cdb 3093 data handling, statistic and errors

8/15/2019 CDB 3093 Data Handling, Statistic and Errors

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Data Handling, Statistic and Errors

Dr Asna M. Zain, RSci AMIChemECDB3093

Analytical Chemistry


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Outline

Sample handling and management

QC and QA

Errors in analysis

Statistical analysis parameters

Descriptive statistics

Inferential statistics

Example questions

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Nature and Scope

Set of instructionReliability in accuracy,

reproducibility

Solve using chemical orphysico-chemical processas underlying principles of

the technique

SubjectChemicalanalysis

Analyticalproblem

Method Validate

Procedures

Based onpurpose and

intended quality

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Techniques and method of analysis

Techniques

A t omi c &

m ol e c ul a r

s p e c t r om e t

r y

AAS FTIR

Gr a v i m e t r

y

M a s s s p e c t r om

e t r y

Ch r om a t o g r a

ph y

HPLCGC

T h er m a l

E l e c t r o c h emi c a l

R a d i o c h emi c

a l

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Validation method

Performance

characteristicof detectorfor singleanalyte

calibrationstandards

Processrepeated formixed analyte

calibrationstandards

Processrepeated for

analyte

calibrationstandard with

possibleinterferingsubstances

and forreagent blank

Processrepeated for

analyte

calibrationstandard withanticipated

matrixcomponent to

evaluatematrix

interference

Analysis ofspike

simulated

matrix – matrix with

added knownamount ofanalyte, to

testrecoveries

Field trials in

routine labwith more junior

personnel totest

ruggedness

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Sampling and sample handling

Reflects the real composition of sample

Due to varying in time and elapse

between sample collection and analysis

proper storage is required to prevent

loss of analyte

Preservative to maintain the sample

condition for storage or for analysis

Prior to analysis such as extraction,

grinding, concentrate or dissolutionAnalysis

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Representative sample

Coning and quartering – solid

grab sample /composite of grab – water/liquid

Random pick

1

2

3

41

2

3

4

1

2

3

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Quality control and quality assurance

QC - ensure theoperational techniques andactivities in analytical labprovide result suitable forintended purpose

Meet specific requirementin context of definedproblem e.g. accuracy andprecision, calibration

Confidence in validity

Cost effective

QA - managerialcomponent/ responsibility ofan analytical lab with all QCprocedures are in place.

Build confidence through labparticipation by inter labstudies.

Proficiency test to the lab

performance or analyst.

Method performance andcertification studiesundertaken

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Errors in analytical measurement

Measurement error – used statistical method to assess the error andminimize by careful experimental design and control

Absolute and relative error Absolute error given by the Ea = Xm – Xt Relative error, Er = (Xm – Xt)/ Xt

Determinate errors Systematic error lead to bias in the measured value from analyst, equipment or

procedure which require record keeping, training or equipment maintenance.

Indeterminate error Random error source from random fluctuations in measured quantities occurs in

closely controlled environment Minimize by careful experimental design andcontrol of the environmental factors

Accumulated error Aggregated error count in every measurement made in analytical procedures

and contributed to the final calculated results.

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Determinate and indeterminate error

Determinate error Indeterminate error Instrumental error include

instrument fault,uncalibrated weights anduncalibrated glasswares

Operative error – due tolack of skill and training

Errors in methods -sourcefrom coprecipitation, slight

solubility, side reactions,incomplete reactions andimpurities in reagents

Accidental error or random error

Use probability or statistic tocome into conclusion about the

error

Indeterminate error should followthe normal distribution orGaussian curve

represent the standard deviationof infinite population and measurethe precision by the spread ofnormal population distribution asin Fig 3.2

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Gaussian distribution

Random errors follow a Gaussian or normal distribution.

We are 95% certain that the true value falls within 2σ (infinite population),IF there is no systematic error.

Fig. 3.2 Normal error curve. ©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)11


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Way to express accuracy - Absolute error

and relative error

Absolute error Relative error

Difference between truevalue and measuredvalue

If true value is 2.62 g andthe measured value is2.52 g, thus the absoluteerror, Ea is -0.10 g

If the Xm is based onaverage of severalmeasurement the valueis called mean error.

