Table of Contents

Error in Measurement | types of errors in measurement

INTRODUCTION TO ERROR IN MEASUREMENT :
The measurement of a quantity is based on some International fundamental standards. These fundamental standards are perfectly accurate, while others are derived from these. These derived standards are not perfectly accurate in spite of all precautions. In general, measurement of any quantity is done by comparing with derived standards which themselves are not perfectly accurate. So, the error in the measurement is not only due to error in methods but also due to standards (derived) not being perfectly accurate. Thus, the measurement with 100% accuracy is not possible with any method.
Error in the measurement of a physical quantity is its deviation from actual value. If an experimenter knew the error, he or she would correct it and it would no longer be an error. In other words, the real errors in experimental data are those factors that are always vague to some extent and carry some amount of uncertainty. A reasonable definition of experimental uncertainty may be taken as the possible value the error may have. The uncertainty may vary a great deal depending upon the circumstances of the experiment. Perhaps it is better to speak of experimental uncertainty instead of experimental error because the magnitude of an error is uncertain.
At this point, we may mention some of the types of errors that cause uncertainty is an experimental in measurement. First, there can always be those gross blunders in apparatus or instrument construction which may invalidate the data. Second, there may be certain fixed errors which will cause repeated readings to be in error by roughly some amount but for some unknown reasons. These are sometimes called systematic errors. Third, there are the random errors, which may be caused by personal fluctuation, random electronic fluctuation in apparatus or instruments, various influences of friction, etc.

CLASSIFICATION OF ERRORS

Errors will creep into all measurement regardless of the care which is exerted. But it is important for the person performing the experiment to take proper care so that the error can be minimized. Some of the errors are of random in nature, some will be due to gross blunder on the part of the experimenter and other will be due to the unknown reasons which are constant in nature.

Thus, we see that there are different sources of errors and generally errors are classified mainly into three categories as follows:
(a) Gross errors
(b) Systematic errors
(c) Random errors

Gross Errors
These errors are due to the gross blunder on the part of the experimenters or observers. These errors are caused by mistake in using instruments, recording data and calculating measurement results. For example: A person may read a pressure gage indicating 1.01 N/m2 as 1.10 N/m2. Someone may have a bad habit of memorizing data at a time of reading and writing a number of data together at later time. This may cause error in the data. Errors may be made in calculating the final results. Another gross error arises when an experimenter makes use (by mistake) of an ordinary flow meter having poor sensitivity to measure low pressure in a system.

Systematic Errors
These are inherent errors of apparatus or method. These errors always give a constant deviation. On the basis of the sources of errors, systematic errors may be divided into following sub-categories :

Constructional Error
None of the apparatus can be constructed to satisfy all specifications completely. This is the reason of giving guarantee within a limit. Therefore, a manufacturers always mention the minimum possible errors in the construction of the instruments.

Errors in Reading or Observation
Following are some of the reasons of errors in results of the indicating instruments :
(a) Construction of the Scale : There is a possibility of error due to the division of the scale not being uniform and clear.
(b) Fitness and Straightness of the Pointer : If the pointer is not fine and straight, then it always gives the error in the reading.
(c) Parallax : Without a mirror under the pointer there may be parallax error in reading.
(d) Efficiency or Skillness of the Observer : Error in the reading is largely dependent upon the skillness of the observer by which reading is noted accurately.

Determination Error
It is due to the indefiniteness in final adjustment of measuring apparatus. For example, Maxwell Bridge method of measuring inductances, it is difficult to find the differences in sound of head phones for small change in resistance at the time of final adjustment. The error varies from person to person.

Error due to Other Factors

Temperature Variation –Variation in temperature not only changes the values of the parameters but also brings changes in the reading of the instrument. For a consistent error, the temperature must be constant.
Effect of the Time on Instruments – There is a possibility of change in calibration error in the instrument with time. This may be called ageing of the instrument.
Effect of External Electrostatic and Magnetic Fields – These electrostatic and magnetic fields influence the readings of instruments. These effects can be minimized by proper shielding.

Mechanical Error – Friction between stationary and rotating parts and residual torsion in suspension wire cause errors in instruments. So, checking should be applied. Generally, these errors may be checked from time to time.

Random Errors
After corrections have been applied for all the parameters whose influences are known, there is left a residue of deviation. These are random error and their magnitudes are not constant. Persons performing the experiment have no control over the origin of these errors. These errors are due to so many reasons such as noise and fatigue in the working persons. These errors may be either positive or negative. To these errors the law of probability may be applied. Generally, these errors may be minimized by taking average of a large number of readings.