Errors of Measurement

It is the fact and from experience, it is observed that a continuous variable can not be measured with perfect (true) value because of certain habits and practices, measurement methods (techniques), and instruments (or devices) used, etc. It means that the measurements are thus always recorded correctly to the nearest units and hence are of limited accuracy. The actual or true values are, however, assumed to exist.

For example, if the weight of a student is recorded as 60 kg (correct to the nearest kilogram), his/her true (actual) weight, in fact, may lie between 59.5 kg and 60.5 kg. The weight recorded as 60.00 kg for that student means the true weight is known to lie between 59.995 and 60.005 kg. Thus, there is a difference, however, it is small it may be between the measured value and the true value. This sort of departure from the true value is technically known as the error of measurement. In other words, if the observed value and the true value of a variable are denoted by $x$ and $x + \varepsilon$, respectively, then the difference $(x + \varepsilon) – x=\varepsilon$, is the error. This error involves the unit of measurement of $x$ and is, therefore, called an absolute error.

An absolute error divided by the true value is called the relative error. Thus the relative error can be measured as $\frac{\varepsilon}{x+\varepsilon}$. Multiplying this relative error by 100 gives the percentage error. These errors are independent of the units of measurement of $x$. It ought to be noted that an error has both magnitude and direction and that the word error in statistics does not mean mistake which is a chance inaccuracy.

An error is said to be biased when the observed value is higher or lower than the true value. Biased errors arise from the personal limitations of the observer, the imperfection in the instruments used, or some other conditions which control the measurements. These errors are not revealed by repeating the measurements. They are cumulative in nature, that is, the greater the number of measurements, the greater would be the magnitude of the error. They are thus more troublesome. These errors are also called cumulative or systematic errors.

An error, on the other hand, is said to be unbiased when the deviations from the true value tend to occur equally often. Unbiased errors tend to cancel out in the long run. These errors are therefore compensating and are also known as random errors or accidental errors.

We can reduce errors of measurement by

• Double-checking all measurements for accuracy
• Double-checking the formulas are correct
• Making sure observers and measurement takers are well trained
• Making the measurement with the instrument has the highest precision
• Take the measurements under controlled conditions
• Pilot test your measuring instruments
• Use multiple measures for the same construct