Relative Importance of Error Components

In every measurement, the observer tries to reduce the experimental error as much as possible. If the quantity of interest depends on many variables, each with its own error, the effort to reduce the error should be directed toward the variable with the largest contribution to the final error. 

Consider the quantity Q = x + y - z and assume x = 3, y = 2, and z = 1. Also assume that the corresponding standard errors are 

From the relative magnitude of the errors, one can see that if it is necessary to reduce the error further, the effort should be directed toward reduction of first, cr second, and cr third. In fact, there is no need to reduce tr further before cr and reach the same magnitude as cr.  

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