Absolute or mean errorexpressed as percentage oftrue value is relative error

Based on the samemeasurement, relative error, Eris (-0.10/2.62) x 100% = -3.8%

The relative accuracy is themeasured value or meanexpressed as a percentage ofthe true value, (2.52/2.62) x100% = 96.2%

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Example 3.6

The results of an analysis are 36.97 g, compared withthe accepted value of 37.06 g.

What is the relative error in parts per thousand, ppt?

Absolute error = 36.97 g – 37.06 g = -0.09 g

Relative error = -0.09 /37.06 x 1000%

= -2.4 ppt

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Statistical analysis

Used statistical model

follow a normal (Gaussian) distribution

Average or normalize data if data set is smallto apply Gaussian distribution

A batch may contain a sample or more withdifferent variety or reason e.g. parameters,

holding time

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Accuracy and precision

You can’t have accuracy without good precision.

But a precise result can have a determinate or systematic error.

©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)

Fig. 3.1. Accuracy and precision.

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R chart and X chart

Use control chart to present or evaluate the batch of QC sample.

R chart was used to present the precision which record the property of interest in a running

sequence. Show centerline or average, standard deviation and warning or control limit

This X chart requires result from known sample composition and used to evaluate accuracy.

Warning limit of 2 standard deviation and control limit of 3 standard deviation.16


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Statistical parameters

software – Excel, SPSS, Minitab, SYSTAT

Descriptive statistic

Check data for any problematic or non normality data set depart from bell shape or withoutliers, use frequency chart or normal plot

Means,

standard deviation, or S (data


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Data distribution

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Select a confidence level (95% is good) for the number of samples analyzed=(degrees of freedom +1).

Confidence limit = x ± ts/√N.

It depends on the precision, s, and the confidence level you select.

Confidence limit Estimate the range within a given probability which the true value might fall defined by

the experimental mean and standard deviation

The range is called confidence interval and the limit is called confidence limit.

The likelihood that the true value fall within the range is called the probability orconfidence level

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Inferential statistic

Researcher need to make inferences about populationof sample

Types of inferential statistic

Significance Test, F test and T-test

Analysis of variance (ANOVA)

Q-Test (to discard bad data)

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Significance test Compare the result of a method with the accepted method

results to decide whether the data is significantly different fromanother set of data (in the mean or availability and spread)

Used statistical table like F test or t test F test indicate a significant different between two method based on

their standard deviation F is defined in term of variances of two methods where the variance

is the square of the standard deviation

F = s12 /s2

2 (Eq. 3.10) where s1

2 > s22

If the calculated F value from Eq. 3.10 exceeds a tabulated F value atthe selected confidence level (e.g Table 3.2 at 95% confidence level),then there is a significant different between variances of the twomethods

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F valueF = s1

2 /s22.

You compare the variances of two different methods to see if there is asignificant difference in the methods, at the 95% confidence level.

©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)

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Example 3.16

You are developing a new calorific procedure for determining the

glucose content in blood serum. You have chosen the standard Folin-

Wu procedure with which to compare your results. From the following

two sets of replicate analyses on the same sample, determine whether

the variance of your method differs significantly from that of the

standard methods using F test.

Your method (mg/dL) Folin-Wu method (mg/dL)

127

125

123

130131

126

129

130

128

131

129127

125

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T


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t-Test

Analysis of variance between means

Require assumption before the test

Do the sample follow a normal distribution? If small is sample then the test isincorrect, moderate sample size of 40-100 to be accurate

the variance for the two groups is about the same. Check homogeneity of varianceassumption, can lead to inaccurate result particularly for small groups with unequalsample sizes

observations to be assumed to be independent, such that one subject does notinfluence another’s subject score.

Statistic calculate the sample means divided by a variance for comparison with the critical valueobtained from a probability table at the selected p value (0.05, 0.01 or 0.001)

if the t statistic is equal or exceed the critical value, then the difference between the two groupmeans is significant at the chosen level of alpha.

The test can be one-sided or two – sided. The former is used when the mean for a particulargroup is hypothesized to be higher than the mean for other group, the latter is used when themean are expected to be different.

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Example 3.18

A new gravimetric method is developed for iron (III) in which the iron

is precipitated in crystalline form with an organoboron cagecompound. The accuracy of the method is checked by analyzing the

iron in an ore sample and comparing with the results using the

standard precipitation with ammonia and weighing of Fe2O3. The

results, reported as % Fe for each analysis, were as follows:

Find the F and t value,

given

Test method Reference method

20.10

20.50

18.6519.25

19.40

19.99

18.89

19.20

19.0019.70

19.40

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ANOVA

Multiple t-test when there are more than a few groups

A comparison of group means – no limitation on the no. of group comparison

ANOVA was used to examine the variability of scores within and betweengroups.

