Calibration procedures and estimation of errors

In science, the word error has a very specific meaning it does not mean mistake . All experimental measurements will differ, to some degree, from the accurate or real value of the quantity being measured. The difference between the observed value of a physical quantity and the accurate value is called the error. It is very important to consider all the possible sources of errors in experimental measurements. Every experimental measurement reported should be accompanied by an estimate of the error - scientifically speaking, measurements without accompanying error estimates are worthless. 

Experimental errors come from two different sources, termed systematic and random errors. However, it is sometimes difficult to distinguish between them, and many experiments have a combination of both types of error. 

Systematic errors usually arise from specific shortcomings in the measuring instrument, the observer, or the way in which the measurement is taken. Sources of systematic error include a badly calibrated measuring device, a faulty instrument movement, an incorrect action by the experimenter (e.g., misreading a volume measurement), or the parallax effect when incorrectly viewing a scale. Repeating the measurement does not necessarily help, because the error may be repeated, and the analyst may 

Random errors arise in all measurements and are inevitable, no matter what the experiment, the quality of the instrument, or of the analyst. They are a consequence of the limitations of experimental, observations. For example, an instrument reading can only be taken within the limits of accuracy of the scale, as read by a particular observer. The position of the pointer between two division marks may be estimated to one fifth of a division by a skilled experimenter, but only to one half a division by another. Such skill may be improved with practice, but will never be totally perfected. Random errors cannot be eliminated, but can be reduced by using more sensitive measuring instruments or an experienced experimenter. The magnitude of random errors can be estimated by repeating the experiment. 

If a large number of readings of the same quantity are taken, then the mean (average) value is likely to be close to the true value if there is no systematic bias (i.e., no systematic errors). Clearly, if we repeat a particular measurement several times, the random error associated with each measurement will mean that the value is sometimes above and sometimes below the true result, in a random way. Thus, these errors will cancel out, and the average or mean value should be a better estimate of the true value than is any single result. However, we still need to know how good an estimate our mean value is of the true result. Statistical methods lead to the concept of standard error (or standard deviation) around the mean value. 

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