Blake Laing Southern Adventist University I uncertainty Measurements have no meaning without a quantified experimental erroruncertainty George What can he conclude Martha ID: 578980
Download Presentation The PPT/PDF document "Quantifying measurement error" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Quantifying measurement error
Blake LaingSouthern Adventist UniversitySlide2
I
uncertainty Measurements have no meaning without a quantified experimental error/uncertainty Slide3
George:
What can he conclude?
Martha:
What can she conclude?
UncertaintySlide4
Uncertainty due to measurement error
A personal error is a mistake. No need to quantify, but we should be able to recognize mistaken dataTwo other measurement errors which are not accidentalRandom error Causes repeated measurements to be different
Causes wide “margin of error”
Systematic error
Repeated measurements are consistent
All measurements are
shifted
in a predictable wayCan be recognized and corrected by “shifting back”Slide5
Accuracy
Precision
Accuracy is not precision
Precision
“how
close
to each other
”
Accuracy
“
how close
to expected
”
Random error
Different error every time
Limits precision
Systematic error
Same error every time
Limits accuracySlide6
Random error
Quantified by statisticsSlide7
Same breakfast: toast with almond butter
Statistics in real life
Morning blood
glucose mass
concentration
day
glucose
(mg/dL)11102119
3123
7
129
13
90
If
weekly average > 120 mg/
dL
, must take insulin
Same breakfast: toast with almond butter
Different results
Summary
Max:
129
mg/
dL
Min:
90
mg/
dL
Mean:
109.5
mg/
dLSlide8Slide9
Random or systematic error?
Gaussian distribution, or “bell-curve”
68% within some “distance” of mean
That “distance” is called the standard deviation
68% within
or
A 68% of past measurements were within
There
was a 68% probability for each measurement
to be within
.
68% confidence interval
I can say with 68% confidence that the
next
measurement will be within
.
The precision of each measurement is quantified by
Systematic error: comparison to known
68% probability that absolute error
Slide10
Random
error/precision in one measurement is quantified by
68% confidence interval
I can say with 68% confidence that the
next
measurement will be within
.means that 68% of repeated measurements will be within one standard deviation of the average95% confidence interval95% of previous measurements within .I can say with 95% confidence that the next measurement will be within
. means that 95% of repeated measurements will be within two
standard deviation of the averageGood way to state precision of instrument
Slide11
Precision of the mean quantified by α
Let’s take 100 measurements!Will standard deviation decrease?
Shouldn’t we know mean value more precisely?
Precision of the mean, or “error of the mean” is quantified by the standard error.
68
%
probability that the mean of a many more measurements would be within
If there were no systematic error…
the mean of many more measurements would be equal to the true value
There is a 68
% probability that the true value is within
More
common:
95%
confidence int.
Slide12
68% CI for the next measurement
=
95% CI for the next measurement
Blood glucose
concentration
day
glucose
(
mg/
dL
)
1
110
Maximum:
129
mg/
dL
2
119
Minimum:
90
mg/dL
3
129
Mean:
109.5
mg/
dL
4
109
σ
:
10
mg/
dL
5
123
N:
16
Days
6
106
α
:
4
mg/
dL
Measure with sanitySlide13Slide14
68% CI for the next measurement
=
95% CI for the next measurement
68% CI for mean value
95% CI for mean value
Blood glucose
concentration
day
glucose
(
mg/
dL
)
1
110
Maximum:
129
mg/
dL
2
119
Minimum:
90
mg/dL
3
129
Mean:
109.5
mg/
dL
4
109
σ
:
10
mg/
dL
5
123
N:
16
Days
6
106
α
:
4
mg/
dL
Measure with sanitySlide15
Systematic error
Comparison to expectationSlide16
Systematic error: compare to “known”
Suppose that medical laboratory glucometer measures
(68% CI)
Compare home device to this
(68% CI)
Absolute error:
Slide17
Compared to what?
Compare abs. err. to expectation
Compare to random error in home device
Is the absolute error large compared to the standar
d error?
Then the mean for the home device has a significant systematic error.
How many
standard errors?
May not need to be calibrated
Slide18
Quantifying measurement error
Problem
Source of error
Measure
Relative measure
Poor accuracy
Systematic error
Absolute error:
Percent error
Poor precision
Random error
One measurement: std. dev.
σ
Mean value: std.
err.
Percentage std.
err.
Problem
Source of error
Measure
Relative measure
Poor accuracy
Systematic error
Poor precision
Random errorSlide19
NotesSlide20
Experimental notesSlide21
Advice from previous students
“Take the time to get well acquainted with standard deviation and standard error on your first few labs... you'll be seeing them all year!”“Learn how to quantify measurements in the beginning - believe me. I
didn't fully learn how to use the tools of the trade till the beginning of the second semester, and it
would have paid to learn it first
.”
“Know the significant figures for sure: locking in the understanding at the start of the semester saves you A LOT of points.”Slide22
Notes from the reader
Need precise, quantitative answers to questionsLess wordy “fluff”, more equations/numbers. In every questions it is implied to use or refer to the appropriate “tool for the job”, such as percent error.Need careful articulation of words to be able to have a carefully-articulated understanding
.
Common mistakes on significant figures
use calculated standard error to determine correct sig figs on the mean
When calculating percent error, watch for the loss of sig figs when subtractingSlide23
Because I always back up my argument with an incisive quantitative analysis. Slide24
Quantifying measurement error
necessary to form quantitative conclusionsSlide25
See Dr. Laing bleed for scienceSlide26
Was that glucometer really so bad?
Expected value: 140 mg/dLMean value: about 267±1 mg/dLSlide27
A faulty assumption is a systematic error
Two hours after breakfastAqueous glucose vs whole bloodblood has a pH of about 7.4 (basic)Distilled water has a pH < 7 (acidic)
Different density
Standard deviation about half of aqueous glucose solution
What is the 95% CI for each measurement?
What is the 95% CI for mean?
Trial
concentration (mg/dL)1104N=32
2
99
Max=
110
mg/dL
3
106
Min=
83
mg/dL
4
102
5
99
Mean=
94.41
mg/dL
6
94
σ=
6
mg/dL
7
94
α=
1
mg/
dLSlide28
Reader notes
It appears that a number of people don’t have a solid grasp on what the 68% confidence intervals xav ± σ
n
m or
x
av
± αn mean. CI for each measurement: is a range of possible values of the measurementAbout 68% of the measurements were within this range.Implies that each measurement had a 68% probability of being within that rangeImplies that it is exceedingly unlikely to be due to random error if one additional measurement is 10 awayCI for mean value
Implies that
if there is no systematic error
, there is a 68% probability that the true value is within this range
Less wordy, more equations/numbers. In every questions it is implied to use or refer to the appropriate “tool for the job”, such as percent error.
Statements like “Systematic error is 180
” are concerning.
Need careful articulation of words to be able to have a carefully-articulated understanding.
Feel free to use pencil on everything but raw data
Slide29
Question 1
Does the standard deviation get much smaller as more measurements are taken? How about the standard error? Demonstrate by making a table of the standard deviation and standard error for 5, 25, and 50 data points using your data, and for all points of the class data. Would σ or α be more appropriate to describe the precision of an instrument?
Number
Standard deviation σ
Standard error α
5
10ish
4ish2510ish
2ish
50
10ish
2ish
300
10ish
1ish or lessSlide30
NotesSlide31
Post-analysis