Errors in Measurements

Any real measurement of a physical quantity can be affected by faults in the measurement process, which lead to errors. These errors are broadly classified into two categories: systematic errors and random errors.

(a) Systematic errors are errors that are not due to random chance, but instead arise from some inaccuracy — in either the observation process or the measurement process itself — that is inherent to the measuring system. Because they stem from a fixed underlying cause, systematic errors always act consistently in one direction, either always positive or always negative, for a given setup. Systematic errors themselves arise from three main sources:

1. Instrumental error — arising from a defective calibration of the instrument itself. For example, an incorrectly 'zeroed' instrument produces this kind of error: a thermometer whose zero mark is not graduated at the true freezing point, the pointer of a laboratory weighing balance that already shows some nonzero reading before any load is placed on it, or an ammeter that reads $0.5\ \text{A}$ even when it is not connected in any circuit at all.
2. Error due to imperfection in experimental technique — arising from a defective setting of an otherwise correctly calibrated instrument. For example, the volume of a liquid read off a graduated tube will come out inaccurate if the tube is not held perfectly vertical while reading.
3. Personal error — introduced by a fault of the observer themself: bias, carelessness, or a poor viewing habit. For example, when measuring the length of an object against a ruler, the observer must look directly down at the ruler from directly above; viewing it from an angle instead introduces an error known as parallax error in the reading (not to be confused with the deliberate astronomical use of parallax in section 1.3.1 — here it is an unwanted reading error, caused by exactly the same geometric effect). Because each of these three sources has an identifiable, fixable cause, systematic errors can generally be minimized (though rarely eliminated completely) by using a correctly calibrated instrument, following the correct experimental procedure, and eliminating personal bias in the observer. …