Errors in Analysis – Pharmaceutical Analysis 1 B. Pharma 1st semester

Errors in Analysis

Errors in Analysis

Learning Objectives

At the end of this lecture, the student will be able to

• Define error

• Classify error

• Discuss about determinate and indeterminate error

• Explain how to minimize the error at each step

• Discuss about the different types of methods for minimizing the errors

• Define Accuracy, precision, Significant figures

Errors in Analysis

Definition: Error is the difference between the true result (and accepted true result) and the measured result

Expression of Errors

Errors are expressed either in absolute terms or in relative terms

Absolute Errors: E abs = Calculated value –True Value

Relative Error: Used in the determination of accuracy of a measurement and is expressed in terms of percentage

Relative Error E rel: Absolute error/True value X100

It is also expressed in parts per thousand (ppt)

Types of Errors:

 Determinate or systematic error

 Indeterminate or random error

Determinate errors

• Determinate errors are caused by faults in the analytical procedure or the instruments used in the analysis

• The name determinate error implies that the cause of this type of error may be found out and then either avoided or corrected

• Determinate errors are systematic errors; that is, they are not random

• Sometimes the determinate error is proportional to the true result, giving rise to proportional errors

• Other determinate errors may be variable in both sign and magnitude, such as the change in the volume of a solution as the temperature changes

• Although this variation can be positive or negative, it can be identified and accounted for

• Determinate errors can be additive or they can be multiplicative

• It depends on the error and how it enters into the calculation of the final result

• This determinate error could be the result of an incorrectly calibrated balance

For example:

• If the balance is set so that the zero point is actually 0.5 mg too high, all masses determined with this balance will be 0.5 mg too high

• If this balance was used to weigh any standard solution used in the laboratory, the standard concentration will be erroneously high, and all of the results obtained using this standard will be erroneously low

• The error is reported as the absolute error, the absolute value of the difference between the true and measured values

How are determinate errors identified and corrected?

• Two methods are commonly used to identify the existence of systematic errors

 Standard methods and

 To run several analyses

• Standard method: is to analyze the sample by a completely different analytical procedure that is known to involve no systematic errors

• They have been evaluated extensively by many laboratories and shown to be accurate and precise

• If the results from the two analytical methods agree, it is reasonable to assume that both analytical procedures are free of determinate errors

• The second method is to run several analyses of a reference material of known, accepted concentration of analyte

• The difference between the known (true) concentration and that measured by analysis should reveal the error

• If the results of analysis of a known reference standard are consistently high (or consistently low), then a determinate error is involved in the method

How to correct the determinate error?

• The cause of the error must be identified and either eliminated or controlled if the analytical procedure is to give accurate results

• Many clinical and analytical laboratories participate in proficiency testing programs, where “unknown” standard samples are sent to the laboratory on a regular basis

• The results of these samples are sent to the government or professional agency running the program

• The unknowns are of course known to the agency that sent the test samples; the laboratory receives a report on the accuracy and precision of its performance

Reasons for determinate errors in analytical procedures:

• uncalibrated balances

• Improperly calibrated volumetric flasks

• Pipettes, malfunctioning instrumentation,

• Impure chemicals

• Incorrect analytical procedures or techniques

• Analyst error

The following are the types of determinate errors may be noted:

a) Operational and personal errors

b) Instrumental and reagent errors

c) Errors of method

d) Additive and proportional errors

Determinate Errors: a) Operational and Personal Errors

• Analyst error: The person performing the analysis causes these errors

• They may be the result of inexperience, insufficient training, or being “in a hurry”

• An analyst may use the instrument incorrectly, perhaps by placing the sample in the instrument incorrectly each time

• Setting the instrument to the wrong conditions for analysis

  Consistently misreading a meniscus in a volumetric flask as high (or low) Improper use of pipettes, such as

These are due to factors for which the individual analyst is responsible and are not connected with the method or procedure

 They form part of the ‘personal equation’ of an observer

 The errors are mostly physical in nature and occur when sound analytical technique is not followed


• Mechanical loss of materials in various steps of analysis

• Under washing or over washing of precipitates

• Ignition of precipitates at incorrect temperatures

• Insufficient cooling of crucibles before weighing

• Allowing hygroscopic materials to absorb moisture before and after weighing

• Allowing the volatile materials to volatile after weighing

• Maintaining incorrect temperature and time for reaction before completion

•Burette reading properly not done

Determinate Errors: a) Operational and Personal Errors

• Some other analyst-related errors are Carelessness, which is not as common as is generally believed transcription errors, that is, copying the wrong information into a lab notebook or onto a label Calculation errors

Elimination of this error:

• Proper training, experience, and attention to detail on the part of the analyst can correct these types of errors

Determinate Errors: b) Instrumental and Reagent Errors

•These arises due to the faculty construction of balances, use of uncalibrated weights, improperly graduated glass wares and other instruments

1. Instrumental errors:

• Numerous errors involving instrumentation are possible, including:

