Speed Ranges during computations

mmiranda0811 · Member

Speed Ranges during computations

BlueB · Veteran Member

Without absolute measuremnets or information, then a speed range would be appropriate. You mention estimated min speed, which is sometimes appropriate and on others a max estimated speed may also be right. Perhaps the frquency that they use a range is the re is some similarity in the scenario.
Estimates and speed ranges are often quite large/vague. Depends on what we each thing is a large range - in some instances +/- 5mph is large or +/- 25mph is concise.
What type of ranges / incidents are you thinking about?

ashman165 · Veteran Member

mmiranda0811 wrote:

Does anyone use speed ranges for their reports? I have a local police department that is using speed ranges more often than minimum speed estimates. Thsi would be fine but sometimes the speed range is quite large.

Many people do. Whether or not it's a valid or good idea depends largely on what it is that one is trying to show.

What kind of cases are talking about?

mmiranda0811 · Member

The cases care varied and I'm seeing low and high ranges. The issue is that I'm seeing this more and more and my prosecutors want something more precise, especially when we go to trial. Jurors want a set number.

BlueB · Veteran Member

Ah, the holy grail. The difference between what they want and what we can give them.
I would suggest that one of the principle factors which makes ranges neccesary, is us, the investigators/reconstructionists. If you or I come up with a speed from skid marks (as an example) , there will be someone else who has done tests and can show that the same data may result in a slightly higher/lower figure than you. Consequently you/I may take that additional info into consideration. Bit by bit, for so many reasons the base line numbers that were loved by lawyers and jurors alike have been eroded, and to avoid lengthy arguments over rival and equally valid answers, the answers themselves become a range rather than a defined result.

omegacrash · Veteran Member

I'll use a speed range from time to time to show stopping distances in cases such as a pedestrian being struck. This is to show where the stopping point would be for different speeds to show a court/jury what speed the person would have to be traveling in order to stop and avoid the collision. Showing the stopping distances for different speeds, I believe, gives a clearer picture of the crash and can show if the crash was avoidable or not. For instance, a person is struck by a vehicle. After determining the area of impact and the drivers point of perception and the speed of the vehicle, I will show the stopping distance for the speed I have calculated and then, if the calculated speed is higher than the posted limit, show the stopping distance for the posted speed limit, and then compute the speed the driver would have to be moving in order to have stopped in time to avoid striking the pedestrian.
Obviously there is more to it but that is just a brief example. It could also be that the investigator is not comfortable with his calculations or was trained to do it that way. You need to be careful how you testify to your findings. Early in my career, when I used a range of speeds, I did not make myself clear on what I was doing and was only allowed to testify on the low end of the range. Make sure you clearly testify why you are using a range and what you are trying to show. Otherwise, your case can go downhill very quickly.

-- Edited by omegacrash on Tuesday 21st of April 2009 06:01:50 AM

ashman165 · Veteran Member

I'm afraid I don't understand at all what is complex to grasp about using a range of speeds. Most people whom I meet randomly have a firm grasp of ranges. It's a natural component of the absence of exactitude we have in our lives, as reflected in our very natural conversations.

While it's likely true that the mathematics behind the conclusions can become intricately nuanced, I don't think that presents much of an issue at all. Perhaps it is if the person doing the arguing for a particular event lacks a firm grasp of what's going on. But it seems to me that it's reasonably obvious - or at least reasonably enough easily tested and "proved" to be the case - that the likelihood of something happening is 1 - the probability the event won't happen. This is elementary probability theory taught in grade school.

By extension, we can apply this to collision dynamics simply because a range establishes a certain bound of speeds which must have been true for this event to take place. So, if you can eliminate the possibility that the event could have happened at all other speeds, then what remains must be the speeds at which the vehicles were traveling. Else, the collision won't happen. This is, I think, rather intuitive.

