The Spearman correlation coefficient. The Spearman rank correlation coefficient

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2019-07-21 06:20:28

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the Spearman rank correlation coefficient

The Discipline "higher mathematics" some causes rejection, since indeed 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 it osvedomlennosti. In psychological science there is not only a humanitarian focus, but also certain formulas and methods for mathematical verification, put forward the research hypotheses. For this purpose different factors.

Correlation Coefficient

This is a common measurement for determining the closeness of the connection between any two signs. The coefficient is also called the nonparametric method. It shows statistics of when. That is, we know, for example, that child aggression and irritability, are interrelated, and the correlation coefficient of rank Spearman correlation shows statistical mathematical relationship of these two characteristics.

How is the ranking factor?

Of Course, that all mathematical definitions or values, there are formulas by which they are calculated. It has a Spearman correlation coefficient. The formula for he as follows:

the Spearman correlation coefficient formula

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 ranked.
  • D - difference between two certain grades, those particular two variables of each test.
  • ∑d2 - The sum of all the squared differences between the ranks of the trait, squares of which are calculated separately for each grade.

Spearman correlation coefficient

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Area of application of mathematical measures of communication

To apply rank coefficient requires that the quantitative characteristic data were ranked, that is, they were assigned a certain number depending on where the sign is located, and from its meaning. It is proven that the two rows of signs, expressed in numerical form, somewhat parallel to each other. The Spearman rank correlation coefficient determines the degree of parallelism, the closeness of the connection characteristics.

For mathematical operations for the calculation and determination of connection characteristics using the specified coefficient, you need to perform some actions:

  1. Each value of any subject or phenomenon is given a number in the order - rank. It can match the value of the phenomenon of ascending and descending.
  2. Further compares the grades the characteristic values of two quantitative rows in order to determine the difference between them.
  3. In a separate table column for each of the difference registers its square, and below results are summarized.
  4. After these steps, apply formula that calculates the Spearman correlation coefficient.

the Spearman correlation coefficient in excel

Properties of the correlation coefficient

The main properties of Spearman's coefficient include the following:

  • Dimension values in the range from -1 to 1.
  • The sign of the coefficient interpretations has not.
  • Strength of links is determined according to the principle: the higher the value, the closer the relationship.

How to validate the resulting value?

To check the communication characteristics between a need to perform certain actions:

rank correlation coefficient Spearman

  1. Put forward the null hypothesis (H0), it is also the main, then formulated another alternative to the first (H1). The first hypothesis will be that the Spearman correlation coefficient is 0 it means that connection will not. Second, on the contrary, States that the factor is not equal to 0, then there is a connection.
  2. The Next step is finding the observed values of the criterion. It is located on the main formula of the Spearman coefficient.
  3. Next find the critical value of the specified criterion. This can only be done by using a special table which displays the different values for the set parameters: level of significance (l) and the number identifying the sample size (n).
  4. Now compare the two resulting values: installed, observed, and critical. For this you need to build a critical area. You need to draw a straight line on it to mark the locations of the critical values of the coefficient with the sign "-" and"+" sign. Left and right of the critical values of the semi-circles from delayed critical region. In the middle, combining the two values, it is noted a semicircle OPG.
  5. After that, the conclusion about the closeness of the connection between the two signs.

Where to use this value

The first science, where he actively used this ratio, was psychology. Because it is a science, not based on numbers, but the proof of any important hypotheses concerning the development of relations, traits of people, knowledge students, need statistical confirmation of the conclusions. It is also used in the economy, particularly when foreign exchange turnover. Are signs without statistics. Very convenient Spearman rank correlation coefficient in this application that the evaluation is carried out independentlyfrom the distribution of the variables as they are replaced by the rank number. Actively used the Spearman coefficient of banking. Sociology, political science, demography and other Sciences also use it in their research. Results are obtained quickly and accurately.

Conveniently and quickly used the Spearman correlation coefficient in Excel. There are special functions which help to quickly obtain the necessary values.

What other correlation coefficients are available?

Besides, what have we learned about correlation coefficient, there are various correlation coefficients that measure, evaluate qualitative characteristics, the relationship between quantitative traits, the closeness of the connection between them, represented in the rank scale. It is such factors as viscerally, rank-viscerally, contingencies, associations, and so on. The Spearman coefficient shows very accurately the closeness of the connection, in contrast to all other methods of mathematical definitions.


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Alin Trodden - author of the article, editor
"Hi, I'm Alin Trodden. I write texts, read books, and look for impressions. And I'm not bad at telling you about it. I am always happy to participate in interesting projects."

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