 Faulty construction of balances

 Use of uncalibrated or improperly calibrated weights

 incorrect instrument alignment

 Incorrect wavelength settings

 Incorrect reading of values, and incorrect settings of the readout (i.e., zero signal should read zero)

• Any variation in proper instrument settings can lead to errors

• In instrumental analysis, electrical line voltage fluctuations are a particular problem

• This is especially true for automated instruments running unattended overnight

• Instruments are often calibrated during the day, when electrical power is in high demand. At night, when power demand is lower, line voltage may increase substantially, completely changing the relationship between concentration of analyte and measured signal

• Regulated power supplies are highly recommended for analytical instruments. The procedure for unattended analysis should include sufficient calibration checks during the analytical run to identify such problems

Elimination of such errors:

• These problems can be eliminated by a systematic procedure to check the instrument settings and operation before use

• Such procedures are called standard operating procedures (SOPs) in many labs

• There should be a written SOP for each instrument and each analytical method used in the laboratory

2. Reagent errors:

• Contaminated or decomposed reagents can cause determinate errors

• Impurities in the reagents may interfere with the determination of the analyte, especially at the ppm level or below

• Prepared reagents may also be improperly labeled

• The suspect reagent may be  tested for purity  using  a known procedure or the analysis should be redone using a different set of reagents and the results should be compared

Determinate Errors: c) Errors of Method

These errors are due to incorrect sampling and form incompleteness of a reaction

For Example: In titrimetric analysis:

 Due to failure of reaction to proceed to completion

 Occurrence of side reactions

 Reactions of substances other than the constituents being determined

 A difference between the observed end point and stoichiometric end point of the reaction

Determinate Errors: d) Additive and Proportional Errors

• The absolute value of an additive error is independent of amount of constituent present in the determination

For example:

 Loss in weight of a crucible in which a precipitate is ignited and errors in weights. The presence of this error is revealed by taking samples of different weights

 Powdered gloves may contain a variety of trace elements and should not be used by analysts performing trace element determinations

• The absolute value of a proportional error depends upon the amount of the constituents

For example:

Estimation of ‘chlorate’—an oxidant by iodometric determination–Presence of ‘Bromate’—another oxidizing agent would give rise to positively higher results, and hence, it must be duly corrected

Indeterminate Errors

 Indeterminate errors are not constant or biased

 They are random in nature

 Are the cause of slight variations in results of replicate samples made by the same analyst under the same conditions

For example:

 A balance that is capable of measuring only to 0.001 g cannot distinguish between two samples with masses of 1.0151 and 1.0149 g

 In one case the measured mass is low, in the other case it is high

 These random errors cause variation in results, some of which may be too high and some too low

 The average of the replicate determinations is accurate, but each individual determination may vary slightly from the true value

 Indeterminate errors arise from sources that cannot be corrected, avoided, or even identified, in some cases

Commonly Identified Indeterminate Errors

• Concentration errors

• Labeling errors

• Calculation errors

• Manual calculation using wrong formula Computational calculation

• Using wrong formula in excel Using different location (wrong cell) in the excel sheet

• Improper use of symbols

• Rounding off errors

Minimization of Errors

Analyst has no control on random errors but systemic errors can be reduced by following methods:

Calibration of apparatus: By calibrating all the instruments, errors can be minimized and appropriate corrections are applied to the original measurements

Control determination: Standard substance is used in experiment in identical experimental condition to minimize the errors

Blank determination: By omitting sample, a determination is carried out in identical condition to minimize the errors occurs due to impurities present in reagent

Independent method of analysis: It is carried out to maintain accuracy of the result

For Example: Iron (III) is first determined gravimetrically by precipitation method as iron (III) hydroxide and then determined titrimetrically by reduction to the iron (II) state

Parallel determination: Instead of single determination, duplicate or triplicate determination is carried out to minimize the possibilities of accidental errors

Standard addition: This method is generally applied to physico-chemical procedures such as polarography and spectrophotometry

Internal standards: It is used in spectroscopic and chromatographic determination

Amplification methods: It is used when a very small amount of material is to be measured which is beyond the limit of the apparatus

Isotopic dilution: It is used for the compound containing radio-active isotope

Understand the Importance of Each Step to Minimize Errors

GENERAL INSTRUCTIONS: For minimizing errors for analytical reagents:

 No bottle is to be opened for a longer time than is absolutely necessary

 No reagent is to be returned to the bottle after it has been removed

 Liquid reagents should be poured from the bottle

 A pipette should never be inserted into the reagent bottle

 Particular care should be taken to avoid contamination of the stopper of the reagent bottle

 When a liquid is poured from a bottle, the stopper should never be placed on the shelf or on the working bench it may be placed upon a clean watch glass

 Many chemists cultivate the habit of holding the stopper between the thumb and fingers of one hand

 The stopper should be returned to the bottle immediately after the reagent has been removed, and all reagent bottles should be kept scrupulously clean, particularly round the neck or mouth of the bottle