This can be a quite elegant solution to the issue, and it's entirely sound as well as valid to use. Proof by induction and proof by negation are perfectly reasonable and oftentimes the most elegant way to address an issue. Particularly when you're trying to convince someone for whom a more rigorous approach won't be at all understood.

mmiranda0811 · Member

The use of ranges certainly has its place in a criminal case as long as the range is within the realm of science. I have used ranges myself but they have been no more than a few MPH off. My issue is that I'm seeing reports with speed ranges of 20 & 30 MPH. This makes it extremely difficult to convince a jury that a person is driving recklessly when the crash occurred. It also gives the appearance that the investigator is taking a shot in the dark when it comes to the speed of the vehicle.

ashman165 · Veteran Member

mmiranda0811 wrote:

The use of ranges certainly has its place in a criminal case as long as the range is within the realm of science. I have used ranges myself but they have been no more than a few MPH off. My issue is that I'm seeing reports with speed ranges of 20 & 30 MPH. This makes it extremely difficult to convince a jury that a person is driving recklessly when the crash occurred. It also gives the appearance that the investigator is taking a shot in the dark when it comes to the speed of the vehicle.

Perhaps now would be a dandy time to iterate that these are all case specific. If you have a specific example in which ranges of "20 & 30 MPH" have occured and are improper, then perhaps it would do us all better to look at the data from these *actual* cases so we can discuss it.

As it sits right now, we just have your unsupported assertion of what you've seen without any context within which to judge the propriety of such decision (assuming that it's actually happened) of the investigators handling the case. Moreover, we only have the filter on the situation you've chosen to apply, which is hardly helpful.

But keeping in this spirit of wild generalities without any supporting data, I'll say that what happened was perfectly reasonable, or not.

jonathangough · Member

Michael,

I can't think of a case where the use of speed ranges (or times or distances) is not appropriate. For example, let's say that you have a simple case of a vehicle that skidded to a stop. You measure the coefficient of friction with a drag sled and get ten different values ranging from 0.72 to 0.77, with an average of 0.75. Do you use the average of these values, or do you use the range (and distribution). On top of that, let's say you measured a 35 metre skid. What about the shadow skid, or the time between application of the brake and the appearance of a visible skid. Again, you have a range. Do you ignore it or include it in your calculations?

Virtually every number involved in any of your calculations has a confidence interval associated with it. If you can't (or won't) address these ranges, then you will find the lawyers grinding you down on the stand.

Jonathan

ashman165 · Veteran Member

jonathangough wrote:

Michael,

I can't think of a case where the use of speed ranges (or times or distances) is not appropriate. For example, let's say that you have a simple case of a vehicle that skidded to a stop. You measure the coefficient of friction with a drag sled and get ten different values ranging from 0.72 to 0.77, with an average of 0.75. Do you use the average of these values, or do you use the range (and distribution). On top of that, let's say you measured a 35 metre skid. What about the shadow skid, or the time between application of the brake and the appearance of a visible skid. Again, you have a range. Do you ignore it or include it in your calculations?

Virtually every number involved in any of your calculations has a confidence interval associated with it. If you can't (or won't) address these ranges, then you will find the lawyers grinding you down on the stand.

Jonathan

Well, hello there, namesake. It might cut against you sharing a name in common with me on here, but welcome.

I suppose I'll address your post in reverse order, as is my habit.

If you won't address ranges in some particular case, then you'll get torn apart by a lawyer provided you don't know what you're talking about, or can't well-articulate what it is you're meaning to convey.

I'm a bit confused by your statement about your statement involving "range (and distribution. . .". I gather from that statement taken in conjunction with your assertion about confidence intervals, that you deal in statistics to some degree, or at least have taken classes about that subject. So, I'm kind of operating under that premise here. That said, I'm curious as to how the distribution of those data would play an important role.

