Chap5 Errors of Chemical Analysis

Errors in Chemical Analysis

CHAP 5

Data quality• Measurements invariably involve errors anduncertainties.– Uncertainties can never be completely eliminated,measurement data can give us only an estimate ofthe “true” value.• Reliability can be assessed in several ways:– Experiments designed to reveal the presence oferrors– Compared with the known compositions– Consult to the chemical literature– Equipment Calibration– Statistical tests

Representative Data• Chemists usually carry two to five portions(replicates) of a sample through an entireanalytical procedure.– Replicates are samples of about the same size thatare carried through an analysis in exactly the same way.• One usually considers the “best” estimate to bethe central value for the set:– Usually, the mean or the median is used as thecentral value for a set of replicate measurements.– The variation in data allows us to estimate theuncertainty associated with the central result

The Mean and Median• The most widely used measure of central valueis the mean, . The mean, also called thearithmetic mean, or the average,

– where xi represents the individual values of x makingup the set of N replicate measurements.• The median is the middle result when replicatedata are arranged according to increasing ordecreasing value.

Example for Mean & Median

Precision• Describes the reproducibility of

measurements• Or, the closeness of results that have beenobtained in exactly the same way.• Three terms are widely used to describe theprecision of a set of replicate data:– standard deviation;– variance;– coefficient of variation.• Deviation from the mean:

Accuracy• Indicates the closeness of the measurement tothe true or accepted value• Expressed in terms of either absolute or relativeerror.• Absolute error:– where xt is the true or accepted value of the

quantity– We retain the sign in stating the absolute error.• Relative error:

The difference between accuracy and precision

Types of Errors in Experimental Data• The precision of a measurement is

readily determined by comparing data from carefully replicated experiments.

• To determine the accuracy, we have to know the true value, which is usually what we are seeking in the analysis.

• Analyst 1: relatively high precision & high accuracy• Analyst 2: poor precision but good accuracy• Analyst 3: excellent precision & significant error in thenumerical average for the data• Analyst 4: poor precision & poor accuracy

Types of Errors• Random (or indeterminate) error:– Affect measurement precision– Causes data to be scattered more or less symmetrically

around a mean value.• Analysts 1 and 3 is significantly less than that for analysts

2 and 4.• Systematic (or determinate) error:– Affect the accuracy of results– Causes the mean of a data set to differ from the accepted

value.• Analysts 1 and 2 have little systematic error;• Analysts 3 and 4 show systematic errors of about -0.7%

and -1.2%.

• Gross error:– Often the product of human errors.– usually occur only occasionally, are

often large, and may cause a result to be either high or low.

– lead to outliers, results that appear to differ markedly from all other data in a set of replicate measurements.

Systematic Errors• Lead to bias in measurement results– Bias affects all of the data in a set in the same

way and that bears a sign• Three types:– Instrumental errors are caused by nonideal

instrument behavior, by faulty calibrations, or by use under inappropriate conditions.

– Method errors arise from nonideal chemical orphysical behavior of analytical systems.– Personal errors result from the carelessness,inattention, or personal limitations of the

experimenter.

Instrument Errors• All measuring devices are potential

sources of systematic errors.• Calibration eliminates most

instrumental systematic errors.• Electronic instruments are subject to

instrumental systematic errors.– Ex: low battery voltage, noises– In many cases, errors of these types

are detectable and correctable.

Method Errors• The nonideal chemical or physical behavior ofthe reagents and reactions on which an analysis

is based• Ex: the slowness of some reactions, the

incompleteness of others, the instability of some

species• Errors inherent in a method are often difficult

to detect and are thus the most serious of the

three types of systematic error.

Personal Errors• Many measurements require personal

judgments. Judgments of this type are often subject to systematic, undirectional errors.

• Analytical procedures should always be adjusted

so that any known physical limitations of theanalyst cause negligibly small errors.• A universal source of personal error is prejudice,or bias. Number bias is another source of

personal error that varies considerably from person to person.

Effect of Systematic Errors onAnalytical Results

• Systematic errors may be either constant or proportional.

• Constant errors– Independent of the size of the sample being analyzed.– The absolute error is constant with sample size, butthe relative error varies when sample size is changed.– The excess of reagent required to bring about a colorchange during a titration is an example.– The effect of a constant error becomes more seriousas the size of the quantity measured decreases.

• Proportional errors- Decrease or increase in proportion to the

sizeof the sample.– The absolute error varies with sample

size,but the relative error stays constant withchanging sample size.– A common cause of proportional errors is

thepresence of interfering contaminants in the

sample

Systematic Instrument andPersonal Errors Detection

• Instrument errors– Some systematic instrument errors can be found and

corrected by calibration.– Periodic calibration of equipment is always desirablebecause the response of most instruments change with

time as a result of wear, corrosion, or mistreatment.• Personal errors– Most personal errors can be minimized by care andself-discipline.– It is a good habit to check instrument readings,notebook entries, and calculations systematically.

Systematic Method Errors Detection

• Take one or more of the followingsteps to recognise and adjust for asystematic error:–Analysis of Standard Samples– Independent Analysis–Blank Determinations–Variation in Sample Size

Analysis of Standard Samples• The best way of estimating the bias of an

analytical method is by the analysis of standard reference materials.

– Standard Reference Materials (SRMS):• Materials that contain one or more analytes atknown concentration levels.• Can sometimes be prepared by synthesis.• Can be purchased from a number of

governmental and industrial sources. Ex: National Institute of Standards and Technology (NIST); Sigma Cheminal Co.

Independent Analysis & Variation inSample Size

• Independent Analysis– A second independent and reliable analytical method

can be used in parallel with the method being evaluated.

– A statistical test must be used to determine whetherany difference is a result of random errors in the twomethods or due to bias in the method under study.• Variation in Sample Size– As the size of a measurement increases, the effect ofa constant error decreases. Constant errors can oftenbe detected by varying the sample size.

Blank Determinations• A blank contains the reagents and solvents used in

a determination, but no analyte.• Many of the sample constituents are added to

simulate the analyte environment, often called the sample matrix.

• In a blank determination:– All steps of the analysis are performed on the

blankmaterial.– Blank determinations reveal errors due to

interferingcontaminants from the reagents and vessels used in

the analysis