Seven Myths in Error Analysis.

Myth 1. Random errors can always be determined by repeating measurements under identical conditions.

Although it is shown in one case (Problem 6.3.) that the inductive and the deductive method provide practically the same random errors, this statement is true only for time-related random errors (Sect. 6.2.5).

Myth 2. Systematic errors can be determined from the fluctuation of the data (i.e., inductive­ly).

It should be quite obvious that it is not possible to determine the scale error from the pattern of data values (Sect. 7.2.4).

Myth 3. Measuring is the cause of all errors.

The standard example of random errors, measuring the count rate of radiation from a radioactive source repeatedly, is not based on measurement errors but on the intrinsic properties of radioactive sources (Sect. 6.2.1). Usually, the measurement contribution to this error is negligible.

Just as radiation hazard is most feared of all hazards because it is best understood, measurements are thought to be the intrinsic cause of errors because their errors are best understood.

Myth 4. Counting can be done without error.

Usually, the counted number is an integer and therefore without (rounding) error. However, the best estimate of a scientifically relevant value obtained by counting will always have an error. These errors can be very small in cases of consecutive counting, in particular of regular events, e.g., when measuring frequencies by counting (Sect. 2.1.4).

Myth 5. Accuracy is more important than precision.

For single best estimates, be it a mean value or a single data value, this question does not arise because in that case there is no difference between accuracy and precision. (Just like shooting only once at a target, Sect. 7.6.) Generally, it is good practice to balance precision and accuracy. The actual requirements will differ from case to case.

Myth 6. It is possible to determine the sign of an error.

It is possible to find the signed deviation of an individual data value but the sign of the error of a best estimate, be it systematic or random, cannot be determined because the true value cannot be known (Sect. 7.2.1). The use of the term systematic error for a systematic deviation is misleading because a deviation is not an uncertainty at all.

Myth 7. It is all right to “guess” an error.

The uncertainty (the error) is one of the characteristics of a best estimate, just like its value, and nearly as important. Correct error analysis saves measuring time and total cost. A factual example for that is given in Sect. 10.1.1 where correct error analysis could have saved 90% of the cost.