As mentioned in the previous post, no measurement is absolute. There are uncertainties involved while making observations. The unawareness of uncertainties in our measurement renders our experimental data insignificant. Thus, from this post onwards, we start our discussion on a topic in Analytical Chemistry called ‘Errors’!!
What is an error?
An error is the difference between the real/true value and the measured value.
If the measured value is,
more than the true value(T) —————➤ Positive error ——————➤+ve fluctuation.
less than the true value(T) —————➤ Negative error——————➤ -ve fluctuation.
What are the causes of errors in any measurement?
Errors can be caused due to various reasons –
i) lack of care in making measurements
ii) incorrectly handling the instrument
iii) using a faulty instrument
iv) limitations in making correct observations etc.
Based on this , errors can be broadly classified as –
A] INDETERMINATE/RANDOM ERRORS.
B] DETERMINATE/SYSTEMATIC ERRORS.
C] GROSS ERRORS.
INDETERMINATE / RANDOM ERRORS
- These errors can be present in any measurement made, irrespective of the utmost care taken while conducting the experiment. These errors are beyond any control. They are indeterminate i.e. whose reason cannot be determined. They originate due to the limited ability of the analyst to control the external conditions or the inability to detect factors that cause errors during the experiment.
- Many times, the results of an experiment are not constant even though the system is extended to its maximum sensitivity. The results fluctuate randomly about a mean value (μ). Such errors are random in size and in sign(they could be positive or negative).
- Indeterminate errors are small in magnitude. They cannot be eliminated but can be minimised.
- The source/cause of fluctuation cannot be pinpointed. They can be caused by a variety of reasons.
e.g. Temperature variations in the atmosphere while conducting the experiment, vibrations in a building caused by moving traffic, humidity in the balance room which cause fluctuations in the balance etc. - Mathematically a numerical relationship exists between the magnitude of the indeterminate error and frequency of its occurrence. For a large number of observations made, the relationship can be pictorially represented by a Gaussian/Normal distribution curve as follows –
The above curve is called the NORMAL DISTRIBUTION/GAUSSIAN/BELL SHAPED CURVE. As seen in the figure above, the curve is symmetric around the mean point ‘T’ (true value) e.g. T = 5. The above curve tells us that –
- The positive errors (right side of the true value T) and the negative errors (left side of T) are equally likely to occur.
- The frequency of small errors E1 is large i.e. small indeterminate errors occur more frequently. Point A (on both sides) denotes the deviation from the true value. E1 is small because it is closer to the true value T. e.g. E1 = 5± 0.05. Thus, point A on the left means 5-0.5 (negative side) and that on the right means 5+0.5 (positive side).
- The frequency of large errors E2 is small. This indicates that random errors, very large in magnitude, are rare. Point B (on both sides of T) represents such errors. E2 is large because it is far away from the true value T.
e.g. E2 = 5 ± 3.5.
- Random errors are present in all experiments. There are always some parameters which are beyond our control. Unlike determinate errors, random errors are not predictable. This makes it difficult for us to detect them. However, since these errors are statistical in nature, it is easier to remove them by statistical methods like averaging.
DETERMINATE / SYSTEMATIC ERRORS
- The cause of these errors can be determined.
- They have a definite value and their magnitude could be larger.
- With proper precautions, it is possible to eliminate them.
- They are unidirectional i.e. they have the same sign and magnitude for replicate measurements. Thus, they are also called “SYSTEMATIC ERRORS”.
- Determinate errors could be –
- Instrumental or reagent errors – e.g. faulty balance or weights, the cloth tape that one uses is stretched out from years of use, evaporation of a volatile reagent, the measuring instrument being miscalibrated etc.
- Methodical errors – Sometimes the method used to conduct the experiment might be inappropriate. Some intermediate stages of the experiment may be incorrectly conducted. Thus basically, these errors arise due to faulty methods. e.g.– the decomposition of precipitate on ignition.
- Personal and operative errors – Such errors are caused by a lack of correct knowledge of the experimental procedure or an inexperienced experimentalist. e.g. blowing out the last drop from the pipette during titration.
GROSS ERRORS
- Gross errors are caused by experimenter’s carelessness or equipment failure.These can be minimised if proper care is taken.
- Any factor other than the ones mentioned above falls in the category of gross errors.
In the next post, we shall learn how to calculate errors and present the experimental data correctly.Till then ,
Be a perpetual student of life and keep learning…
Good day!
References and Further Reading –
1) https://explorable.com/random-error
2) Analytical Chemistry, 6th Edition by Gary D. Christian.
3) https://www.lhup.edu/~dsimanek/scenario/errorman/measures.htm
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