random errors in chemical analysis -iistaff.buffalostate.edu/nazareay/che301/che301l5.pdf ·...
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![Page 1: Random Errors in Chemical Analysis -IIstaff.buffalostate.edu/nazareay/che301/che301l5.pdf · 2016-02-03 · Random Errors in Chemical Analysis -II. A measurement x 1, with m and s](https://reader030.vdocuments.mx/reader030/viewer/2022040600/5e8da4b16163a501e42405b2/html5/thumbnails/1.jpg)
Lecture 5
Random Errors in
Chemical Analysis -II
![Page 2: Random Errors in Chemical Analysis -IIstaff.buffalostate.edu/nazareay/che301/che301l5.pdf · 2016-02-03 · Random Errors in Chemical Analysis -II. A measurement x 1, with m and s](https://reader030.vdocuments.mx/reader030/viewer/2022040600/5e8da4b16163a501e42405b2/html5/thumbnails/2.jpg)
A measurement x1, with
m and s
m
I am making a second measurement x2
of the same analyte.
Random!
m
It has the same m We do not know it!
It has the same s
As an estimate of my unknown m
I will use average 2
21 xxx
sssss 22 22
2
2
121
22
2
2
21 ssss
av
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…………
If I am making N measurements of the same value
N
xxxx N
...21
Nav
ss
![Page 4: Random Errors in Chemical Analysis -IIstaff.buffalostate.edu/nazareay/che301/che301l5.pdf · 2016-02-03 · Random Errors in Chemical Analysis -II. A measurement x 1, with m and s](https://reader030.vdocuments.mx/reader030/viewer/2022040600/5e8da4b16163a501e42405b2/html5/thumbnails/4.jpg)
![Page 5: Random Errors in Chemical Analysis -IIstaff.buffalostate.edu/nazareay/che301/che301l5.pdf · 2016-02-03 · Random Errors in Chemical Analysis -II. A measurement x 1, with m and s](https://reader030.vdocuments.mx/reader030/viewer/2022040600/5e8da4b16163a501e42405b2/html5/thumbnails/5.jpg)
Case 3: We know:
Standard deviation sReal value ?
Take N measurements; calculate average as
N
xxxx N
...21
Nx
sm
2 with 95% probability
Coinfidence interval (CI)
![Page 6: Random Errors in Chemical Analysis -IIstaff.buffalostate.edu/nazareay/che301/che301l5.pdf · 2016-02-03 · Random Errors in Chemical Analysis -II. A measurement x 1, with m and s](https://reader030.vdocuments.mx/reader030/viewer/2022040600/5e8da4b16163a501e42405b2/html5/thumbnails/6.jpg)
Case 4 We know nothing:
Mean - ? Standard deviation -?
Take N measurements; calculate average as
N
xxxx N
...21
Calculate standard deviation as
1
)(...)()( 22
2
2
1
N
xxxxxxs N
Confidence interval?
I do not know s !
![Page 7: Random Errors in Chemical Analysis -IIstaff.buffalostate.edu/nazareay/che301/che301l5.pdf · 2016-02-03 · Random Errors in Chemical Analysis -II. A measurement x 1, with m and s](https://reader030.vdocuments.mx/reader030/viewer/2022040600/5e8da4b16163a501e42405b2/html5/thumbnails/7.jpg)
![Page 8: Random Errors in Chemical Analysis -IIstaff.buffalostate.edu/nazareay/che301/che301l5.pdf · 2016-02-03 · Random Errors in Chemical Analysis -II. A measurement x 1, with m and s](https://reader030.vdocuments.mx/reader030/viewer/2022040600/5e8da4b16163a501e42405b2/html5/thumbnails/8.jpg)
Case 4 We know nothing:
Mean - ? Standard deviation -?
Take N measurements; calculate average as
N
xxxx N
...21
Calculate standard deviation as
1
)(...)()( 22
2
2
1
N
xxxxxxs N
N
stx 95m with 95% probability
Coinfidence interval (CI)
![Page 9: Random Errors in Chemical Analysis -IIstaff.buffalostate.edu/nazareay/che301/che301l5.pdf · 2016-02-03 · Random Errors in Chemical Analysis -II. A measurement x 1, with m and s](https://reader030.vdocuments.mx/reader030/viewer/2022040600/5e8da4b16163a501e42405b2/html5/thumbnails/9.jpg)
6 8 10 12 14 16
m=12.34
s=0.50
N=2
6 8 10 12 14 16N=3
6 8 10 12 14 16
6 8 10 12 14 16
N=4
N=6
![Page 10: Random Errors in Chemical Analysis -IIstaff.buffalostate.edu/nazareay/che301/che301l5.pdf · 2016-02-03 · Random Errors in Chemical Analysis -II. A measurement x 1, with m and s](https://reader030.vdocuments.mx/reader030/viewer/2022040600/5e8da4b16163a501e42405b2/html5/thumbnails/10.jpg)
11.8 12.2 12.6
m=12.34
s=0.50
N=6
11.8 12.2 12.6
11.8 12.2 12.6
N=15
N=60
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I titrate an unknown solution using a class A
50 mL burette. My results show standard deviation
of 0.05 mL. How many mesurements I need
in order to get confidence interval of ±0.01 mL?
44.02
05.07.12
N=2
08.04
05.018.3
N=4
038.09
05.03.2
N=9
02.020
05.01.2
N=20
009.0120
05.098.1
N=120
Ubur = 0.05 mL
22
randomburtotal uuu
44.005.044.0 22 totalu
095.005.008.0 22 totalu
06.005.0038.0 22 totalu
054.005.002.0 22 totalu
05.005.0009.0 22 totalu
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A very simple rule:
CIs overlap – the same
CIs do not overlap - different