Such as I understand the concept, a distribution just informs the reader of how the data are grouped together. The distribution tells us the likelihood of getting a value, or a particular range of values in a sample of some population, while the confidence interval tells us the how confident we are that the true measure of center lives between two numbers in a range. I suppose this could be situationally handy to know, but I'm hard-pressed to see how it's directly relevant in this particular case. Of course, this doesn't even begin to address the type of average we'd like to use, and why it's the best choice. So, could you explain a little bit where you're going with that? Thanks! (I ask about this with respect to your example because in such a situation, we're attempting to determine a minimum speed traveled. That particular formula, aptly named at that, makes no attempt to represent that it's a true measure of speed; it's merely a derivation of physics which says that x amount of speed equivalent kinertic energy is required to leave behind this particular mark.)

So, it would seem that, evidenced by your example, you can imagine a situation in which a range of values wouldn't be appropriate. But even if I accept that you can't think of a case, I'm left with the original issue I had in mind upon reading your first sentence: big deal if you can't think of one. This is, to my mind, an argument of incredulity, which is roughly to say that "I can't think of x, therefore no x exists."

Were I on the other side of the aisle during a case, I'd surely have my side's attorney all over a person testifying about the "Slide to Stop" formula using a set of ranges, because that doesn't naturally comport with the formula's use.

mmiranda0811 · Member

I just completed a three day, vehicular homicide trial where the first investigator on scene used a speed range of between 41 MPH & 93 MPH. During cross examination he finally stated this was done with the calculator on his phone and he figured the range using 20 % to 100% braking efficiency. This wide range caused quite a stir with the jurors and if not for the quick mind and skill of the prosecutor and the testimony of the primary investigator, this could have caused a hugh problem in proving our case. They helped the jury understand what had occurred.

jonathangough · Member

ashman165 wrote:

I'm a bit confused by your statement about your statement involving "range (and distribution. . .". I gather from that statement taken in conjunction with your assertion about confidence intervals, that you deal in statistics to some degree, or at least have taken classes about that subject. So, I'm kind of operating under that premise here. That said, I'm curious as to how the distribution of those data would play an important role.

Johnathan,

I'll forgive your parents for the misspelling of your name.

However, as far as the issue of ranges and distribution are concerned, most of the parameters involved in calculations to do with MVA's have uncertainties associated with them. For example, if we are given the information that a skid occurred on dry asphalt and measured x metres, then it is necessary to assume a coefficient of friction before we can calculate speed. I have a database of approximately 1000 dry asphalt skid tests with ABS that I use as a reference. If I use the range from the very highest to the very lowest and then give a speed range of 40 to 70 km/h (for example), I'm giving my client information that is much less useful than if I told him that there was a 90% chance that the speed was between 50 and 60 km/h.

Once you get into calculations with more variables, this effect becomes much greater. If you have a momentum calculation where there are uncertainties in the incoming and outgoing angles of both vehicles, the coefficient of friction, and the weights of the vehicles, etc. it is much more valuable to be able to calculate the speeds with associated confidence intervals than it is to calculate absolute maxima and minima. The use of a spreadsheet with MonteCarlo analysis allows this to be done quickly and efficiently.

Jonathan

ashman165 · Veteran Member

jonathangough wrote:

ashman165 wrote:

I'm a bit confused by your statement about your statement involving "range (and distribution. . .". I gather from that statement taken in conjunction with your assertion about confidence intervals, that you deal in statistics to some degree, or at least have taken classes about that subject. So, I'm kind of operating under that premise here. That said, I'm curious as to how the distribution of those data would play an important role.

Johnathan,

I'll forgive your parents for the misspelling of your name.

However, as far as the issue of ranges and distribution are concerned, most of the parameters involved in calculations to do with MVA's have uncertainties associated with them. For example, if we are given the information that a skid occurred on dry asphalt and measured x metres, then it is necessary to assume a coefficient of friction before we can calculate speed. I have a database of approximately 1000 dry asphalt skid tests with ABS that I use as a reference. If I use the range from the very highest to the very lowest and then give a speed range of 40 to 70 km/h (for example), I'm giving my client information that is much less useful than if I told him that there was a 90% chance that the speed was between 50 and 60 km/h.

