Accuracy and Precision CH104w01 Analytical ChemistryAccuracy and Precision CH104w01 Analytical Chemistry

8/19/2019 Accuracy and Precision CH104w01 Analytical ChemistryAccuracy and Precision CH104w01 Analytical Chemistry

1/15

• Accuracy is the closeness of a measured value to the trueAccuracy is the closeness of a measured value to the true

value.value.

• For example, the measured density of water has become moreFor example, the measured density of water has become moreaccurate with improved experimental design, technique, andaccurate with improved experimental design, technique, and

equipment.equipment.

ACCURACYACCURACY

Density of HDensity of H22O at 20° CO at 20° C

(!cm(!cm""##

11

1.01.0

1.001.00

0.990.990.99!0.99!

0.99!00.99!0

0.99!0"0.99!0"


2/15

• #ercent error is used to estimate the accuracy of a#ercent error is used to estimate the accuracy of a

measurement.measurement.

• #ercent error will always be a positive.#ercent error will always be a positive.

• $hat is the percent error if the measured density of titanium %&i'$hat is the percent error if the measured density of titanium %&i'

is (.() g*cmis (.() g*cm"" and the accepted density of &i is (.)0 g*cmand the accepted density of &i is (.)0 g*cm""++

ACCURACYACCURACY


3/15

verage - 1)." g*/ verage - 1)." g*/

tandard eviation - !.1 g*/tandard eviation - !.1 g*/

$hat is the true concentration of s in this experiment+$hat is the true concentration of s in this experiment+

2stimate the accuracy of this method.2stimate the accuracy of this method.

3ow precise is this method+3ow precise is this method+

• $recision is the areement %et&een re'eated measurements of the$recision is the areement %et&een re'eated measurements of the

same sam'le. $recision is usually e'ressed as a standard deviation.same sam'le. $recision is usually e'ressed as a standard deviation.

• For example, the precision of a method for measuring arsenic %s' wasFor example, the precision of a method for measuring arsenic %s' wasdetermined by measuring 4 different solutions each containing 1(." g*/ ofdetermined by measuring 4 different solutions each containing 1(." g*/ of

s. s.

$R)C*+*O,$R)C*+*O,

-easured-easuredConcentrationConcentration

(!/#(!/#

1.(1.(

1".51".5

1".51".5

1(.!1(.!

15.015.0

1".51".5

14.14.

1(." g*/1(." g*/

!.1 g*/!.1 g*/


4/15

• escribe the accuracy and precision of these ( targets.escribe the accuracy and precision of these ( targets.

ACCURACY A,D $R)C*+*O,ACCURACY A,D $R)C*+*O,

ccurate, and ccurate, and

preciseprecise#recise, but#recise, but

not accuratenot accurate ccurate, but ccurate, but

not precisenot precise6ot accurate,6ot accurate,

and notand not

preciseprecise


5/15

• +ystematic (or determinate# errors are re'roduci%le and+ystematic (or determinate# errors are re'roduci%le and

cause a %ias in the same direction for each measurement.cause a %ias in the same direction for each measurement.

• For example, a poorly trained operator that consistently ma7esFor example, a poorly trained operator that consistently ma7es

the same mista7e will cause systematic error. ystematic errorthe same mista7e will cause systematic error. ystematic error

can be corrected.can be corrected.

• Random (or indeterminate# errors are caused %y the naturalRandom (or indeterminate# errors are caused %y the natural

uncertainty that occurs &ith any measurement.uncertainty that occurs &ith any measurement.

• 8andom errors obey the laws of probability. &hat is, random8andom errors obey the laws of probability. &hat is, random

error might cause a value to be over predicted during its firsterror might cause a value to be over predicted during its first

measurement and under predicted during its secondmeasurement and under predicted during its second

measurement. 8andom error cannot be corrected.measurement. 8andom error cannot be corrected.

)RROR+)RROR+


6/15

• y convention, a measurement is recorded by writing all exactlyy convention, a measurement is recorded by writing all exactly

7nown numbers and 1 number which is uncertain, together with7nown numbers and 1 number which is uncertain, together with

a unit label.a unit label.• ll numbers written in this way, including the uncertain digit, are ll numbers written in this way, including the uncertain digit, are

called significant figures.called significant figures.

• For example, the blue line is !.4" cm long. &his measurementFor example, the blue line is !.4" cm long. &his measurement

has " significant figures. &he first ! digits %!.4 cm' are exactlyhas " significant figures. &he first ! digits %!.4 cm' are exactly

7nown. &he third digit %0.0" cm' is uncertain because it was7nown. &he third digit %0.0" cm' is uncertain because it was

interpolated or estimated 1 digit beyond the smallestinterpolated or estimated 1 digit beyond the smallest

graduation.graduation.

*,)R$O/A*O, A,D +*1,**CA, *1UR)+*,)R$O/A*O, A,D +*1,**CA, *1UR)+


7/15

• $hat is the volume of water in this graduated cylinder+ lways$hat is the volume of water in this graduated cylinder+ lways

measure the volume of a liquid at the bottom of the meniscus.measure the volume of a liquid at the bottom of the meniscus.

&he units are m/.&he units are m/.

• &he volume of water is )!. m/. &he )! m/ are exactly 7nown,&he volume of water is )!. m/. &he )! m/ are exactly 7nown,

and the 0. m/ is uncertain because it was interpolated orand the 0. m/ is uncertain because it was interpolated or

estimated 1 digit beyond the smallest graduation.estimated 1 digit beyond the smallest graduation.

