The difference between systematic error and random error
The difference between the measured value and the mathematical expectation of the measured value is called random error, which indicates the degree of dispersion of the measured value.
The difference between the mathematical expectation of the measured value and the reference value is called the systematic error, which indicates the degree to which the mathematical expectation of the measured value deviates from the reference value.
There is an essential difference between random error and systematic error. The mathematical expectation of random error is zero, and the mathematical expectation of systematic error is itself. That is to say, under the same conditions, when an experiment occurs, it appears large and small, positive and negative, and there is no clear rule of error, it is random error. Changing the experimental conditions, the error of a certain law appears is systematic error. In this case, although the number of experiments n tends to infinity, the mathematical expectation of the error value tends to a constant, which is the systematic error.
From the mathematical expression of random error η = x-E (x), it can be seen that this is a theoretical definition. Generally, the arithmetic mean is used as the best estimate of the mathematical expectation value, so the concept of residual is introduced. The key to our study of random error is to master the characteristics and application methods of the residual, and to correctly use the residual to calculate the experimental standard deviation.
The key to studying systematic error is to know how to determine the constant of the systematic error and use it as a correction value to compensate or reduce the impact of the error. Because the correction value is equal to the negative systematic error, if the constant of the systematic error cannot be determined, it is of no practical significance to just do general analysis and evaluation.
By classifying errors, there are
Measurement Error = Measured Value - Reference Value = (Measured Value - Mathematical Expectation) + (Mathematical Expectation - Reference Value)
Therefore, there is
Measured value = reference value + random error + systematic error
For the "gross error" commonly used in the past, it is caused by an abnormal error, and the measured value containing such an error cannot participate in data processing, nor can it be used as an error component.
According to the definition of measurement error, it can be seen that the measurement error is generally not directly quoted in the actual measurement process, but directly quoted as two components of the measurement error, namely random error and systematic error. Among them, the residual error, as the estimated value of random error, is a necessary element to calculate the standard deviation of the experiment; while the negative systematic error can be used as the correction value to correct the measured value.
The reason why the residual is a necessary element for calculating the experimental standard deviation is that the experimental standard deviation is the square root of the quotient obtained by dividing the square of the residual error by the degree of freedom. That is to say, the experimental standard deviation cannot be calculated without the residual. The residual is an estimate of the random error, which is a component of the measurement error. It can be seen that the measurement error is closely related to the experimental standard deviation. Measurement uncertainty is a parameter used to characterize the dispersion of measured quantities, and the parameter referred to in it is the experimental standard deviation. Therefore, measurement error and measurement uncertainty are two important concepts that are inseparable. From the definition of measurement error, classification of measurement error, distribution of measurement error, estimation of measurement error, data processing of measurement error, especially the experimental standard deviation derived from measurement error, a complete theoretical system of measurement error has been formed, which has laid a solid theoretical foundation for the evaluation of measurement uncertainty.
