Types of error: systematic, random, absolute, approximate

Being an exact science, mathematics does not tolerate bringing situations to the general without taking into account the specific features of a particular example. In particular, it is impossible to do the right measurement in mathematics, physics, literally "by eye," without taking into account the emerging error.

What is it about?

Scientists have been found different types of error, so nowadays one can safely say that no sign after the comma is left without attention. Of course, it is impossible without rounding, otherwise all the people on the planet would only be engaged in that, by going deep into the thousandth and ten thousandths. As you know, many numbers can not be divided into each other without a remainder, and the measurements obtained in the course of experiments is an attempt to divide the continuous into separate parts in order to measure them.

Practically the accuracy of measurements and calculations is really very important, as it is one of the main parameters that allow to speak about the correctness of the data. Types of error reflect how close the figures are to reality. As for the quantitative expression: the error in measurement is what shows how true the result is. The accuracy is higher if the error is less.

The laws of science

According to the found patterns operating in the existing theory of errors, in a situation where the accuracy of the result should be higher than the available, twice, it will be necessary to increase the number of experiments fourfold. In the case where the accuracy is increased three times, the experiments should be more than 9 times. The systematic error is eliminated.

Metrology considers the measurement of errors to be one of the most important steps to ensure the uniformity of measurements. It is necessary to take into account: the accuracy is subject to the influence of a wide range of factors. This led to the development of a very complex classification system, which operates only with the proviso that it is conditional. In real conditions, the results strongly depend not only on the inherent error process, but also on the characteristics of the process of obtaining information for analysis.

Classification system

Types of error, distinguished by modern scientists:

• absolute;
• Relative;
• Reduced.

It is possible to divide this category into other groups, based on the reasons for the inaccuracy of the calculations and experiments. They say that they appeared:

• Systematic error;
• Chance.

The first quantity is constant, depends on the characteristics of the measuring process and remains unchanged if, under each subsequent manipulation, the conditions remain the same.

But a random error can change if the tester repeats similar studies carried out using the same apparatus and being in conditions identical to the first period.

A systematic, random error appears simultaneously and is in any tests. The value of a random variable is unknown in advance, as it is provoked by unpredictable factors. Despite the impossibility of exclusion, algorithms have been developed to reduce this value. They are applied at the stage of processing the data obtained during the research.

Systematic in comparison with the random differs in the nature of the sources that provoke it. It is revealed in advance and can be considered by scientists taking into account the relationship with its causes.

And if you understand more?

To have a complete understanding of the concept, you need to know not only the types of error, but also what are the components of this phenomenon. Mathematicians identify the following components:

• Associated with the methodology;
• Caused by tools;
• Subjective.

Making an error calculation, the operator depends on the specific, only to him inherent, individual characteristics. They form the subjective component of the error, which violates the accuracy of information analysis. Perhaps, the reason will be in the lack of experience, sometimes in the errors associated with the start of the countdown.

Predominantly, the calculation of error takes into account two other items, that is, instrumental and methodological.

Important component components

Accuracy and error are concepts without which neither physics, nor mathematics, nor a number of other natural and exact sciences based on them are possible.

At the same time, it must be remembered that all techniques known to mankind for obtaining data in the course of experiments are imperfect. This is the reason for the methodical error, which is absolutely impossible to avoid. It is also influenced by the accepted system of calculus and inaccuracies inherent in the calculation formulas. Of course, its influence is also exerted by the need to round results.

There are gross blunders, i.e., errors caused by incorrect behavior of the operator during the experiment, as well as failure, improper operation of the instruments or the occurrence of an unforeseen situation.

It is possible to detect a rough error of the values by analyzing the obtained data and revealing the incorrect values when comparing the data with special criteria.

What do maths and physics say today? Accuracy can be prevented by preventive measures. Several rational ways of reducing this concept have been invented. To do this, eliminate one or the other factor, leading to inaccurate results.

Category and classification

There are errors:

• Absolute;
• Methodical;
• Random;
• Relative;
• Reduced;
• Instrumental;
• Basic;
• Additional;
• Systematic;
• Personal;
• Static;
• Dynamic.

The error formula for different species differs, since in each specific case takes into account a number of factors that have influenced the formation of inaccuracy in the data.

If we talk about mathematics, then, with this expression, only relative and absolute errors are singled out. But when in a given time interval there is interaction of changes, we can speak about the presence of dynamic, static components.

The error formula, taking into account the interaction of the target object with external conditions, contains an account of additional, basic digits. The dependence of the readings on the input data for a particular experiment will speak of a multiplicative error or an additive error.

Absolute

By this term it is customary to understand the data, which are calculated by separating the difference of the indicators taken during the experiment by the actual ones. The following formula was invented:

A Qn = Qn - A Q0

And Qn is the data sought, Qn is the one found in the experiment, and the zero ones are the base figures with which the comparison is made.

The

By this term it is customary to understand such a value, which expresses the ratio between the absolute error and the norm.