*,)R$O/A*O, A,D +*1,**CA, *1UR)+*,)R$O/A*O, A,D +*1,**CA, *1UR)+


8/15

• :eros between non;ero digits are significant. &hat is, )0 cm:eros between non;ero digits are significant. &hat is, )0 cm

has " significant figures.has " significant figures.

• /eading ;eroes merely locate the decimal point and are never/eading ;eroes merely locate the decimal point and are neversignificant. &hat is, 0.0(94 cm equals (.94 x 10significant. &hat is, 0.0(94 cm equals (.94 x 10

significant figures.significant figures.• &railing ;eros are significant as follows= )0.0 m/ has "&railing ;eros are significant as follows= )0.0 m/ has "

significant figures, )0. m/ has ! significant figures, and )0 m/significant figures, )0. m/ has ! significant figures, and )0 m/has 1 significant figure.has 1 significant figure.

+*1,**CA, *1UR)+ A,D 3)RO++*1,**CA, *1UR)+ A,D 3)RO+

atumatum%grams'%grams'

6umber of6umber ofignificantignificant

FiguresFigures

atumatum%milliliters'%milliliters'

6umber of6umber ofignificantignificant

FiguresFigures

10,0"(10,0"(1.901.90

0."!0."!0.000(50.000(51)01)0

0.00001500.0000150

1)0.1)0.0.40)0.40)

0.0)(0.0)().5 x 10).5 x 10


9/15

• $hen adding or subtracting do 6>& extend the result beyond$hen adding or subtracting do 6>& extend the result beyond

the first column with a doubtful figure. For example, ?the first column with a doubtful figure. For example, ?

+*1,**CA, *1UR)+4 ADD**O,4 A,D +U5RAC*O,+*1,**CA, *1UR)+4 ADD**O,4 A,D +U5RAC*O,


10/15

• $hat is 15.4( @ !.5+$hat is 15.4( @ !.5+

• $hat is 15.4( < !.5+$hat is 15.4( < !.5+

+*1,**CA, *1UR)+4 ADD**O,4 A,D +U5RAC*O,+*1,**CA, *1UR)+4 ADD**O,4 A,D +U5RAC*O,


11/15

• $hen multiplying or dividing the answer will have the same$hen multiplying or dividing the answer will have the same

number of significant digits as the least accurate number usednumber of significant digits as the least accurate number used

to get the answer. For example, ?to get the answer. For example, ?

!.00) g * (.9) m/ - 0.(0) g*m/!.00) g * (.9) m/ - 0.(0) g*m/

• $hat is 15.4( x !.5+$hat is 15.4( x !.5+

• $hat is 15.4( * !.5+$hat is 15.4( * !.5+

+*1,**CA, *1UR)+4 -U/*$/*CA*O,4 A,D D*6*+*O,+*1,**CA, *1UR)+4 -U/*$/*CA*O,4 A,D D*6*+*O,


12/15

• n n averaeaverae is the best estimate of the true value of ais the best estimate of the true value of a

parameter.parameter.• standard deviationstandard deviation is a measure of precision.is a measure of precision.

• verages and standard deviations require several steps to verages and standard deviations require several steps to

calculate. Aou must 7eep trac7 of the number of significantcalculate. Aou must 7eep trac7 of the number of significant

figures during each step. ofigures during each step. o ,O,O discard or round any figuresdiscard or round any figuresuntil the final number is reported.until the final number is reported.

+*1,**CA, *1UR)+ A,D CA/CU/A*O,+ HA R)7U*R)+*1,**CA, *1UR)+ A,D CA/CU/A*O,+ HA R)7U*R)

-U/*$/) +)$+-U/*$/) +)$+


13/15

+*1,**CA, *1UR)+ A,D CA/CU/A*O,+ HA R)7U*R)+*1,**CA, *1UR)+ A,D CA/CU/A*O,+ HA R)7U*R)

-U/*$/) +)$+-U/*$/) +)$+

2 +inificant

iures

8 +inificant iure

2 +inificant iures

0 +inificant iures

8 +inificant iure

8 +inificant iure

+inificant iures∞


14/15

• $hat is average and standard deviation for the following "$hat is average and standard deviation for the following "

measurements of the same sample+measurements of the same sample+


15/15

• merican #ublic 3ealth ssociation, merican $ater $or7s ssociation, merican #ublic 3ealth ssociation, merican $ater $or7s ssociation,

$ater 2nvironment Federation. 199). tandard Bethods for the 2xamination$ater 2nvironment Federation. 199). tandard Bethods for the 2xamination

of $ater and $astewater. 19th ed. $ashington, C= merican #ublic 3ealthof $ater and $astewater. 19th ed. $ashington, C= merican #ublic 3ealth ssociation. ssociation.• arnes, .., D.. Chandler. 19!. Chemistry 111rtega,

.B. Baynard, . ar7ar. !00). &he development and use of an innovative.B. Baynard, . ar7ar. !00). &he development and use of an innovative

laboratory method for measuring arsenic in drin7ing water from westernlaboratory method for measuring arsenic in drin7ing water from western

angladesh. 2nvironmental 3ealth #erspectives. 11"%9'=1195

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Accuracy and Precision CH104w01 Analytical ChemistryAccuracy and Precision CH104w01 Analytical Chemistry