Spearman's correlation coefficient. Rankman correlation coefficient

The discipline of "higher mathematics" in some causes rejection, because truly not everyone is given to understand it. But those who were fortunate enough to study this subject and solve problems using various equations and coefficients, can boast of almost complete understanding in 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. For this, different coefficients are applied.

Spearman's correlation coefficient

This is a common measurement by definition of the tightness of the connection between any two features. The coefficient is also called the nonparametric method. It shows the connection statistics. That is, we know, for example, that the child's aggression and irritability are related, and the Spearman's correlation coefficient shows the statistical mathematical relationship of these two signs.

How is the rank coefficient calculated?

Naturally, for all mathematical definitions or quantities, there are formulas for calculating them. It also has a Spearman correlation coefficient. The formula for him is:

At first glance, the formula is not quite clear, but if you understand, everything is very easy to calculate:

• N is the number of characteristics or indicators that are ranked.
• D is the difference of the two definite ranks corresponding to the specific two variables of each subject.
• Σd ^{2 is the} sum of all squares of the differences in the rank of the characteristic, the squares of which are calculated separately for each rank.

Scope of mathematical measure of communication

To apply a rank coefficient, it is necessary that the quantitative characteristics of the characteristic be ranked, that is, they have been assigned a certain number depending on the location on which the attribute is located and on its value. It is proved that two series of signs, expressed in numerical form, are somewhat parallel to each other. Spearman's rank correlation coefficient determines the degree of this parallelism, the tightness of the connection of the signs.

For a mathematical operation to calculate and determine the relationship of characteristics using the specified coefficient, it is necessary to perform some actions:

1. Each value of a subject or phenomenon is assigned a number in order - rank. It can correspond to the value of the phenomenon in ascending and descending order.
2. Further, the ranks of the value of the attributes of two quantitative series are compared in order to determine the difference between them.
3. In a separate column of the table, for each resulting difference, its square is prescribed, and the results are summarized below.
4. After these actions, a formula is used to calculate the Spearman correlation coefficient.

Properties of the correlation coefficient

The main properties of the Spearman coefficient include the following:

• Measuring values in the range from -1 to 1.
• The sign of the coefficient of interpretation has not.
• The tightness of the connection is determined by the principle: the higher the value, the closer the connection.

How to check the received value?

To check the relationship between the characteristics among themselves, you must perform certain actions:

1. The null hypothesis (H0) is advanced, it is basic, then another is formulated, alternative to the first (H ₁ ). The first hypothesis is that the Spearman correlation coefficient is 0, which means that there will be no connection. The second, on the contrary, says that the coefficient is not equal to 0, then there is a connection.
2. The next step is to find the observed value of the criterion. It is found by the basic formula of the Spearman coefficient.
3. Further, the critical values of the given criterion are found. This can only be done using a special table, where different values are displayed for the given indicators: the significance level (l) and the number that determines the sample size (n).
4. Now we need to compare the two values obtained: the observed observed, and also the critical value. For this it is necessary to construct a critical region. It is necessary to draw a straight line, mark the points of the critical value of the coefficient with a "-" sign and a "+" sign. To the left and to the right of the critical values, critical regions are laid as semicircles from the points. In the middle, combining two values, is marked by a semicircle of OPG.
5. After this, a conclusion is drawn about the tightness of the connection between the two signs.

Where is it better to use this value

The very first science, where this coefficient was actively used, was psychology. After all, this is a science that is not based on figures, however, to prove any important hypotheses concerning the development of relations, the character traits of people, students' knowledge, statistical confirmation of the conclusions is required. It is also used in the economy, in particular, with currency turnover. Here the signs are evaluated without statistics. Spearman's rank correlation coefficient in this field of application is very convenient in that evaluation is performed independently of the distribution of variables, since they are replaced by a rank number. The Spearman coefficient in banking is actively applied. Sociology, political science, demography and other sciences also use it in their studies. Results are obtained quickly and as accurately as possible.

It is convenient and fast to use the Spearman correlation coefficient in Excel. There are special functions that help you quickly get the necessary values.

What other correlation coefficients exist?

In addition to what we learned about the Spearman correlation coefficient, there are still different correlation coefficients that allow us to measure, evaluate qualitative characteristics, the relationship between quantitative characteristics, and the tightness of the relationship between them, represented in the rank scale. These are factors such as the biserial, rank-biserial, contigents, associations, and so on. The Spearman coefficient very accurately shows the tightness of the connection, unlike all the other methods of its mathematical determination.