Measurement is involved in every aspect of experimental chemistry and the most important part of this includes the understanding of the skill of the observer and the scope of measurement of a given instrument.
To identify any measurement as meaningful, we need to identify some kind of standard against which the measurement is made. Apart from the standards, we also need to know the units of measurement. Nowadays, the standard way of measurement is by using the SI units which are used by the scientists all over the world to come to a commonly understandable result. To understand the results of an experiment, we need to know three important terms – Accuracy, i.e. the extent to which the experiment conforms to the truth, Reliability, the extent to which an experiment is reproducible in the stated conditions and, Validity i.e. the extent to which the experiment is able to test the hypothesis.
To delve further into this, the two terms “accuracy” and “precision” need to be understood.
Let three students- A, B and C are doing a titration experiment in which the expected end point is reached at the burette reading of 23.5 ml. Each of the student repeats the experiment thrice and record their observations as follows:
|Observation No.||Burette reading (A)||Burette reading (B)||Burette reading (C)|
|1||24.6 ml||23.5 ml||23.5 ml|
|2||24.6 ml||22.1 ml||23.5 ml|
|3||24.8 ml||28.7 ml||23.4 ml|
A has precision but no accuracy since the results are consistent but not close to the correct result.
B has reported one result close to the correct one, but the other two results are neither accurate nor precise.
C has reported the results which are both accurate and precise.
This error resulting from the expertise (or lack of it) of the observer is called human error.
The second aspect of any measurement is the scope and limitation of an instrument. Let’s consider two graduated cylinders – X and Y each having a capacity of 10 ml. The cylinder X has 10 marks on it, each corresponding to 1 ml while Y has 100 marks on it, each corresponding to 0.1 ml. If we are to accurately measure a volume of 4.6 ml using any of these two cylinders, the cylinder Y will be the ideal one since it has markings that correspond to 0.1 ml. But, the cylinder X will only give a rough estimate since it has no markings between the those for 4 ml and 5 ml.
The error resulting from the limitation of any instrument is called the instrumental error.
- Any kind of measurement is a quantitative analysis.
- All measurements contain some degree of error.
- Human error results from the level of expertise of the observer.
- Instrumental error results from the limitation of the instrument.
The uncertainty in the measurements is the precursor to that in the calculated result. The range of uncertainty in a result is indicated by the plus or minus sign. A result reported as 1.67 ± 0.02 indicates that the person doing the experiment has confidence that the result lies within the range of 1.65 to 1.69. In a chemistry lab, the rage of uncertainty is such that an uncertainty value of only one significant figure is sufficient to convey the accuracy of the result. In some cases, the results are displayed only in terms of significant figures. The uncertainty in such cases, is considered to be present only in the last digit. For example, a result of 1.67 would indicate an uncertainty of ±0.01, i.e. the result lies within 1.66 to 1.68.
Types of Errors
Any error is the deviation of the result from the true value. As is implied from this statement, the exact value of the observable must be known to determine the exact degree of deviation from it. Since most of the times, the exact result is unknowable, the errors are classified so as to identify its source and rectify the result if possible. Using the most sophisticated instruments too lead to slightly varying results each time. Taking this into consideration, the errors are often classified into two distinct categories:
- Systematic errors – These errors occur due to the pattern of usage of an instrument or the pattern of observation by the observer. These may result from the fundamental errors in manufacture of the instrument, error in calibration or interference in observation by environmental factors. These are usually observed as being related to the result in form of a constant percentage or proportion. Due to this reason, these may sometimes be very hard to locate. Once identified, systematic errors can be removed.
- Random errors – These errors are non-reproducible and often result from the inconsistency in the method of observation. Random errors arise out of unpredictable instabilities in the values recorded by the apparatus, or from interpretation of the values. These variations may partly result from the interference of the situation with the measurement procedure.
Another type of error may also be encountered sometimes due to the lack of proper experimental conditions or lack of concentration of the experimenter. This type of error is called blunder or erratic error. An example of such an error is the mistake by the observer in recording the readings or poor electrical connection within the instrument which can result in erratic values. These errors are often wayward and fall well outside the range of uncertainty.
Absolute and relative uncertainty in expressing the errors
Errors can be represented as either being at a definite difference with the desired result or as a fraction or percentage of the desired result. In terms of validity of an experiment, the uncertainty is related to the precision of the measurement. The more precise the experiment, less is the uncertainty. The relative error is the best judge of the precision since it takes into account the percentage and not the actual value. For example, a measurement at the nanometer scale may have an error which has a value lesser in magnitude, but higher in percentage compared to another measurement at the centimeter scale. The elimination of random errors can lead to the reduction of relative error/ uncertainty and as a result, make the experiment more precise.
Error propagation primarily happens during the calculation of final results from the initial experimentally observable quantities. The additions and subtractions result in propagation of absolute errors in a big way but minimal propagation in relative errors. The multiplication, division and other complex functions built upon those, usually propagate the relative errors in a huge way but don’t affect the absolute errors significantly.
In summary, the improvement in the accuracy and validity of an experiment depends on:
- Keeping all variables, other than those being studied, at a constant value.
- Elimination of all systematic errors by cautious arrangement and in doing the experiment.
- Reduction in random errors to the extent possible by using the mean from multiple measurements.
- Any kind of measurement incorporates some errors.
- Errors arising out of pattern of usage of instrument or the pattern of observation by the observer are called systematic errors.
- Errors arising out of the inconsistency in the method of observation are called random errors.
- Errors due to the lack of proper experimental conditions or lack of concentration of the experimenter are called erratic errors or blunders.
- Absolute errors represent the actual difference from the desired observation.
- Relative errors represent the percentage of difference from the desired observation.
- Absolute errors propagate through addition or subtraction while relative errors propagate through multiplication and divisions.