• Allow the flask to stand for a while before making the final adjustment to the mark to ensure that the solution is at room temperature

• It should be noted, however, that for some solutions as, for example, iodine and silver nitrate, glass containers only may be used, and in both these cases the bottle should be made of dark (brown) glass

• Solutions of EDTA are best stored in polythene containers

• Immediately after the solution has been transferred to the flask, it should be labelled with:

(1) The name of the solution

(2) Its concentration (if any)

(3) The data of preparation and

(4)The initials of the person who prepared the solution, together with any other relevant data

GENERAL INSTRUCTIONS: For minimizing errors for weighing:

The chief sources of error are the following:

• Change in the condition of the containing vessel or of the substance between successive weighing by absorption or loss of moisture, by electrification of the surface caused by rubbing, by its temperature being different from that of the balance case

• Effect of the buoyancy of the air upon the object and the weights

• Hygroscopic, efflorescent, and volatile substances must be weighed in completely closed vessels

• Substances which have been heated in an air oven or ignited in a crucible are generally allowed to cool in a desiccator containing a suitable drying agent

• Substances which have been heated in an air oven or ignited in a crucible are generally allowed to cool in a desiccator containing a suitable drying agent

• The time of cooling in a desiccator cannot be exactly specified, since it will depend upon the temperature and upon the size of the crucible as well as upon the material of which it is composed

• Platinum vessels require a shorter time than those of porcelain, glass, or silica

• It has been customary to leave platinum crucibles in the desiccator for 20-25 minutes, and crucibles of other materials for 30-35 minutes before being weighed

• It is advisable to cover crucibles and other open vessels

GENERAL INSTRUCTIONS: For Minimizing Errors for graduated flasks:  Vessels intended to contain definite volumes of liquid

• The neck is made narrow so that a small change in volume will have a large effect upon the height of the meniscus

• The error in adjustment of the meniscus is accordingly small

• To read the position of the meniscus, the eye must be at the same level as the meniscus, in order to avoid errors due to parallax

For Minimizing Errors for graduated flasks:  Vessels intended to contain definite volumes of liquid

GENERAL INSTRUCTIONS: For Minimizing Errors Reading a burette / pipette:

The analyst reads the burette from a position above a line perpendicular to the burette and makes a reading of 12.58 mL or 12.67 mL

The analyst reads the burette from a position along a line perpendicular to the burette and makes a reading of 12.6 mL

GENERAL INSTRUCTIONS: For Minimizing Errors Reading a burette / pipette:


• Sample preparation should be performed in a:

 Laboratory fume hood

 For safety use Goggles

 Lab coats or aprons

 Gloves  resistant to the chemicals in use should be worn at all times in the laboratory

Errors in Assay

• Incorrect weighing and transfer of analyte and standards

• Insufficient extraction of the analyte from the matrix e.g. tablets

• Incorrect use of pipettes, burettes, volumetric flasks for volume measurement

• Measurement carried out using improperly calibrated instrumentation.

• Failure use an analytical blank

• Selection of assay conditions that cause degradation of the analyte

• Failure to allow for or to remove interference by excipients in the measurement of an analyte

Errors in Titrimetric Analysis

• Failure of reactions to proceed to completion Involvement of either induced or side reactions

• Reactions due to substances other than the one being assayed

• A noticeable difference occurring between the stoichiometric equivalence point of a reaction and the observed end-point

Accuracy, Precision

• Accuracy

How close mean of measured values is to true value

• Precision

Repeatability of measurements

Accuracy, Precision

Example: Determine the accuracy and precision of the mass of a piece of a metal performed by three different students, where mass of a piece of metal is 0.520gm. Data obtained by each student are recorded as follow.

Student                A:            0.521,    0.521,    0.509     Average:              0.515

Student                B:            0.516,    0.515,    0.514     Average:              0.515

Student                C:            0.521,    0.520,    0.520     Average:              0.520

Significant Figures

• Digit:  Any one of the ten numerals, including zero

• Significant figure: A digit which denotes the amount of the quantity in the place in which it stands

For example: 2.7808 g and 1.0032 g → zero is significant, whereas in 0.0050 g → zero is not significant but only to locate the decimal point, the value can also be written as 5mg


• Error: The difference between the true result (or accepted true result) and the measured result

• Classification of errors: Determinate error → which can be determined, indeterminate error → which cannot be determined

• Classification of determinate error:

a) Operational and personal errors

b) Instrumental and reagent errors

c) Errors of method

d) Additive and proportional errors

• Minimization of error: Calibration of apparatus, Controlled determination, Blank determination, Independent methods of analysis, Parallel determination, amplification method, standard addition method, internal standard method, isotopic dilution

• Correct way of using analytical reagents, bottles, samples, weighing, burette, pipette and graduated flasks can minimize the errors

•Accuracy: How close is mean of measured values is to true value

• Precision: Repeatability of measurements

• Significant figure: A digit which denotes the amount of the quantity in the place in which it stands

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