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
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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
The objective and scope of the study dictate these.
At least 1 hour and at least 30 data (if you want to assume normal distribution)
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.
u = uj/N
f(ui – u)2
N - 1
dDetermining the sample size… (p.89)
Need to know a bit of statistical principles here…
It’s all based on the normal distribution curve.
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)
At 95% Confidence level, Z = 1.96 (This is the most important number to remember.)
Null hypothesis H0: 1 = 2
Alternative H1: 1 = 2Comparing two mean speeds
This test is done to compare the effectiveness of an improvement to a highway or street by using mean speeds.
Alternative H1: 1 2
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 = 250 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(7.52/250 + 7.42/280) = 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.