Subject scores within groups vary due to differences in individual and random

error

ANOVA assume the observation are independent, normal and group variancesare equal

ANOVA test determine if any group mean is significant different from any othergroup mean by overall F test.

If no different (i.e. F-test is not significant), then the is no point in comparing anyof the groupsretain null hyphothesis.

If F-test is significant indicate at least one group mean is significantly differentfrom one other group mean. investigate the hypothesis for the groups.

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Q-testQCalc = outlier difference/range.

If QCalc

> QTable

, then reject the outlier as due to a systematic error.

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Example of Q-test

Performed Q-test to find outlier data from

the following measurement and made your

conclusion to the data.

Sydney Cherry Tien Dick

10.2

10.8

11.6

9.9

9.4

7.8

10.0

9.2

11.3

9.5

10.6

11.6

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Correlation

Association between two variables that takes on avalue between +1.0 and -1.0

If the two variables are positively correlated, then asone increases, the other increase.

If the two variables are negatively correlated, thenone variable increases, the other decreases

It there are not associated at all the correlation iszero

A scatter plot of zero correlation will show a circularfields of points on x-y axis or no particularrelationships between x and y.

A positive correlation appear as linear line andincreasing but negative correlation will appear aslinear with decreasing line.

Made inferences for association between twovariables in population, by assume data are normaldistribute

Pearson correlation , or

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Regression

Regression consider a continuous group of variables such as age, divide thegroup into the continuous nature of the age

Regression create a linear equation to predicts the score in a dependentvariable.

The equation represent a line that best fit through a scatter plot of pointsdescribing the relationship between variable and one or more independentvariables

The beta weight or coefficient of the independent variables in the equation giveinfo on relationships between the independent and dependent variables

The slope of single line best fit data of the x-y axis, represent the beta weightand reflect changes in the value of the dependent variable that associated witheach change of one unit in the independent variable.

Regression analysis assume independence, normality and constant variance, andlinear relationship between independent and dependent variables.

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A least-squares plot gives the best straight line through experimental points.Excel will do this for you.

Fig. 3.7. Straight-line plot.

©Gary Christian,Analytical Chemistry,6th Ed. (Wiley)

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Riboflavin (Vit B3) is determined in a cereal sample by its fluorescence

intensity in 5% HAc sol. A calibration curve was prepared by measuringthe fluorescence intensities of a series of standards of increasingconcentrations. The following data were obtained. Used the methodleast squares to obtain the best straight line for the calibration curveand to calculate the concentration of riboflavin in the sample.

Fig. 3.8. Least-squares plot of data from Example 3.21.

This Excel plot gives the same results for slope and intercept as calculated inthe example.

©Gary Christian,Analytical Chemistry,6th Ed. (Wiley)

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M=(xi-x)(yi-y)

(xi-x)2

b= y-mx


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Manual solution for example 3.21

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EXCEL spreadsheet solution for 3.21

Select LINEST from the statistical function list (in the Paste Function window

– click on f x in the tool bar to open).LINEST calculates key statistical functions for a graph or set of data.

Fig. 3.10. Using LINEST for statistics.35


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Use of spreadsheets in analytical

chemistry

We often use relative cell references in formulas.

If a number from a given cell is to be a constant in the formula, place $ infront of that cell’s descriptors.

Fig. 3.5. Relative and absolute cell references.36


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EXCEL Mathematical function

Excel has a number of mathematical and statistical functions.

Click on f x on the tool bar to open the Paste Function.

Math & trig syntaxes:

LOG10

PRODUCT

POWER

SQRTStatistical syntaxes:

AVERAGE

MEDIAN

STDEV

TTEST

VAR

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References

Gary D. Christian, 2003 Analytical Chemistry, 6th Ed., Wiley,QD101.2 C57 2003

Daniel C Harris, Exploring Chemical Analysis Second Ed., W.HFreeman and Company, 2000 QD 75.2. H368.

Seamus P.J. Higson, Analytical chemistry, Oxford University Press,2004 QD 101.2.H54

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