ERRORS IN MEASUREMENT
Errors in Measurement
Classification of Errors
Accuracy and Precision
Calibration of the Instrument
Analysis of the Errors
Error Analysis on Common Sense Basis
Statistical Analysis of Experimental Data
Answers to SAQs
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.
After studying this unit, you should be able to
understand the nature of errors and their sources in the measurement,
know accuracy and precision in the measurement, and
explain the various methods of analysis of the errors.
2.2 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:
2.2.1 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.
2.2.2 Systematic Errors
These are inherent errors of apparatus or method....
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