/
Quantifying measurement error Quantifying measurement error

Quantifying measurement error - PowerPoint Presentation

cheryl-pisano
cheryl-pisano . @cheryl-pisano
Follow
386 views
Uploaded On 2017-08-15

Quantifying measurement error - PPT Presentation

Blake Laing Southern Adventist University I uncertainty Measurements have no meaning without a quantified experimental erroruncertainty George What can he conclude Martha ID: 578980

measurement error measurements standard error measurement standard measurements systematic precision deviation confidence random probability quantified glucose accuracy notes compare

Share:

Link:

Embed:

Download Presentation from below link

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.


Presentation Transcript

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/

dLSlide8
Slide9

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 sanitySlide13
Slide14

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