For some reason the word 'error' is unpopular in our context. One reason might be destruct of the concept of an ideal result of measurement-without which the terms 'accuracy' and 'error' lack meaning. But, as already indicated, if there is no such thing as an ideal result then the experimentalist has to find an alternative logic when using the concepts of probability. Another potential reason is that the word 'error' might be thought to imply that a mistake has been made and the measurement scientist rightly wishes to avoid giving that impression. But perhaps the principal cause of the unpopularity of the word 'error' in measurement science is a perception that the techniques of so called 'error analysis' are inadequate. The techniques of the subject that was known by that name in the middle of the twentieth century do indeed seem limited.
Numbers obtained from a measurement are approximate values. There is always some uncertainty due to the limitations of the measuring devices used and the skill of the individual making the measurement. The figures used to report a result should reflect the precision of the test and the sensitivity of the measuring device that produced the value. To express this precision, the number should contain all the digits that are known plus one digit that is estimated. These are the significant figures. The term significant refers to the number of digits that are meaningful with regard to the accuracy of the value.
Data fitting is the tool used by experimentalists to verify a theoretical prediction, many more points than the minimum are measured in order to minimize the effects of random errors generated in the acquisition of the data. But this over determination in the system parameters faces us with the dilemma of what confidence level one gives to the accuracy of specific data points and which data points to accept or reject.