Once you get into calculations with more variables, this effect becomes much greater. If you have a momentum calculation where there are uncertainties in the incoming and outgoing angles of both vehicles, the coefficient of friction, and the weights of the vehicles, etc. it is much more valuable to be able to calculate the speeds with associated confidence intervals than it is to calculate absolute maxima and minima. The use of a spreadsheet with MonteCarlo analysis allows this to be done quickly and efficiently.

Jonathan

Oh, okay. My parents appreciate your largess.

I think this clears up where I was having difficulty in understanding your argument.

Yes, a range and confidence interval would be quite handy in a situation in which you're using statistics to show that a certain road might have some particular coefficient of friction, and how sure you are the alleged coefficient of friction is what it probably had. This, however, to my mind, would be bad form because it's much better to actually go to the roadway in question and test it as opposed to guessing from statistics about similar roads. Moreover, I'm not sure that there's any probative value in using statistics to speak about a roadway which you haven't actually measured. In short, you're giving your client much less information about his case than if you'd actually done tests on the scene in question.

What is one to tell the jury? That there are data suggesting that at least one thousand roadways in all of the world have a particular range of coefficients of friction? This, of course, presumes that a roadway in and of itself has a coefficient of friction, which is patently untrue. It is no more the case than a light bulb possesses its own light. The coefficient of friction, like the light in light bulb, is a function of 2 disparate things happening in the same place at the same time.

But even if I were going to assume arguendo (albeit dubitante) that a roadway does in and itself have some absolute coefficient of friction, I'm not seeing how what one thousand other roadways in the world brings to bear on the roadway I have in question. Besides, here we're dealing with your alleged percentage of 90, which still implies that one out of ten times you make that argument, you'll be wrong. Of course, that will only work itself out if you do many trials with that particular assumption. In a small sample, it's is quite likely that you'll get a string of trials in which the true coefficient of friction will not be within the range you assert. Remember the rub in statistics of this sort; any sample is roughly equally likely to be drawn. This includes a sample mean which doesn't bear any relation to the population mean, and by extension a sample standard deviation which is not the population standard deviation.

About the Central Limit Theorem (the second fundamental theorem of probability) and how this applies: this section is intentionally left largely blank. Suffice it to say that as n sample size increases, the sample distribution approaches the normal distribution without regard to the actual distribution. (See last sentence in paragraph above for relevance.)

Then there are the issues we'd have to resolve with your sample size and how it wouldn't support a confidence of interval of 90% within any range.

And of course there'd be an issue with it being irrelevant what a thousand other roadways were like because it's at best anecdotal evidence that your roadway might mimic those others. Then again, it might not.

This, of course, excludes all the conversations about the mathematics behind the formulae used, and their error. So, yes, it's true that more variables that are introduced, there is a potential for more error (though this isn't necessarily true, and indeed is often not true), it doesn't do to say simply because there might be some error here, we're okay to add in more error there. Indeed, I'd argue the contrary is true: if there is some error here we can't eliminate, we should work that much the harder there to remove as much of its error as possible.

Statistics doesn't do that.

I'm also not sure of the sagaciousness of using a statistical model (which doesn't even claim to be an accurate model. It only claims that it is possibly accurate) instead of using the absolute extrema, not that the end points in a confidence interval aren't being used as the same thing here. The only difference, as I understand it, is that using the absolute extrema says out right that these are the bounds beyond which nothing else is possible whereas statistics will say that these are the absolute bounds beyond which nothing else is possible, except in the cases when these statistics are wrong and thus don't hold. But we have no way to test that, so you should just assume that they are right, because they are, except for when they're not.

The absolute extrema (and I'll accept arguendo that these are absolutes) are proveable as finite bounds instead of a conjecture about what the bounds likely are to be.

Now for the distribution issue. The distribution tells us how common the uncommon is. For instance, if all the data are within .01 of some number, the distribution is far more useful than if it fluctuates by .1. Indeed, it's a whole order of magnitude better.

