Q1. A standard sample of pooled human blood serum contains 42.0 g of albumin per litre. Five laboratories (A–! each do six determinations (on the same da"! of the albumin concentration# $ith the follo$ing results (g l −1 throughout!% &omment on the bias# precision and accurac" of each of these sets of results.
Ans$er. First $e dra$ dot plot diagram for ' laboratoe".
-aborator" A ('
()
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(+
(,
40
41
42
4(
44
4'
-aborator" ('
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40
41
42
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-aborator" & ('
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41
42
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-aborator" / ('
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41
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-aborator" ('
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Solutions to exercises chapter 1 2 Bolouri
$ith calculate the mean for ' laboratories and pa" attention to dot plots $e can sa"%
laboratory
A
B
C
D
E
Mean
41.,
41.,
4.2
,.1
41.'
STD
0.'
1.*
0.42
.2
1.
Bias/preci sion /accuracy
precise# little bias# mean accurate
poor precision# little bias# mean accurate but not ver" reliable
precise but biased to high values# poor accurac"
poor precision# biased to lo$ values# poor accurac"
similar to A# but the last result might be an outlier
Q2. sing the same sample and method as in 3uestion 1# laborator" A maes six further determinations of the albumin concentration# this time on six successive da"s. 5he values obtained are 41.'# 40.+# 4.# 41.,# 42.2 and 41.* g l−1 &omment on these results. Ans$er.
-aborator" A % ' test in a da" ('
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40
41
42
4(
44
4'
-aborator" A % ) tests in ) successive da"s ('
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40
41
A laboratory
' test in a da" ($ithin6da" precision!
42
4(
44
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A ) tests in ) successive da"s ( bet$een6da" precision!
Solutions to exercises chapter 1 Bolouri
Mean
41.,
41.,
STD
0.'
0.+
Bias/precision /accuracy
precise# little bias# mean accurate
A still sho$s little bias# but precision is poorer# re7ecting reproducibilit" (i.e. bet$een6da" precision! rather than repeatabilit" ($ithin6da" precision!.
Q3. 5he number of binding sites per molecule in a sample of monoclonal antibod" is determined four times# $ith results of 1.,'# 1.,'# 1.,2 and 1.,*. &omment on the bias# precision and accurac" of these results. 8umber of binding sites must be an integer# clearl" 2 here# so results are precise#but biased to lo$ values. 5he bias does not matter much# as t$o binding sites can be deduced.
Q4. /iscuss the degrees of bias and precision desirable or acceptable in the follo$ing anal"ses% (i! /etermination of the lactate concentration of human blood samples. (ii! /etermination of uranium in an ore sample. (iii! /etermination of a drug in blood plasma after an overdose. (iv! Stud" of the stabilit" of a colorimetric reagent b" determination of its absorbance at a single $avelength over a period of several $ees. (i! (ii! (iii! (iv!
lood lactate levels var" a lot in health" patients# so great precision and accurac" are not needed. nbiased results could be crucial because of the great economic importance of ranium. Speed of anal"sis is crucial here# so precision and accurac" are less important. 5he aim is to detect even small changes over time# so precision is most important.
Q5. For each of the follo$ing experiments# tr" to identif" the ma9or probable sources of random and s"stematic errors# and consider ho$ such errors ma" be minimi:ed% (i! 5he iron content of a large lump of ore is determined b" taing a single small sample# dissolving it in acid# and titrating $ith ceric sulphate after reduction of Fe(;;;! to Fe(;;!.
Solutions to exercises chapter 1 4 Bolouri
(ii! 5he same sampling and dissolution procedure is used as in (i! but the iron is determined colorimetricall" after addition of a chelating reagent and extraction of the resulting coloured complex into an organic solvent.(iii! 5he sulphate content of an a3ueous solution. i.
Sample might not be representative# and
ii.
Sampling problem as in (i!# and also incomplete extraction# leading to bias (checed $ith standard!. =andom errors inspectrometr"# $hich again should be relativel" small.
iii.
=andom errors in gravimetr" should be ver" small% more signi>cant $ill be chemical problems such as co6precipitation# giving biased results.
