Relative Positional Precision

Relative Positional Precision Is Statistical

You can teach yourself statistics by measuring the same things a few times and comparing your results. The more precise you are in your measuring, the more likely the results will differ very little. The more likely that errors creep in then your results will vary quite a bit. Since it is known that no measurement can be exact, there is hence a need to use techniques where the variance in what we measure must be within the limits of our acceptable precision.

There are two methods to show that surveyed positions of points are within an acceptable range:

1, Use a statistical analysis.

2, Resurvey it using a more precise method, using a more precise instrument, more precise setups and/or meaned repetitive observations (which unfortunately is a statistical process).

Any further questions? I have a question for you, what is your surveying training, education and experience?

You can learn statistics in an academic method or on the job by experience, some of which will be most likely bad.

Statistics is inherent in everything we do. Sports, weather, salmonella in your food, poker or any other form of gambling. For instance if you play the Powerball Lottery and drive more than 1 mile to buy a ticket you have a better chance of dying in a car accident during that purchase than actually winning the lottery. Fortunately I have to drive 0.2 miles.

I have a civil engineering BS and 42 credit hours in surveying and not a single statistics course. However in Surveying 1 we learned statistics the old fashion way, taping long distances with a 100' tape, plumb bobs and chaining pins and be turning repetitive angles with transits. Again and again in course after course something new was learned about statistics.

Paul in PA

You need to start with a few basic concepts.

1. Every measurement you make contains error. There is no way around this rule. Understand it and deal with it, but never ignore it.

2. You should never adjust data that contains blunders. Blunders are different from errors. You can eliminate blunders with carefully planned procedures, well trained personnel and meticulously maintained equipment.

3. There are two different types of error. Systematic error can be predicted and corrected or eliminated. (A good example of systematic error is the temperature corrections we used to apply when taping with steel tapes.) Once you have accounted for the systematic errors, the only thing left in your data should be random error.

4. Random errors are equally likely to be positive or negative and are more likely to be small than large. Thus, if you graph random random error you should end up with a bell shaped curve. You deal with random error using statistical methods. Here is where understanding standard deviation comes into play.

I could go on and on (and have to the tune of an 8 hour class on the subject). Suffice to say for now that those are the 4 most important basic concepts to understand.

Hope that helps.

Larry P

After Larry's points, the first real statistical concepts you need are mean and standard deviation.

Set your first goal as just learning what these mean in a practical sense (not just mathematical). Don't worry about anything beyond those until you have a feeling for those.

Paul's exercises would be one way to develop an intuitive feeling.

Relative Positional Precision..while important..

Name a surveyor who was brought to court and found negligent on not conforming to the R.P.P. standard.

While I feel its very important to meet the requirement, in an ALTA survey, this is the least of your concerns.

When we count something, such as beans in a jar, you and I should both get the same number of beans. The beans are discrete elements. Neither of us can mistake a partial bean or have to decide what is a bean and what is not.

On the other hand, any measurement is not discrete. Measurements are quantifications of a discrete element, but the scale used is an arbitrary one based on some standard unit. The value reported will be an estimated one lying between two of the smallest marked increments of the standard unit.

The purpose of making the measurement is to be able to report something about a particular characteristic of that item; length, width, area, temperature, etc. The actual dimension is not known and cannot be known due to the arbitrary nature of the measurement scale itself. The role of a statistical analysis is to be able to make a statement about the quality of the measurement.

Now comes the concept of accuracy v. precision.

When making measurements, we try to develop a method that is repeatable and easy to perform. We make multiple measurements and compare the results. If the values are all very close together, meaning that the difference between the individual measurements is very small compared to the actual measurement, we can say that they are precise.

The example used most often is shooting arrows at a target. If we shoot five arrows that all hit within a two inch circle in the one point ring, the shooting is precise, but not accurate. If we shoot five arrows that end up all around the bully's eye in the one point ring, we can say that the shooting is accurate, but not precise.

Precise does not mean correct. That's the purpose of accurate. In a set of accurate measurements, each measurement is of by a similar amount and the values are all around the actual value.

We can say that the board is 4.257 feet long, plus or minus 0.002 feet. We mean that we believe the board's actual length to be between 4.255 and 4.259 feet. That's pretty precise. We can also say that the length of the snake was 4.274 feet, plus or minus 0.5 feet. That's not very precise. That's where the standard deviation comes in, together with the number of decimal places we report in our measurement and our deviation, it makes a statement about the quality of our data. Of course, it's assumed that you've taken enough measurements to make a significant statement about the quality, but, that's another issue.

Statistics is a language that is used to describe the precision and accuracy of our set of measurements.

