The discipline of "higher mathematics" is rejected by some, since not everyone is truly given the opportunity to understand it. But those who are fortunate enough to study this subject and solve problems using various equations and coefficients can boast of an 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 during research. For this, various coefficients are used.
Spearman's correlation coefficient
This is a common dimension for determining the tightness of the connection between any two features. The coefficient is also called the nonparametric method. It shows connection statistics. That is, we know, for example, that a child’s aggression and irritability are interconnected, and the Spearman rank correlation coefficient shows a statistical mathematical relationship between these two signs.
How is rank coefficient calculated?
Naturally, for all mathematical definitions or quantities, there are formulas by which they are calculated. Spearman's correlation coefficient also has it. His formula is as follows:
At first glance, the formula is not entirely clear, but if you look, everything is very easy to calculate:
- n is the number of signs or indicators that are ranked.
- d is the difference of the defined two ranks corresponding to the specific two variables of each subject.
- ∑d 2 - the sum of all the squares of the differences of the ranks of the attribute, the squares of which are calculated separately for each rank.
The scope of the mathematical measure of communication
To apply the rank coefficient, it is necessary that the quantitative data of the attribute be ranked, that is, they will be assigned a certain number depending on the place where 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 attributes.
For a mathematical operation to calculate and determine 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, the ranks of the values of the attributes of the two quantitative series are compared in order to determine the difference between them.
- In a separate column of the table, for each difference obtained, its square is written, and the results are summarized below.
- After these actions, the formula is used to calculate the Spearman correlation coefficient.
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.
- The tightness of communication is determined by the principle: the higher the value, the closer the connection.
How to check the received value?
To check the relationship of the signs with each other, certain actions must be performed:
- The null hypothesis (H0) is put forward, it is the main one, then another, alternative to the first (H 1 ) is formulated. The first hypothesis will be that the Spearman correlation coefficient is 0 - this 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.
- The next step will be to find the observed value of the criterion. It is found by the basic formula of the Spearman coefficient.
- Next are the critical values of a given criterion. This can be done only with the help of a special table, where various values are displayed for given indicators: significance level (l) and a number that determines the sample size (n).
- Now we need to compare the two obtained values: the established observable, as well as the critical. 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 the “-” sign and the “+” sign on it. To the left and to the right of the critical values, the critical regions are laid out in semicircles from the points. In the middle, combining the two values, is marked by a semicircle of organized crime groups.
- After this, a conclusion is drawn about the tightness of the relationship between the two features.
Where 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 numbers, but to prove any important hypotheses regarding the development of relations, personality traits of people, students' knowledge, statistical confirmation of the conclusions is required. It is also used in the economy, in particular, in foreign currency transactions. Here, attributes without statistics are evaluated. Spearman's rank correlation coefficient in this field of application is very convenient in that the assessment is made regardless of the distribution of variables, since they are replaced by a rank number. Actively applies the Spearman coefficient in banking. Sociology, political science, demography and other sciences also use it in their research. The results are fast and accurate.
Conveniently and quickly used Spearman's correlation coefficient in Excel. There are special functions here that help you quickly get the values you need.
What other correlation coefficients exist?
In addition to what we learned about Spearman's correlation coefficient, there are various correlation coefficients that allow you to measure, evaluate qualitative attributes, the relationship between quantitative attributes, the tightness of the relationship between them, presented in the rank scale. These are coefficients such as biserial, rank-biserial, contingencies, associations, and so on. The Spearman coefficient very accurately shows the tightness of the connection, in contrast to all other methods of its mathematical determination.