Error Notes

Error Notes


Error is the difference between the true result (or accepted true result) and the measured result. If the error in the analysis is large serious consequences may result. as reliability, reproducibility, and accuracy are the basis of analytical chemistry

A patient may undergo expensive & even dangerous medical treatment based on an incorrect laboratory result because of an analytical error


And the difference between the experimental value & true value is termed as absolute error. this error may be negative/positive

Types of error

Two principle types of error in analysis

  1. Determinate or systematic error/ constant 
  2. Indeterminate/ random error/ accidental 


Determinate error

-They are caused by faults in the analytical procedure/ the instruments used in the analysis

-Determinate error is also known as systemic error i.e they are not random

-The cause of this type of error may be found out & then either avoided/corrected

-A particular determine error may cause the analytical results produced by the method to be always too high

-Another determinate error may render all results too low

-Sometimes the error remains constant

-All results are too high or too low by the same amount

-Determine errors can be additive / they can be multiplicative. it depends on the error & how it enters into the calculation of the final result

-This determines error could be the result of an incorrectly calibrated balance

-If the balance is set so that the zero points are actually 0.5mg too high all masses determined with this balance will be 0.5mg too high

Absolute error = Measured mean value – True value

The determinate error can arise from uncalibrated balance, improperly calibrated volumetric flasks or pipettes, malfunctioning instruments impure chemicals, incorrect analytical procedure or techniques & analyst error

Indeterminate error

-This cannot be pinpointed to any specific well-defined reasons

-This is also known as a random error because this type of error is random in nature

-This type of error takes place in several successive measurements performed by the same analyst under the same conditions and identical experimental parameters

-Sources of random error include the limitations of reading balances, electrical noise in instruments & vibration caused to the building by heavy vehicular trafficking, which are beyond anyone control

For ex- A balance that is capable of measuring only to 0.001g can not distinguish between two samples with masses of 0.0151& 10149 g

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

occur by accident

It is eliminated by analyst is impossible

Sources of error

1)Analyst error

  • They may be the result of inexperience, insufficient training
  • An analyst may use the instrument incorrectly
  • The error also occurs due to placing the sample in the instrument incorrectly each time
  • Setting the instrument to the wrong conditions for analysis
  • Misreading a meniscus in a volumetric flask as high (or low)


2)Operational & Personal 

These are due to factors 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

eg- Mechanical loss of material during analysis

Underwashing/ over-washing of precipitate

Ignition of  PPts at the incorrect temperature


Some other analyst related errors are


     b)Transcription error:- copying the wrong information into a lab notebook/on label

Proper training, experience & attention to details on the part of the analyst can correct these type of error

3)Reagents & Instrumentation

  • Contaminated/ decomposed reagents can cause the determinate error
  • Prepared reagents may also be improperly labeled
  • Impurities in the reagent may interfere with the determination of the analyte, especially at the ppm level or below
  • Numerous errors involving instrumentation are possible including
  1. Faulty construction of balance
  2. Incorrect instrument of alignment
  3. Incorrect wavelength settings
  4. Use of uncalibrated or improperly
  5. Calibrated weights

These problems can be eliminated by a systematic procedure to check the instrument settings & operation before use. Such procedure is called a standard operating procedure (SOP) in many laboratories

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 low completely changing the relationship between the concentration of analyte and measured signal


4)Analytical method

The most serious error is those in the method itself

Error is due to the following reason

  • Incorrect sampling
  • Incomplete reaction for chemical methods
  • Unexpected interference from the sample itself or reagents used
  • Loss of analyte during sample preparation by volatilization/ Precipitation


Contamination of sample by external sources can be a serious source of error & may be extremely variable

Aluminum levels in the dust in the normal laboratory are so high that dust prohibits the determination of low ppb levels of aluminum in samples

Methods of minimization of error

Calibration of apparatus

  • All apparatus like weight, flasks, burettes & pipettes should be calibrated
  • The appropriate corrections applied to the original measurement
  • In some case errors cannot be eliminated
  • Apply correction for that effect
  • An impurity in a weighed precipitate may be determined & its weight deducted

2.  Running a blank determination

It  is carried out as a separate determination, the sample being omitted, under exactly the same experimental conditions as employed in the actual analysis of a sample

The object is to find out the effect of the impurities introduced through the reagents & vessels

3. Running a control determination

Determination carried out as nearly as possible identical experimental conditions upon a quantity of a standard substance that contains the same weight of the constituent

4.Use of independent methods of analysis

Determination of strength of HCl both by titration with a solution of a strong base & by precipitation & weighed as AgCl

If the results obtained by the two radically different methods are concordant. it is highly probable that the values are correct within small limits of error

5. Running parallel determination

  • It serves as a check on the results of a single determination & indicates only the precision of the analysis
  • The values obtained should not less than three parts per thousand
  • If the larger variation is there then it must be repeated until satisfactory concordance is obtained
  • Duplicate/ triplicate determination is suffice

6. Standard addition

  • A known amount of the constituent being is added to the sample, which is then analyzed for the total amount of constituent present
  • The difference between the analytical results for samples with and without added constituent gives the recovery of the amount of added constituent
  • If the recovery is satisfactory our confidence in the accuracy of the procedure is enhanced
  • Even under constant experimental conditions (same operator, same tools, same laboratory, etc) repeated measurement of series of identical samples always lead to results that differ among themselves and from the true value of the sample therefore quantitative measurements cannot be reproduced with absolute reliability

7. Random errors

Random are the components of measurements errors that vary in an unpredictable manner in replicated measurement

Measuring techniques (eg noise)

Sample properties (eg inhomogeneities)

Chemical effect

Even under carefully controlled conditions, random error cannot in principle be avoided they can only be minimized & evaluated with statistical methods

8.Systemic error

•The closeness of agreement between the expectation of a test result of measurement result and true value

•According to their character & magnitude it is classified as random & systematic


  • Accuracy is the concordance between the data and true value
  • It is an agreement between the data and true value
  • If the true value is not known the mean calculated from results obtained from several different analytical methods which are very precise & close agreement with one another may be considered the true value in the practical sense
  • The difference between the mean & true value is known as the absolute error
  • Absolute error = Mean value – True value
  • Relative error = Absolute error/ True value

1)Absolute Method

The substance must be of known purity

The rest of the accuracy of the method under consideration is carried out by taking varying amount of the constituent & proceedings according to the specified instruction

The amount of the constituent must be varied, because the determinate errors in the procedure may be a function of the amount used

Method – I

It is a measure of accuracy in the absence of foreign substance

The difference between the mean of an adequate number of results & the amount of the constituent actually present

It is usually expressed as parts per thousand

Method – II

The constituent in the presence of another substance

It requires testing the influence of a large number of elements each in varying the amount

Separation is required before a determination

The accuracy of the method is largely controlled by the separation

2) Comparative method

  • In analysis, it is impossible to prepare solid synthetic samples of the desired composition
  • Necessary to sort a standard sample is in question
  • It is determined by one or more accurate method of analysis
  • It involves secondary standard not satisfactory from the theoretical standpoint
  • It is useful in applied analysis


The concordance of a series of measurement of the same quantity

The mean deviation or the relative mean deviation is a measure of precision

It is a measure of reproducibility of data within a series of result

Results within series that agree closely with one another are said to be precise

Precise results are not necessarily accurate for a determined error may be responsible for the inaccuracy of each result in a series of measurement

It is usually reported as the average deviation, standard deviation, or range

Precision is a measure of the agreement

Among the values in a group of data

Pharmaceutical analysis Question bank

Written by: Ms. Mayuri Lendave