The relative positional tolerance statement require by the Land Title Survey standards is simply a statement describing how precise our measurements are regards the location of a particular point. We can't ever make a statement about the accuracy of our survey measurements because, unlike the target, we do not have a bully's eye to compare our measurements to. We assume that in our measurements are precise, because of the techniques we employe, they will be accurate, too.

Let's use analogy. We'll use lengths of lath for the distances we measure. At the end of each lath, we'll drill a hole. We'll bolt each piece of lath together into a framework lattice. The size and shape of the holes needed to slip the bolts through the ends of the lath will vary. Some will be quite large; others will be quite small. Most holes will be oval in shape, longer in one axis than the other.

The relative positional tolerance statement that we are required to make is a statement about the "quality" of the "holes" in our survey. Are they small and pretty circular or are they huge and pretty oval?

Going much further is going to require math. How far do you want to go?

I'm impressed that Larry can pack a stats course into eight hours. I've got four or five semesters of stats classes under my belt and I still have to pull out the slide rule to understand position, at times.

Standard deviation...for people like me..

Math is funner with pictures...

Does it work on Cats too?

Just curious!

James

Thanks all.

I've been surveying for about 20 years. My education is the technical college kind with some Civil Engineering classes thrown in for good measure.

I understand everything that you all were saying (especially the dogs LOL).

The main problem I have is translating all that into something that is easily explained to others. The dog link helped. Does that say something about my level of intelligence? ha!

The trouble I have is when talking about "Relative Positional Precision" the discussion quickly becomes mired down in terminology. Going to a text book to get a definition of a term seems to lead down a wormhole of other terms and definitions.

Does a surveyor need to take an 8 hour course in statistics to be able to comfortably say they have met the tolerance in the standard?

While I agree with Joe that it may never come up in court, what happens if it does and the first question to the surveyor is "Can you please explain to us the concept of Relative Positions Precision" or a volley of statistics questions?

Just sayin....

How many attorney's actully understand statistics?...I'd say few.

Attorneys are smarter than to challange a surveyor on something they know a surveyor has more knowledge than he/she does...

Do have a book with all the answers sitting there?!

Send me a copy!

Thanks Joe.

Relative Positional Precision Is Statistical

Just out of curiosity, what engineering school does not require statistics?

Case made, it is assumed that given our profession we understand statistics. To be honest you should have a good working knowledge of calculus to understand the propagation of errors in your measurements as well.

Does it work on Cats too?

They tried it with cats but the standard deviation was 1000 times larger than the variance. More study is needed.

Now that we all have various electronic instruments, it is often the case that our RPP or RPT of measurements among monuments exceeds the RPP of the monument itself. WHAT?
WV case: 2 acres, one boundary a state road, prescriptive R/W, no documentation of any sort. A large jagged stone corner marker. A bent up 3" iron pipe. A concrete monument busted up by repeated application of a brush hog. I think I can prove 95% confidence of measurements among them plus or minus 0.05'; but what is the actual center of the jagged stone? The center of mass? The jagged tip top way off apparent center? How about the black top road: the paint line down the middle? The beat up pipe: surly not the top; dig it up and try to guess the position of the bottom? But these are easy compared to the 36" oak or the stone pile or other amorphous objects used for corners. Our measurement accuracy has exceeded the accuracy of the monuments. We have allowed title attorneys and ACSM academics to put us in a position of certifying that we have met a standard that cannot be met in the real world, with real world objects.

Amen!!

I love when I see 3 decimals places to the centerline of a stonewall...

I've always thought all this ALTA positional tolerance emphasis is total BS. Doesn't signing and sealing a survey indicate that you are a professional, have studied this stuff and understand how to measure and have confidence in your results? I know this isn't necessarily true in all cases. ALTAs are are about jumping through ridiculous hoops and taking on way more liability than we should.

> How many attorney's actully understand statistics?...I'd say few.
>
> Attorneys are smarter than to challange a surveyor on something they know a surveyor has more knowledge than he/she does...

Attorneys should be challenging surveyors not on the math itself, but their use of math over boundary law principles. We should understand these concepts better than an attorney but as a whole I would say we don't.

There is a great book on statistical analysis of survey measurements:

"Errors in Practical Measurementin Surveying, Engineering, and Technology" by B. Austin Barry, published by John Wiley & Sons in 1978 and re-published by Landmark Enterprises in 1991.

Very readable and fairly easy to understand. See page 15 for excellent description of precision vs accuracy.

Does it work on Cats too?

The problem is that you have to heard them cats into one area before you even start to work on measuring them......good luck with that.;-)