1. Dnyanasadhana College, Thane. Department of Chemistry T. Y. B. Sc
Dnyanasadhana College, Thane. Department of Chemistry T.Y.B.Sc. Analytical Chemistry Paper-IV Sem-V Treatment of Analytical Data Dr.G.R.Bhagure

2. Any measurement involves the interaction of following three components
Analyst
Sample
Method
ERROR

3. Errors: The word “error” has a very specific meaning in science: error is simply the difference between an observed result and the “true,” “actual,” “known,” or “accepted” value. It is a way of expressing accuracy, or how close a measurement is to the “true” value. Error can be reported several ways.

4. Indeterminate or random Error
Types of error
Determinate error
Indeterminate or random Error
Gross error

5. Determinate or systematic error1
Determinate error are those for which source can be observed or detected. 2
The error can often be eliminated or taken into consideration. 3
Analytical chemists attempt to use methods and techniques that have determinate error eliminated as much as possible. 4
A common cause of determinate error is instrumental or procedural bias. 5
For example: a miscalibrated scale or instrument, a color-blind observer matching colors.
Another cause is an outright experimental blunder.

6. Examples:
using an incorrect value of a constant in the equations, using the wrong units,
reading a scale incorrectly.
Determinate errors can be more serious than indeterminate errors for three reasons. (1) There is no sure method for discovering and identifying them just by looking at the experimental data. (2) Their effects can not be reduced by averaging repeated measurements. (3) A determinate error has the same size and sign for each measurement in a set of repeated measurements, so there is no opportunity for positive and negative errors to offset each other

7. Indeterminate or random error:
This type of error has no assignable source and cannot be eliminated, but it can be understood mathematically
It causes measurements to fluctuate (vary slightly high and low) around the true value.
The error are for which source can not be observed or not detected or can be pinpointed
Indeterminate or random error:

8. Sr. No.
Characteristics
Determinate
error
Indeterminate Error 1
Origin
Source can be observed
No Source can be observed 2
Magnitude
Large
Small 3
Direction
Unidirectional
No direction 4
Reproducibility
Reproducible
Not Reproducible 5
Effect
Affect the measurement
No Affect on measurement 6
Remedy
Minimization possible, elimination in some cases possible
No elimination

9. Gross Error
This type of error occur due to a fault or blunder on the part of analyst.
● Analyst is responsible for this type of error.
Ex.● Preparation of solution in ordinary tap water.
● Unwashed/dirty/ glass ware used for expt.
● Forget to add indicator in the titrand

10. Types of
Determinant error
Instrumental errors
Methodic errors
Operational errors
Personal error

11. Ex. Counting /noting burette reading
INSTRUMENTAL ERRORS:
1. Uncertainty in the last digit of the measurement due to least count of the instrument or volumetric glass ware.
Ex. Counting /noting burette reading
2. Improper response: Optimum condition for the working of the Instrument. Instrument works in that condition only.
Ex. Working of glass electrode to measure pH using pH meter.
pH of solution 1-10 can be recorded properly.
If the solution is having pH greater than this range electrode system will give Improper response

12. These types of errors obtained due to classical methods2
Addition of excess amount of titrant 3
Incomplete reaction 4
Incomplete decomposition 5
Co-precipitation and post Co-precipitation 1
Solubility of salt
These types of errors obtained due to classical methods
as these methods involves no. of steps.
Methodic Errors
MnNH4PO  Mn2P2O7 +2NH3+H2O

13. Operational errors Weighing of the hot crucible
Loss of precipitate during filtration
Blowing of last drop of in the nozzle of the precipitate
Improper recording of the instrument
Under washing or over washing of the ppt.
Ignorance of temp.

14. Personal error
The error due to physical limitation of the analyst and some time bias during measurement are called as Personal error.
Ex.Colourblindnees of the person unable to detect end point .

