Spearman's correlation coefficient. Coefficient of rank correlation of Spearman

Education

Discipline "higher mathematics" in somecauses rejection, because truly not everyone can understand it. But those who were lucky enough to study this subject and solve problems using various equations and coefficients can boast of almost complete knowledge of it. In psychological science there is not only a humanitarian orientation, but also certain formulas and methods for mathematical verification of the hypothesis put forward in the course of research. To do this, apply different factors.

Spearman's correlation coefficient

This is a common measurement by definition.the narrowness of the connection between any two signs. The coefficient is also called the non-parametric method. It shows connection statistics. That is, we know, for example, that in a child aggression and irritability are interconnected, and the Spearman’s rank correlation coefficient shows a statistical mathematical connection between these two signs.

How is the rank factor calculated?

Naturally, for all mathematical definitions or quantities, there are formulas by which they are calculated. She also has the Spearman correlation coefficient. His formula is as follows:

At first glance, the formula is not entirely clear, but if you look at it, everything is very easily calculated:

n is the number of features or indicators that are ranked.
d is the difference of certain two ranks corresponding to the specific two variables of each subject.
∑d^{2 -}the sum of all the squares of the difference of the ranks of the attribute, the squares of which are calculated separately for each rank.

Scope of mathematical measure of communication

To apply a rank factor is necessary,so that the quantitative data of the feature is ranked, that is, they are assigned a specific number depending on the place where the feature is located and on its value. It is proved that two rows of signs, expressed in numerical form, are somewhat parallel to each other. The coefficient of Spearman's rank correlation determines the degree of this parallelism, the closeness of the relationship of signs.

For a mathematical operation on the calculation and determination of the relationship of signs using the specified coefficient, you need to perform some actions:

Each value of a test subject or phenomenon is assigned a number in order — rank. It can correspond to the value of the phenomenon in ascending and descending order.
Next ranks the values of the attributes of the two quantitative rows in order to determine the difference between them.
For each resulting difference, its square is written in a separate column of the table, and the results are summarized below.
After these actions, the formula is used by which the Spearman's correlation coefficient is calculated.

Correlation coefficient properties

The main properties of the Spearman coefficient include the following:

Measuring values ranging from -1 to 1.
The sign of the coefficient of interpretation does not have.
Communication tightness is determined by the principle: the higher the value, the closer the connection.

How to check the resulting value?

To check the relationship of signs between themselves, you must perform certain actions:

The null hypothesis (H0) is advanced, which is the main hypothesis, then another alternative alternative to the first one is formulated (H₁). The first hypothesis will be that the Spearman correlation coefficient is 0, which means that there will be no connection. The second one, on the contrary, says that the coefficient is not equal to 0, then there is a connection.
The next step is to find the observed value of the criterion. It is found by the basic formula of the Spearman coefficient.
Next are the critical values givencriteria This can be done only with the help of a special table, where different values are displayed for the given indicators: the level of significance (l) and the number that determines the sample size (n).
Now we need to compare the two obtained values: established observable as well as critical. For this you need to build a critical area. It is necessary to draw a straight line on it to mark the point of the critical value of the coefficient with the sign "-" and with the sign "+". To the left and right of the critical values, critical areas are laid out by semicircles from the points. In the middle, combining two values, is marked by a semicircle of the organized criminal group.
After this, it is concluded that there is a close relationship between the two signs.

Where better to use this value

The very first science where it was actively usedthis coefficient was psychology. After all, this is a science that is not based on numbers, however, to prove any important hypotheses regarding the development of relationships, personality traits, students' knowledge, statistical confirmation of the conclusions is required. It is also used in the economy, in particular, with foreign exchange turnover. Signs without statistics are evaluated here. The Spearman's rank correlation coefficient in this area of application is very convenient in that it is assessed independently of the distribution of variables, since they are replaced by a rank number. Actively used Spearman ratio in banking. Sociology, political science, demography and other sciences also use it in their research. Results are obtained quickly and as accurately as possible.

The Spearman's correlation coefficient is used conveniently and quickly in Excel. Here there are special functions that help to quickly obtain the necessary values.

What other correlation coefficients exist?

In addition to what we learned about the coefficientSpearman correlations, there are still various correlation coefficients that allow to measure, evaluate qualitative signs, the relationship between quantitative characteristics, the closeness of the relationship between them, presented in the rank scale. These are coefficients such as biserial, rank-biserial, contacts, associations, and so on. The Spearman coefficient very accurately shows the closeness of the connection, unlike all other methods of its mathematical definition.