L2: Error and Uncertainty Flashcards
What are the two main tasks of surveying?
Making observations / taking measurements
Analyzing and computing the measurements
What is the rule for rounding 5s and why is it used?
Always round to the nearest EVEN number
This balances out the rounding error to avoid systematic bias
What are two synonyms for a mistake?
Blunder
Gross Error
List a few common gross errors
In general they are due to carelessness or incompetence
Some examples:
- omitting a whole tape length when measuring distance
- sighting the wrong target in a round of angles
- transposing error (ex: 28.342 to 28.432)
- misreading a levelling staff
What are the three main categories of sources of error (briefly describe each)?
NATURAL errors: caused by variations in wind, temperature, humidity, atmospheric pressure (and to a lesser extent atmospheric refraction and gravity)
INSTRUMENTAL errors: imperfection in the construction or adjustment of instruments and from the movement of individual parts
PERSONAL errors: from the limitations of human senses of sight and touch (ex: slightly misaligned crosshair or target slightly out of plumb)
Identify the three main types of errors
Gross
Systematic
Random
(if they ask for two say systematic and random)
Describe systematic errors
Generally attributable to known circumstances, they are are consistent throughout a series of measurements (having the same magnitude and sign throughout)
They usually follow some sort of mathematical law and therefore can be calculated and applied as a correction
What are the two main sources of systematic errors (give an example of each)?
NATURE: refraction of light rays, thermal expansion/contraction of steel tape
INSTRUMENTS: maladjustment of theodolite/level, index error in spring balances, ageing crystals in EDM equipment
What is the formula for precision between two values?
Difference between the values divided by the average of the two values
Describe random errors
Errors that remain after all other errors have been removed
Their magnitude and sign are NOT constant
They are beyond the control of the observer
Usually assume a normal distribution of random variables
Often you can eliminate the effects of random error by taking the average of several measurements
What is the difference between precision and accuracy?
Precision: a relative grouping without regard to nearness to the truth
Accuracy: absolute nearness to the truth
Scatter is an indicator of precision but not necessarily accuracy
Describe the three statistical principals behind the analysis of random errors
1) Small errors occur frequently and are therefore more probable than large ones
2) Large errors occur infrequently and are therefore less probable than small ones (very large errors are often due to mistakes not random errors)
3) Positive and negative errors of the same magnitude are equally probable and happen with equal frequency
What is the true value?
The value that would be obtained by a perfect measurement
What is the formula for relative error?
Rx = εx / x
Where:
Rx - relative error
εx - true error
x - observed value
What is the most probable value (MPV) and how can it be calculated?
The closest approximation to the true value
Found by taking the arithmetic mean of a set of data
What is the formula for accuracy?
Accuracy = True Value - MPV
What are four principals regarding errors in observations?
1) No observation is exact
2) Every observation contains errors
3) The true value of an observation is never known
4) The exact error present is always unknown
What are small residuals indicative of?
High precision
Therefore lower standard deviation and therefore thinner normal distribution
What are the two parameters defining a normal distribution function?
1) MPV
2) standard deviation
What is the formula for the standard deviation of a data set?
Sx = ± sqrt( (sum of individual differences from mean squared) / (n-1) )
Where:
Sx - standard deviation
n - number of measurements
What is the formula for the standard error of the MPV?
Sx̄ = ± Sx / Sqrt(n)
Where:
Sx̄ - standard error
Sx - standard deviation
n - number of measurements
What is a confidence interval?
The limits or ranges within which true values are assumed to occur
What is error propogation?
The process of evaluating errors in quantities computed from observed values that contain errors
What is the formula for the error of a series of n measurements?
E series = ± E*sqrt(n)
Where:
E series - total error of the series
E - error of individual measurements
n - number of measurements
What is the formula for the error of a product of two measurements A and B?
E prod = ± sqrt( (AEa)² + (BEb)² )
Where:
E prod - total error of the product
A - measurement A
Ea - error of measurement A
B - measurement B
Eb - error of measurement B
What is the formula for the error of a mean in a series of measurements?
E m = E series / n
OR
E m = E / sqrt(n)
Where:
E m - error of a mean (standard error)
E series - error of the series
E - error of an individual measurement
n - number of measurements
List the following classifications from most to least accurate: First Order, Second Order, Third Order
Most accurate: First Order
Second Order
Least accurate: Third Order
Why do we not always go for extreme accuracy?
Trade off with cost
