What constitutes a significant drop in speed of vehicles on a 40mph road? A friend had an incident near where he lives recently that is similar to my line of work (currently) that made me think what constitutes a significant drop in speed as a result of a change in road dimensions?
In short, the friend lives in a small village and there had been problems of people speeding through it (predominantly east to west – they get through traffic mostly in one direction). The local authority did a speed survey to the east and west of the village, narrowed the road in the village and then did three surveys afterwards (to the east of the village as a direct comparison, at the new measure in the village and to the west again as a direct comparison).
They found that traffic had slowed by 4 miles per hour on average on the approach to the east of the village (40mph limit), by comparing the results of the two, 7 day long surveys (the average on most days was 3.5mph – 4.5mph slower). This obviously had a reduced 85th percentile figure as well (as the majority of traffic was going that bit slower).
The thought being that drivers anticipated the road narrowing once they were aware of it and slowed down slightly (the survey was about 300m before the narrowing but in eyesight of the narrowing). The survey on the exit showed little change (less than 1mph as presumably drivers accelerated away from the measure and out of the village onto wider roads).
I think the other survey that they did at the measure was just to get an idea of the effect of the measure (e.g. what effect it had at that point, they were unsure of where they were going to site it originally so couldn't survey the exact spot beforehand).
What I wondered was if the 4mph reduction on approach was actually significant? It was obviously a noticeable drop (10% of the posted limit), but could it be explained by just a general variance in traffic speeds (e.g. could it be expected)? My thought was over a week this would be unlikely.
Apparently the traffic flows over the two survey weeks were similar – within 5% (so a reasonably fair comparison in that respect), and there were no outside events to effect the survey (e.g. inclement weather, roadworks and diversions etc.).
I just couldn’t figure how you could class what a significant reduction in speed would be in this case? I have done similar work myself (this kind of data usually comes split down into 5mph speed differentials – e.g. 0-5, 5-10, 10-15 etc.) so you can work out the means, 85th percentile’s etc.
Most of the time, I will just take a quick look at the differences before or after in the mean average and 85th percentile as it accounts for the bulk of traffic and make my judgment from there (and only dig further if I need to which is a rare occasion), but it did just make me think what would be a statistically significant drop?
 A: Answered in comments, copied below:

The counts, even rough ones, could settle the issue. A busy section of
road will handle thousands of cars daily, tens of thousands weekly. A
gross overestimate of the standard deviations of the speeds would be,
say, 50 mph. Divided by the square root of the count this would be
less than 1/2 mph, which overestimates the sampling error of each
mean. Since the means differ by 7 to 9 times this number, they will be
strongly significant: so the drop is real. Of greater interest is how
that translates to increased safety (and, possibly, counterbalancing
factors like increased transportation costs).

– whuber
Clarifying comment by OP:

Apologies for asking such a basic question when I think about it. I've
always just looked at things like this and taken them at face value
(e.g. 3-4mph = a genuine drop) and not thought about it. So if I am
understanding it right because of the size of the counts ensures a big
enough population (e.g. over 5000 vehicles), take the standard
deviations of all of the speeds over the week, divided by square root
of the sample size to get the sampling error. As the directly
comparable drop (4mph in this case) is substantially bigger than the
sampling error this would therefore make it genuine?
Yes, that's the basic thought process. The gray area typically is
where the difference of means ("effect size") is between around 2 to 5
times their SDs: that's when you need to conduct a t-test or something
like it. There are other complications, too: these data are not
statistically independent, because when cars travel in groups they
don't have independently varying speeds. But once you discover the
effect size is very large compared to the standard error of the mean
difference, usually you can proceed with confidence that the
difference is real (and not a sampling artifact).

– whuber
(If the traffic intensity is very high then the correlation might be close to 1, but then the speed will also be reduced).
