviation
Variance s2
u = uj/N
f(ui – u)2
s =
N - 1

7. Descriptive statistics (cont)
Median speed
The speed at the middle value in a series of spot speeds. Or, 50th-percentile speed
Modal speed
The speed value that occurs most frequently in a sample of speeds
ith-percentile speed
The spot speed below which i percent of the vehicles travel, e.g. 85th-percentile speed
Pace
The range of speed that has the greatest number of observations; usually 10-mph range
85%
50%

8. Determining the sample size… (p.89)
Need to know a bit of statistical principles here…
It’s all based on the normal distribution curve.
68.3%
N =
Zα/2  d 2
95.0%
N = Min. sample size
Z α/2 = 1.96 for 95% conf. Level
= Estimated standard deviation
Rural 2-lane: 5.3 mph
Rural 4-lane: 4.2 mph
Urban 2-lane: 4.8 mph
Urban 4-lane: 4.9 mph
d = Precision level (depends on the study)
Frequency
-/sqrt(n) 
+/sqrt(n)
-1.96/sqrt(n)
+1.96/sqrt(n)
At 95% Confidence level, Z = 1.96 (This is the most important number to remember.)

9. Example 4.2 by spreadsheet (Click Example 4.2 in the lecture schedule.)

10. Comparing two mean speeds
This test is done to compare the effectiveness of an improvement to a highway or street by using mean speeds.
If you want to prove that the difference exists between the two data samples, you conduct a two-way test. We discuss only this one in this class.
If you are sure that the improvement would improve the performance of the highway or street, you conduct a one-way test. This will be discussed in CE562.
Null hypothesis H0: 1 = 2
Alternative H1: 1 = 2
Alternative H1: 1  2

11. Comparing two mean speeds (cont)
Step 1: Find mean and SD of the two samples
u1 = 35.5 mph u2 = 38.7 mph
S1 = 7.5 mph S2 = 7.4 mph
n1 = n2 = 280
Step 2: Compute the standard deviation of the difference in means (Assumes S12 and S22 are similar)
Sd = SQRT(S12/n1 + S22/n2) = SQRT(7.52/ /280) = 0.65
Step 3: Test the hypothesis. If |u1- u2| > ZSd, the mean speeds are significantly different at the confidence level of Z.
|35.5 – 38.7| = 3.2 mph > 1.96*0.65 = 1.3mph
It can be concluded that the difference in mean speeds is significant at the 95% confidence level.