In calculating this type of error, not only the shortcomings associated with the operation of the instruments involved in the experiment, but also the methodological component, as well as the approximate error of counting are important. The latter value is provoked by the shortcomings of the scale of division present on the measuring instrument.

Closely associated with this concept and instrumental error. It occurs when the device was made incorrectly, erroneously, incorrectly, why the indications given to it become insufficiently accurate. However, now our society is at such a level of technological progress, when the creation of instruments that do not have an instrumental error is as yet unattainable. What can we say about the obsolete samples used in school and student experiments? Therefore, calculating control, laboratory work, to neglect the instrumental error is unacceptable.

Methodical

This variety is provoked by one of two reasons or complex:

• The mathematical model used in the studies turned out to be insufficiently accurate;
• Incorrect measurement methods are chosen.

Subjective

The term is applied to a situation where errors in the process of computations or experiments due to the lack of qualification of the person performing the operation have been made.

It can not be said that it only arises when an uneducated or stupid person took part in the project. In particular, the error is provoked by imperfection of the human visual system. Therefore, the reasons may not depend directly on the participant of the experiment, nevertheless they are classified as a human factor.

Statics and dynamics for the theory of errors

A certain error is always associated with how the input and output quantities interact. In particular, the process of interrelation in a given time interval is analyzed. It is customary to talk about:

• The error that appears when calculating a certain quantity is constant in a given time interval. This is called static.
• Dynamic, coupled with the appearance of a difference, revealed by measuring unstable data, described by the item above the type.

What is primary and what is secondary?

Undoubtedly, the permissible error is provoked by the basic quantities influencing the specific problem, however, the effect is not uniform, which allowed the researchers to divide the group into two categories of data:

• Calculated in the norm of operating conditions under the standards of numerical expressions of all figures affecting the numbers. These are called basic.
• Additional, formed under the influence of atypical factors, which do not correspond to normal values. The same type is also said in the case when the main quantity exceeds the limits of the norm.

And what happens around?

The term "norm" has already been mentioned more than once, but it has not been explained what exactly the conditions in science are called normal, and also mention that other types of conditions are also singled out.

So, the normal ones are such conditions when all the quantities affecting the work process are within the limits of the normal values revealed for them.

But workers are a term that applies to conditions in which the values change. In comparison with the normal here, the framework is much broader, however the influencing quantities must fit into the working area specified for them.

The working norm of the influencing quantity assumes such an interval of the axis of values, when it is possible to normalize due to the introduction of an additional error.

What does the input value affect?

When calculating the error, it is necessary to remember that the input quantity influences which types of errors arise in a particular situation. At the same time they say about:

• Additive, which is inherent in the error, calculated as the sum of different values taken in modulus. At the same time, the indicator has no influence whatsoever how large the measured quantity is;
• Multiplicative, which will change when the measured quantity is affected.

It should be remembered that the absolute additive is an error that has no connection with the magnitude, which is measured by the purpose of the experiment being conducted. In any part of the range of values, the indicator remains constant, and the parameters of the measuring instrument, including sensitivity, do not affect it.

The additive error indicates how small the value obtained with the application of the selected measuring instrument can be.

But the multiplicative will not change in a random way, but proportionally, since it is related to the parameters of the measured value. How much error is high is calculated by studying the sensitivity of the instrument, since the value will be proportional to it. This sub-type of error arises precisely because the input quantity affects the measuring means and changes its parameters.

How to remove the error?

In some cases, you can exclude the error, although this is not true for each species. For example, if we are talking about the above, the error class in this case depends on the parameters of the device and the value can be changed by choosing a more accurate, modern means. At the same time, it is impossible to completely exclude the lack of measurements related to the technical features of the machines used, since there will always be factors that reduce the reliability of the data.

Classical distinguish four methods of eliminating or minimizing the error:

• Elimination of the cause, source before the experiment.
• Elimination of inaccuracies in data collection activities. To do this, use replacement methods, try to compensate for the sign and to contrast observations with each other, and also resort to symmetrical observations.
• Correction of the results obtained during the making of corrections, that is, a computational way of eliminating the error.
• Determination of what are the limits of the systematic error, taking them into account in the case where elimination is not possible.

The most optimal option is to eliminate the causes, sources of error in the course of experimental data acquisition. Despite the fact that the method is considered to be the most optimal, it does not complicate the workflow, on the contrary, it even makes it easier. This is due to the fact that the operator does not need to exclude the error already in the course of directly receiving the data. Do not have to edit the finished result, adjusting it to the standards.

But when it was decided to eliminate errors already in the course of measurements, resort to one of the popular technologies.

Known exclusion options

Most widely apply the introduction of edits. To use them, you need to know exactly what the systematic error inherent in a particular experiment.

In addition, the replacement option is in demand. By resorting to it, specialists instead of the value of interest use a substituted, delivered in a similar environment. This is common when measuring electrical quantities.

Contrast is a method that requires conducting experiments twice, while the source in the second stage influences the outcome in the opposite way compared to the first. The logic of working with this method is similar to the one called "compensation by sign", when the value in one experiment should be positive, in the other - negative, and the concrete value is calculated by comparing the results of two measurements.