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

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

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.

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

Determinate or systematic error 1 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.

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

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:

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

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

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

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

These types of errors obtained due to classical methods 2 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 MnNH4PO4 ---- Mn2P2O7 +2NH3+H2O

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.

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 .

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

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

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

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

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

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

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

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

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.

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

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. 10.45)

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).

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

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

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

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.

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

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