# How to show statistically significant incident locations

First let me preface with I tried to search for this solution first but I don't really know how to word it and could not find any results so excuse me if this is a duplicate. I would like to know how to prove or test to show if this problem is statistically significant or not.

I am using Arc 10.3.1 and have a feature class of incidents and a feature class of roads. I queried out the major roads and buffered them to find out how many incidents fall within that road buffer.

I have approximately 6000 miles of roads. Of that 6000 miles, 900 miles are a major road. I also have 2010 incidents. Of those incidents 725 occurred on a major road. (ie 15% of the roads account for 35% of the problems) I would like to know of tutorial or guide that would show me how to prove or not prove if the incidents on a major road are significant or not.

• Have a look at this web page for advice on which test to use. – Hornbydd Sep 12 '15 at 17:25
• As at least one answer suggests, this can be evaluated with a chi-squared test. However, for this to work correctly, the incidents must be statistically independent. That's something you have to decide. BTW, ordinarily "significant" would be interpreted as "meaningful"--and no statistical test can determine that. All that a chi-squared test can do is indicate whether the difference between 15% and 35% should be attributed to chance or to some systematic difference in road conditions. – whuber Sep 12 '15 at 20:20

Finding the "right" test is often a difficult task. I'm reading through the problem you are formulating and I'm thinking to start out we don't actually need to look at this problem spatially, at all. I'm suggesting a Chi-Squared test to compare the counts of incidents between the major and non-major roads for significant difference to start. From there maybe find a test that can compare crash rates.

I'm a fan of looking over the dataset and finding the simplest possible test and applying that one first. Hopefully, the simplest test will give you a hint towards choosing a more complex test, or an indicator that explicitly considers space in its formulation. Satisfying or adjusting for stationarity assumptions for most spatial stats is hard enough as it is. Further, only a few people I know of really really really have dealt with questions of spatial stats constrained to network space.

It's such a huge subject. I fear it even though I love GIS.

Best Luck here.

• Yes, this is what I was looking for. Let me run through this as its alot to wrap my brain around but I think we are on the right track! – ed.hank Sep 11 '15 at 19:50

Although I am not a traffic engineer I have put together a segment collision diagram for them using GIS. One of the rates that they determine for the diagram is the accident rate per million vehicle miles (MVM). In order to determine this value you need to know the number of incidents on the segment between two dates, the number of days between the two dates, the annual average daily traffic (AADT) trip count of the segment, and the segment length in miles. The formula is then:

``````Round(Collision_Total * 1000000 / (Annual_Average_Daily_Traffic * Days_Between_Begin_and_End_Dates * Round(Segment_Length_in_Miles, 3)), 3)
``````

This standardizes the incident rate to a standard unit of length, traffic volume and time and so that the number of incidents on roads of different lengths with different trip rates and during different time periods can be compared. Once you know this value for a large enough sample of roadways, then you can do statistical analysis of different road classifications to determine the averages and standard deviations that apply for this rate.

Typically you need traffic counts that are relevant to each given road segment and the period being analyzed to determine the AADT. The maximum time range analyzed for this rate is normally 3 years, since using longer periods may make the AADT estimate less reliable.

• I am actually dealing with potholes but i think your formula would apply well in my case too, as traffic count should have some correlation to potholes, etc... I have a lot to wrap my brain around so thanks for your input! – ed.hank Sep 11 '15 at 19:51
• This accident rate is also used when the engineers analyze roads for speed limits. In any case any type of incident can be used in this formula where it is important to standardize the incident rate for segment length, reporting periods and trip rates. – Richard Fairhurst Sep 11 '15 at 19:57
• Higher classification roads also tend to have thicker pavement sections that may resist wear better than smaller roads. Correlation to a Pavement Management database should let you account for this and road age information, which also affects road condition performance. Using a rate like this may expose where a given road is under performing for its age and the expected volume the road was designed for. Then you could check for underlying soil conditions, environmental factors, unexpectedly high volumes, etc, or determine if the road standard needs to change to meet its life expectancy, – Richard Fairhurst Sep 11 '15 at 20:28

You have ended up with a road buffer (polygon) layer with an attribute of incidents for each road.

To show the incidents on a major road are significant, you should use Spatial-Statistics toolbox. This toolbox is part of ArcGIS Desktop. There is a tool inside that toolbox that helps to find statistically significant major road. It is called Hos Spot Analysis (Getis Ord G*).

There are a few tutorials that put you on the right track. Here is the one-place resource center for spatial statistics toolbox.

• No actually I dissolved all the roads into one large road set so I have a count of total incidents that occurred on a major road vs total incidents in the entire city. I dont really want to know where hot-spots are as much as I want to be able to prove that if if 15% of the roads are accounting for 35% of the incidents than this indeed is a problem. Now keep in mind we know that major roads are more travelled and therefore more likely to have an issue reported, etc. The tutorial you posted btw is excellent! – ed.hank Sep 11 '15 at 18:53
• From one of the output products of that analysis is you can infer what you are after. please check the tutorial and report back here. – Farid Cheraghi Sep 11 '15 at 19:08
• Gotcha, thanks, let me dive in a little deeper into it. – ed.hank Sep 11 '15 at 19:24