ACCURACY, PRECISION & ERRORS -STATISTICAL TOOLS OF MEASUREMENT

STATISTICS INVOLVED IN PHARMACEUTICAL ANALYSIS

Statistics is of great importance in calculating the result from the analytical data obtained. These are accuracy, precision, errors and significant figures. To understand accuracy, precision and error some terms should be very clear in mind i.e. observed value & standard value.

Observed value – These are the values which an analyst obtains after analysis of sample e.g. an analyst after analysis of a sample says that the sample is 80% pure. This 80% is observed value.

Standard value – Sometimes it is also called as true value. This is the value which the sample claims e.g. a tablet sample claims paracetamol 100 mg. This 100 mg is standard value.

Accuracy, Precision & Errors

These can be easily explained by an example. Two analysts (Analyst 1 & analyst 2) are analyzing a sample five times using same method and instruments (sample claims it is 100% pure i.e. standard value is 100%). The results  of the of the tests performed by the two analysts are given in the table below-

TEST NUMBER ANALYST 1 ANALYST 2
1 99.10 % 98.95 %
2 99.30 % 98.91 %
3 99.80 % 98.96 %
4 99.50 % 98.92 %
5 100.00 % 98.93 %

Now, if we calculate the average/mean value of the results obtained by analyst 1, we get

99.10 + 99.30 + 99.80 + 99.50 + 100.00

Mean = —————————————————————— = 497.7 / 5 = 99.54 %

5

Error = 100 – 99.54 = 0.46 %

Now, if we calculate the average/mean value of the results obtained by analyst 2, we get

98.95 + 98.91 + 98.96 + 98.92 + 98.93

Mean = —————————————————————— = 494.67 / 5 = 98.934 %

5

Error = 100 – 98.934 = 1.066 %

Accuracy – Accuracy means how near the observed value is to the standard value.

Precision – Precision means nearness between several measurements of the same quantity.

If we compare the results of the two analysts, error of analyst 1 is 0.46% and of analyst 2 is 1.066%, following things can be concluded-

  1. Results of analyst 1 is more accurate than the results of analyst 2 because comparably, error of analyst 1 (0.46%)is much less than the error of analyst 2 (1.066%)
  2. Results of analyst 2 is much more précised than the results of analyst 1 because there is very less difference in each other.

Now we will discuss about error, its types and methods of minimizing error.

ERROR

Error – The difference between the observed value and the standard value. Larger the difference, more be the error. If two analysts performs a analysis using the same instrument and for measurement, its not essential that both will get the same results. There may be difference in their measurements. This difference is called as error.

Types of error

Broadly we can divide error into three types namely personal error, systematic error and random error.

  1. Personal error – it arises due to the use of faulty procedure. For example
  2. two persons if taking reading of thermometer, there readings may differ.
  3. two persons if pipetting some chemicals, quantity may differ because some use lower meniscus and some upper meniscus while pipetting.
  • during titration, if the end point is pink color, a person can do mistake because of the confusion in colors like light pink or dark pink.
  1. Systematic error or determinate error – it arises due to instrumental fault i.e. use of uncalibrated (calibration means to check the machine whether it working properly or not, if not it will be corrected) instruments.

Example – if a person is using a digital weighing machine to weigh a sample and the machine is giving weight 50 mg. he takes the weight of the sample as 50 mg. This reading may be wrong because may e the machine is uncalibrated, may be the correct result is 48 mg or 52 mg. This type of error comes under systematic error.

  1. Random error or indeterminate error – These errors are beyond our control and arises due to sudden change in environmental conditions like
  2. Sudden change in temperature, humidity
  3. Voltage fluctuation

Sources of error

Human error and equipment error are the sources of error.

  1. Human error – Examples of human error are-
  2. Incorrect measurement
  3. Use of contaminating glasswares e.g. a person uses a pipette to pipette 5 ml nitric acid and without washing he uses it for pipetting hydrochloric acid. Here the hydrochloric acid gets contaminated.
  • Dirty working place, glasswares, instruments
  1. Equipment error – taking measurement without checking, its giving correct reading or not.

Methods for minimizing errors –     

  1. Correct measurements
  2. Working place and instruments should be clean
  3. Glasswares should be washed, cleaned and dried.
  4. Calibrated instruments should be always used
  5. Use of correct procedure
  6. Running a blank determination
  7. Use of two methods and results are compared

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