3.2.2.2. Instrument Errors 



In the instrument field one commonly encounters the "instrument error". This 

 can be split into two parts : determinate errors and indeterminate errors. 



Where the error is determinate, one sometimes refers to this as a "set". Where 

 the error is indeterminate, it is referred to as instrument precision, or instrument 

 reproducibility. The word precision denotes the extent to which a result is free from 

 accidental errors. It is important to note that a result may be extremely precise and 

 at the same time highly inaccurate, the precise result being in error by the magni- 

 tude of the determinate error. 



3.2.2.3. Dependent and Independent Errors 



Errors can furthermore be classified into dependent errors and independent er- 

 rors. Where a quantity Y is a function of a quantity X, an error in X will produce 

 a corresponding error in Y. This error in Y is known as the dependent error. Where 

 the measurement of Y involves an accidental error which is not a function of X, it 

 would be classed as an independent error. The total observed indeterminate error in 

 X would be a function of dependent and independent errors observed. 



Where the term "error" is used without classification or enlightenment, it is 

 assumed that it means the indeterminate error, which in turn is a sum of the depend- 

 ent and independent errors. 



3.3. Accuracy 



The accuracy of a value is a measure of how close to the true value or probable 

 value the indicated measurement is likely to be. It in reality is the probable error, 

 and takes into account both the determinate and indeterminate components of error. 



3.4. Average Values and Average Errors 



Average values and average errors are distinguished from probable values and 

 probable errors by the fact that the former are arbitrarily defined by mathematics, 

 and do not necessarily have any physical significance unless the assumptions which 

 are made are valid. 



3.4.1. Average Value 



In considering a series of measurements of the same conditions, the average 

 value or arithmetic average of the measurements is mathematically defined as the 

 sum of the values of the individual measurements divided by the number of meas- 

 urements taken. This is also sometimes called the "mean value". It should be noted 

 that the average value is not necessarily the most probable value; it is simply the 

 arithmetic average of the measurements which were taken. 



3.4.2. Deviation 



The net difference between any one reading of the series and the average value 

 is called a deviation. Sometimes it is called a deviation. Sometimes it is called a de- 

 viation from the mean ; sometimes it is called a variation ; and it is sometimes loosely 

 termed as "error". In its most mathematical sense it is called the residual. However, 

 all these alternate terms should be avoided and it should simply be known as a de- 

 viation from the average or, more simply, deviation. 