I suppose that statistics might be sufficient to disprove (at least enough to cast a reasonable doubt on) some assumption the state is making, but I'm not sure that it would be sufficient overcome the burden of the state to prove that x and y happened. But surely statistics can show that the result achieved is unlikely to be the case for the defense's view.

Of course, I'm speaking here of criminal liability, not civil. That's a whole other kettle of fish.

-- Edited by ashman165 on Tuesday 5th of May 2009 09:39:44 AM

-- Edited by ashman165 on Tuesday 5th of May 2009 09:40:35 AM

-- Edited by ashman165 on Tuesday 5th of May 2009 09:41:36 AM

jonathangough · Member

Johnathan,

Your comments about measurements and accuracy suggest that you haven't been out at an accident scene and made actual measurements.

If you take something as simple as a skid mark and have 10 people measure it, they will all come up with different values. Similarly, if those 10 people all measure the coefficient of friction, they will come up with different values. If you insist that your measurements are perfect and everyone else is wrong, then go ahead and assume that there are no ranges and confidence intervals. I'd rather accept the fact that there is some uncertainty in the measurements (as shown in a number of SAE publications) and make my calculations accordingly.

Jonathan

ashman165 · Veteran Member

jonathangough wrote:

Johnathan,

Your comments about measurements and accuracy suggest that you haven't been out at an accident scene and made actual measurements.

If you take something as simple as a skid mark and have 10 people measure it, they will all come up with different values. Similarly, if those 10 people all measure the coefficient of friction, they will come up with different values. If you insist that your measurements are perfect and everyone else is wrong, then go ahead and assume that there are no ranges and confidence intervals. I'd rather accept the fact that there is some uncertainty in the measurements (as shown in a number of SAE publications) and make my calculations accordingly.

Jonathan

A far better method of response on your part would have been to address why your apparent misapplication of statistics warrants serious attention. Instead of doing that, you build up some kind of bastardized stawman argument which purports to impugn my response. In short, you offered up nothing in the way of support of your technique. Even if we assume that I'm completely wrong, it doesn't logically follow that you are correct. This is why in science (and to a greater extent mathematics) requires evidence (and proof respectively) in support of one's assertions. Merely discrediting some competing idea in no way provides support for one's own theories, hypotheses.

Just so we're clear here, you have misconstrued accuracy and precision.

And of course, not only did you not provide any support for why your technique might be valid, you failed to speak to any of the issue I brought up; namely, you completely disregarded the very fundamental rules of probability.

BlueB · Veteran Member

A healthy discussion was made on some skid test results wher it was debated that the reulst applied to about 85% of vehicles and that meant some 15% would be outside that range. Fair enough. Then you consider that the 15% tended to have unusual variables that caused them to be outside the range of the majority, and those variables were not applicable in the subject case.
It is always comforting when your report is queried in such minute detail. It kind of says that you have it about right and they are simply trying to stretch the boundaries to their favour.
And lets be realistic, if the case stands or falls depending on the third decimal place of mu, then it was a pretty unsafe case in the first place.

ashman165 · Veteran Member

From this I can surmise that the debate was only focused on the third decimal place? Really?

Do you have some data from these you can throw up so we can have a look? I'd be very interested to look at these data to see if they only argued over something in the thousandths place. Perhaps it was the case that the 15% of vehicles weren't the ones with confounding variables. Remember that in these types of statistical analyses, any sample is roughly equally likely to be drawn. So, it could very well be the case that these 85% were the ones with the confounding variables.

Of course, I'm left to ponder if the lurking variables were the same in each car, or if each one had a different something another going on which took them outside of the 85th percentile. Also, how many cars were in this test? Because if the sample size was small, then very little, if any, meaningful information can be drawn from the tests because the potential for error is substantially high.

-- Edited by ashman165 on Tuesday 12th of May 2009 10:41:06 AM