Discipline "Higher Mathematics" is some rejection, as not everyone can truly understand it.But those who are fortunate enough to study this subject and to solve problems using a variety of equations and the coefficients can boast almost complete it osvedemlennosti.In psychological science, there is not only a humanitarian focus, but also certain formulas and methods for mathematical verification Advances in the course of research hypotheses.For this purpose different ratios.
Spearman correlation coefficient
This is a common measurement to determine the closeness of the connection between any two signs.The coefficient is also called non-parametric methods.It shows statistics of communication.That is, we know, for example, that the child's aggression and irritability are linked, and Spearman's rank correlation coefficient shows a statistical mathematical relationship of these two characters.
How do you calculate the coefficient of rank?
Naturally, for all mathematical definitions or values has its own formula by which they are calculated.She has and Spearman correlation coefficient.The formula he following:
At first glance, the formula is not entirely clear, but if you look, everything is very easily calculated:
- n - is the number of signs or indicators that are ranked.
- d - the difference between two specific grades, corresponding to two specific variables of each test.
- Σd2 - the sum of the squares of the differences of rank indication, the squares of which are calculated separately for each rank.
Scope mathematical measure due
To apply rank coefficient is necessary to sign the quantitative data were ranked, that is, it has been assigned a specific number depending on the place in which a sign is located, and from its value.It is proved that two rows of features expressed in numerical form, several parallel.Spearman's rank correlation determines the degree of parallelism, closeness of the connection features.
for mathematical operation on the calculation and determination of communication features with the help of this coefficient need to make some action:
- each value of any subject or phenomenon is given a number in order - rank.It can match the effects of ascending and descending order.
- Next rank compares the characteristic values of the two series of quantitative order to determine the difference between them.
- In a separate column of the table for each of the resulting difference registers its square, and the results are summarized below.
- After these steps, use the formula used to calculate the correlation coefficient.
Properties of the correlation coefficient
The main properties of the Spearman coefficient include the following:
- measurement values range from -1 to 1.
- sign interpretations ratio has not.
- closeness of the relationship is determined by the principle: the higher the value, the closer the connection.
How to check the value obtained?
To check communication between the signs of a need to perform certain actions:
- Pull out the null hypothesis (H0), it is also the primary, then the other is formulated, the first alternative (H1).The first hypothesis would be that the correlation coefficient is equal to 0 - meaning that the communication will be.The second, on the contrary, states that the coefficient is not 0, then there is a connection.
- The next step is finding the observed value of the criterion.It is the basic formula for the coefficient of Spearman.
- Next are the critical values of a given criterion.This can be done only with a special table displaying different values for given parameters: the significance level (l) and a number that specifies the sample size (n).
- Now we need to compare the two resulting values are set observed, as well as critical.To do this, you must build the critical region.It is necessary to draw a straight line on its critical point to note coefficient with sign "-" and the sign "+".To the left and right of the critical values of the points are deposited semicircles critical areas.In the middle, combining two meanings, there is a semicircle OPG.
- After that concludes crowded link between the two signs.
Where better to use this value
very first science, which is actively used this factor was psychology.After all, it is a science, not based on the figures, but in order to prove any significant hypotheses concerning the development of relationships, personality traits of people, knowledge of students, requires statistical confirmation of the findings.Also, it is used in the economy, particularly when currency rpm.There are estimated without signs statistics.Very convenient Spearman rank correlation coefficient in this application in that the evaluation is performed independently from the distribution of the variables, as they are replaced by a ranking number.Actively used Spearman coefficient in banking.Sociology, political science, demography and other sciences also use it in their research.The results are obtained quickly and as accurately as possible.
conveniently and quickly using Spearman correlation coefficient in Excel.Here, there are special features that allow you to quickly obtain the necessary values.
What other correlations exist?
Moreover, what we have learned about the Spearman correlation coefficient, there are various correlation coefficients, allowing to measure, evaluate the quality characteristics, the relationship between quantitative traits closeness of the relationship between them is represented in the ranking scale.These are such factors as bisserialny, rank-bisserialny, kontengentsii, associations, and so on.Spearman's coefficient shows very precisely closeness of the relationship, as opposed to all other methods of its mathematical definition.