15. Minimization of errors
Calibration of apparatus and Instruments
Running Blank determination
Use of Independent method of analysis
Running control determination
Running Parallel determination
standard addition method
Internal standard method
Amplification method

16. Calibration of apparatus and Instruments
Operational and instrumental error can be minimized
Calibration of apparatus and Instruments
Methodic and operational errors can be minimized
Running Blank determination
Standard sub. Analysed and its result compared with the true value
Deviation of the obtained result from the true or expected value will be measure of Methodic and operational errors
Running of control determination

17. Use of Independent method of analysis
Analysis of same sample by two method of analysis ,one which will be chosen & results obtained can be compared.
Methodic and operational errors can be different
Use of Independent method of analysis
Analysis of same sample by two different method by same analyst, or different .
Methodic error will differ in two cases ,if same analyst
Methodic and personal error will be differ in two cases if different analyst.
Running Parallel determination
Sample is analysed alone then sample + standard substance analysed
Methodic and operational errors will be same for two measurements
standard addition method

18. Internal standard method
Fixed amount of reference material is added to all standard solutions ,blank and sample .
Ex. Na is added in the analysis of soil while determining lithium
Internal standard method
detector singles are amplified to rectify the improper response of detector.
With the knowledge of type of error analyst can modify existing method, type of error and magnitude.
Amplification method

19. Measures of Error Absolute Error
Absolute error = observed result – “true” value
. The formula is used this way consistently so that the meaning of the sign of the error is clear:
Positive error means the observed result is too large,
Negative error means the measured result is smaller than true

20. Relative Error Relative error = absolute error/true value or
Relative error compares the size of an error to the value of the true measurement. Thus,
Relative error = absolute error/true value or
relative error = (observed result – true result)/true value..
Relative error can be expressed as a decimal, percentage, parts per thousand, parts per million, etc

21. Accuracy Accuracy: Precision:
Accuracy: It can be defined as closeness of the observed value to the true or accepted value.
Accuracy
It can be defined as closeness of the observed value to the true or accepted value.
Accuracy:
It is degree of agreement amongst the observation
Precision: OR

22. Parameter
Accuracy
Precision
Defination
Closeness of a measured value with true or accepted value
Agreement amongst the observation
Indicator
Reliability of method
Reproducibility of method
Measure
Measured in terms of absolute and relative error
Standard deviation is the measure of the precision
Evaluation
Evaluated for single observation
Evaluated for set of observation
Calculation
Can be calculated if true or accepted value is known
No need to know true or accepted value is
Relation between Accuracy & Precision
Good degree of accuracy accompanied by good precision
Good precision can not guarantee good precision accuracy

23. Precision and Accuracy
Measurements that are close to the “correct” value are accurate.
Measurements which are close to each other are precise.
Measurements can be
accurate and precise;
precise but inaccurate;
neither accurate nor precise.

24. Measures of Central Tendency and Dispersion
Mean
The mean is the most widely used measure of the central value. It is denoted by x x

25. Median:
When quick measure of central value is to be decided and when gross errors are suspected the central tendency of a group of results can be expressed in terms of median by arranging the observations either in ascending or descending sequence. Median means the middle value.
Ex. 1) 10.3,10.4, 10.5,10.7,10.8 (odd number of total observation the median is middle value i.e. 10.5)
2) 10.2, 10.3,10.4, 10.5,10.7,10.8 ( even number of total observation, the median is average of the middle pair of observations i.e )

26. Mode:  
The observation which occurs most frequently (i.e. which is repeated maximum number of times) in a series of observations is known as mode. It is yet another quick measure of central value if the number of observations is not too small.
For example, the mode of the set of data: 12,6, 12,7, 12.9, 12,7, 12.6, 12.8, 13.0, 12.5, 12.6, the value 12.6 is the mode since this is occurring with maximum frequency (three times).

27. Measures of Dispersion
Deviation
The error of a measurement can not be stated if the true value of the quantity is not known. It is meaningful then to take the difference between a particular measured value (observation) and the arithmetical mean of a series of measurements and this difference is called as its deviation for apparent error.
A deviation is generally taken without regard to sign. It is defined mathematically as,
d= Xi-X

28. Average Deviation
The average deviation (a.d.) or the mean deviation is the average of individual deviations:

29. Relative Average Deviation :
The ratio of the average deviation to the mean is known as Relative Average Deviation (RAD) which can be expressed as percent average deviation when multiplied by 100, thousand average deviation when multiplied by 1000.
X 100
X 100o

30. Measures of Dispersion for set of observation
1) Range:
The difference between the largest and smallest values in a set of measurements is known as the range.
It tells the spread of data. The range is often used, with appropriate factors that depend on the number of measurements, as a quick statistics to a rough estimate of precision.

31. 2) Standard Deviation:
It is defined as the square root of the mean of the squares of Indiudual deviations. Mathematically
3) Variance: Square of standard deviation is called as Variance.
Variance=s2

32. 4) Coefficient of Variation: Ratio of standard deviation to mean ,and its expressed as percentage.
COV =