Measurement Error

Definition: The measurement error is defined as the difference between the true or actual value and the measured value. True value is the average of the infinite number of measurements, and the measured value is the precise value.

Types of Errors in Measurement

The error may arise from the different source and are usually classified into the following types. These types are

1. Gross Errors
2. Systematic Errors
3. Random Errors

Their types are explained below in details.

1. Gross Errors

This class of errors mainly covers human mistakes in reading instrument and recording and calculating the measurement result. The responsibility of the mistake normally lies with the experimenter. The experimenter may grossly misread the scale.

For example – The experimenter due to an oversight, read the temperature as 31.5º C while the actual reading may be 21.5º C. He may transpose the reading while recording. Also, the experimenter may read 28.5º C and record 28.5º C instead. Such types of error will be committed by human beings.

The complete elimination of such type of errors is probably impossible. The experimenter only tries to anticipate and correct them. Some types of gross error are easily detected while others may be very difficult to detect. Such type of error can only be avoided by adopting two methods.

• Great care should be taken in reading and recording the data.
• Two, three or even more reading and recording should be taken in the quantity under measurement. These readings should be taken preferably by different experimenters, and the reading should be taken at a different reading point to avoid re-reading with the same error.

2. Systematic Errors

The systematic errors are mainly classified into three categories.

1. Instrumental Errors
2. Environmental Errors
3. Observational Errors

2 (i) Instrumental Errors

These errors mainly arise due to the three main reasons.

(a) Inherent Shortcomings of Instruments – Such types of errors are inbuilt in instruments because of their mechanical structure. They may be due to manufacturing, measurement or operation of the instruments or measuring devices. These errors may cause the error to read too low or too high.

For example – if the spring of a permanent magnet instrument has become weak, the instrument will always read high. Errors may be caused because of friction, hysteresis or even gear black ash.

(b) Misuse of Instrument – The error may be caused in the measurement is due to the fault of the operator than that of the instrument. A good instrument used in an unintelligent way may give an enormous result.

For example, the misuse of the instrument may cause the failure to adjust the zero of instruments, poor initial adjustment, using lead to too high resistance. These improper practices may not cause a permanent damage to the instrument, but all the same, they cause errors.

(c) Loading Effect  – It is the most common type of error which is caused by the instrument in measurement work. For example, when the voltmeter is connected to the high resistance circuit it gives a misleading reading, and when it is connected to the low resistance circuit, it gives the dependable reading. This means the voltmeter has a loading effect on the circuit.

The error caused by the loading effect can be overcome by using the meters intelligently. For example, when measuring a low resistance by ammeter-voltmeter method a voltmeter having a very high value of resistance should be used.

2 (ii) Environmental Errors

These errors are due to the external condition of the measuring devices. Such types of errors mainly occur due to the effect of temperature, pressure, humidity, dust, vibration or because of the magnetic or electrostatic field. The corrective measures employed to eliminate or to reduce these undesirable effects are

• The arrangement should be made to keep the conditions as constant as possible.
• Using the equipment which is free from these effects.
• By using the techniques which eliminate the effect of these disturbances.
• By applying the computed corrections.

2 (iii) Observational Errors

Such types of errors are due to the wrong observation of the reading. There are many sources of observational error. For example, the pointer of a voltmeter resets slightly above the surface of the scale. Thus an error occurs (because of parallax) unless the line of vision of the observer is exactly above the pointer. To minimise the parallax error highly accurate meters are provided with mirrored scales.

3. Random Errors

The error which is  caused by the sudden change in the atmospheric condition, such type of error is called random error. These types of error still remain even after the removal of the systematic error. Hence such type of error is also called residual error.