accuracy and precision of measurement © 2012 project lead the way, inc.introduction to engineering...
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Accuracy and Precision
of Measurement
© 2012 Project Lead The Way, Inc.Introduction to Engineering Design
Recording Measurements
• A measurement always includes a value• A measurement always includes units• A measurement always involves
uncertainty– A measurement is the best estimate of a
quantity– A measurement is useful if we can quantify
the uncertainty
Sources of Error in Measurement
• Potential errors create uncertainty• Two sources of error in measurement
– Random Error• Errors without a predictable pattern• E.g., reading scale where actual value is between
marks and value is estimated• Can be determined by repeated measurements
– Systematic Error• Errors that consistently cause measurement value
to be too large or too small• E.g., reading from the end of a meter stick instead
of from the zero mark
Uncertainty in Measurements• Scientists and engineers often use significant
digits to indicate the uncertainty of a measurement– A measurement is recorded such that all certain digits
are reported and one uncertain (estimated) digit is reported
Uncertainty in Measurements
• Another (more definitive) method to indicate uncertainty is to use plus/minus notation
– Example: 3.84 ± .05 cm • 3.79 ≤ true value ≤ 3.89• This means that we are certain the true
measurement lies between 3.79 cm and 3.89 cm
Uncertainty in Measurement
• In some cases the uncertainty from a digital or analog instrument is greater than indicated by the scale or reading display– Resolution of the instrument is better than the
accuracy• Example: Speedometers
How can we determine, with confidence, how close a measurement is to the true value?
Uncertainty in Measurement
• Uncertainty of single measurement− How close is this measurement to the true value?− Uncertainty dependent on instrument and scale
• Uncertainty in repeated measurements− Random error− Best estimate is the mean of the values
Accuracy and Precision
• Accuracy = the degree of closeness of measurements of a quantity to the actual (or accepted) value
• Precision (repeatability) = the degree to which repeated measurements show the same result
High AccuracyLow Precision
Low AccuracyHigh Precision
High AccuracyHigh Precision
Accuracy and Precision• Ideally, a measurement device is both accurate
and precise• Accuracy is dependent on calibration to a
standard– Correctness– Poor accuracy results from procedural or equipment
flaws– Poor accuracy is associated with systematic errors
• Precision is dependent on the capabilities of the measuring device and its use– Reproducibility– Poor precision is associated with random error
Your Turn
Two students each measure the length of a credit card four times. Student A measures with a plastic ruler, and student B measures with a precision measuring instrument called a micrometer.
Student A Student B85.1mm 85.701 mm
85.0 mm 85.698 mm
85.2 mm 85.699 mm
84.9 mm 85.701 mm
Your TurnPlot Student A’s data on a number line
Student A Student B85.1mm 85.301 mm
85.0 mm 85.298 mm
85.2 mm 85.299 mm
85.1 mm 85.301 mm
Plot Student B’s data on a number line
Your TurnStudent A’s data ranges from 85.0 mm to 85.2 mm
Student B’s data ranges from 85.298 mm to 85.301 mm
The accepted length of the credit card is 85.105 mm
85.1
05
Accepted Value
Your Turn
Which student’s data is more accurate?
Which student’s data is more precise?
Student A
Student B
Quantifying Accuracy
Error = measured value – accepted valuemean of
s
Student A Student B85.1mm 85.301 mm
85.0 mm 85.298 mm
85.2 mm 85.299 mm
85.1 mm 85.301 mm
Student A:
A = 85.10 mm
Student B:
B = 85.2998 mm
The accuracy of a measurement is related to the error between the measurement value and the accepted value
Quantifying Accuracy
Calculate the error of Student A’s measurementsError A = mean of measured values – accepted value
Error A = 85.10 mm – 85.105 mm = − 0.005 mm
A =
85
.10
85.1
05
Error- 0.005
Acc
ep
ted
V
alu
e
Quantifying Accuracy
A =
85
.10
Acc
ep
ted
V
alu
e85
.105
Error- 0.005 Error
0.1948
B=
85
.299
8
Calculate the error of Student B’s measurementsError B = mean of measured values – accepted value
Error B = 85.2998 mm – 85.105 mm = 0.1948 mm
Error|0.1948|= 0.1948
Quantifying Accuracy
A =
85
.10
Acc
ep
ted
V
alu
e85
.105
Error- 0.005 Error
0.1948
B=
85
.299
8
Calculate the error of Student B’s measurementsError B = mean of measured values – accepted value
Error B = 85.2998 mm – 85.105 mm = 0.1948 mm
Error|- 0.005|= 0.005
Error|0.1948|= 0.1948
Quantifying Accuracy
A =
85
.10
Acc
ep
ted
V
alu
e85
.105
Error- 0.005 Error
0.1948
B=
85
.299
8
Calculate the error of Student B’s measurementsError B = mean of measured values – accepted value
Error B = 85.2998 mm – 85.105 mm = 0.1948 mm
Error|- 0.005|= 0.005
Student AMORE ACCURATE
Quantifying Precision
Precision is related to the variation in measurement data due to random errors that produce differing values when a measurement is repeated
Quantifying Precision
Student A Student B85.1mm 85.301 mm
85.0 mm 85.298 mm
85.2 mm 85.299 mm
85.1 mm 85.301 mm
Student A: sA= 0.08 mm
Student B: sB = 0.0015 mm
The precision of a measurement device can be related to the standard deviation of repeated measurement data
Quantifying Precision
Use the empirical rule to express precision• True value is within one standard deviation of the
mean with 68% confidence• True value is within two standard deviations of the
mean with 95% confidence
Quantifying Precision
Express the precision indicated by Student A’s data at the 68% confidence level• True value is 85.10 ± 0.08 mm with 68%
confidence 85.10 − 0.08 mm ≤ true value ≤ 85.10 + 0.08 mm
Student A:
A= 85.10 mmsA= 0.07 mm
85.02 mm ≤ true value ≤ 85.18 mm with 68% confidence
Quantifying Precision
Express the precision indicated by Student A’s data at the 95% confidence level• True value is 85.10 ± 2(0.08) mm with 95%
confidence 85.10 − 0.16 mm ≤ true value ≤ 85.10 + 0.16 mm
Student A:
A= 85.10 mmsA= 0.07 mm
84.94 mm ≤ true value ≤ 85.26 mm with 95% confidence
The Statistics of Accuracy and Precision
A B
C D
High AccuracyHigh Precision
Low AccuracyLow Precision
High AccuracyLow Precision
Low AccuracyHigh Precision
Gauge Blocks (Gage Blocks)
• A block whose length is precisely and accurately known Standard = basis of comparison
• Precision measuring devices are often calibrated using gauge blocks Calibrate = to check or adjust by
comparison to a standard