Subsection 1.1.2 Errors in Measurement
Measurement is a base of science. In every measurement there is some uncertainty. This uncertainty is called an error. The concept of errors can be understood by knowing the terms accuracy and precision. Accuracy refers to how closely a measured value agrees with the correct (true) value. Precision refers to how closely individual measurements agree with each other. For example, suppose the true value of a certain length is near 5.678 cm. In one experiment, the measured value is found to be 5.5 cm by using a measuring instrument of resolution 0.1 cm, while in another experiment, the length is determined to be 5.38 cm by using a measuring device of greater resolution, say 0.01 cm. The first measurement is more accurate (as it is closer to the true value) but less precise (as its resolution is only 0.1 cm), while the second measurement is less accurate but more precise. Thus every measurement is approximate due to errors in measurement. In general, the errors can be classified as (a) systematic errors and (b) random errors. The errors that appear due to faulty instruments or imperfact instrumental design are known as systematic errors. It is a repeatable error in the measurement. The systematic errors are
- Instrumental errors: These errors arise due to imperfact calibration or design of the measuring instrument. Usually they are called a Zero Error. It is either a positive or a negative type. These errors can be removed by correcting the measuring device, e.g., in vernier calipers the zero mark of vernier scale may not coincide with the zero mark of the main scale.
- Personal errors: They arise due to wrong observations, an individual’s bias, lack of proper setting of the apparatus, e.g., parallax error, a person viewing a car’s speedometer from the driver’s seat will get an accurate reading because she has a direct line of sight. A person viewing the speedometer from the passenger seat will overestimate the reading because of the viewing angle between his eye, the meter, and the arrow.
The errors that appear due to system noise or disturbance of measuring location are known as random errors. It is a unpredictable and non-repeatable. Experimental error is one of the random errors. Experimental errors arise due to some external conditions of the instrument such as pressure, temperature, humidity, or magnetic fields, e.g., a thermometer placed under the armpit will always give a temperature lower than the actual value of the body temperature. This type of errors may also occur due to random and unpredictable fluctuations in experimental conditions (e.g. variation in temperature, supply voltage, local atmospheric pressure, etc) and personal errors (e.g., change in readings if the observer repeats the same observation).
