How to find correlation coefficient?
In mathematical statistics, the correlation is a statistical and probabilistic dependence, which does not have a strict functional character. Correlation dependence appears in the case when one of the signs is dependent both on the given second one, and on a number of other random factors. The correlation coefficient is a mathematical measure of the dependence of two random variables.
Types of correlation coefficients can be negative and positive. The calculations performed using correlation are not very complicated, but require special care from the contractor in the calculations. With these calculations, you will definitely need an engineering calculator. Before finding out how to find the correlation coefficient, it is necessary to clarify the meaning of the coefficients:
- In the case when the value of the module is closer to 1, then this is a direct indicator of the presence of a strong bond.
- If the value is closer to 0, then this already means a weak connection, or none at all.
- When the correlation coefficient is 1, then we are talking about a functional relationship, which indicates the possibility of describing, using a mathematical function, the change in two quantities.
The order and method of calculating the correlation coefficient
Find the sample correlation coefficient, you can use two methods:
- rank method, or the Spearman method,
- the square method, or the Pearson method.
The ranking method is as follows:
- It is required to make two rows consisting of paired matched signs. In this case, we introduce the following notation: the first row is x and the second row is y. The first row of the sign must be presented in ascending or descending order. The numerical values of the second row are located opposite the values of the first row.
- Then, in each of the comparison rows, we replace the order number (rank) with the characteristic value. Numbers (ranks) denote the place of indicators, or values, of the first and second rows. And the numerical values of the second sign should be assigned to the ranks in absolutely the same order as in the distribution of the first sign of their values. It is necessary to take into account that if a sign in a row has the same values, then ranks should be determined as an average of the sum of the ordinal numbers of these values.
- Next, we determine the difference in rank between the indicators: (d) = x - y.
- After that, squaring the resulting difference in rank (d2).
- And finally, we get the sum of squared differences, after which we substitute all the obtained values into the following formula: Pxy = 1- (6 Ʃd2) / n (n2-1).
The squares method includes the following algorithm:
- In order to find the correlation coefficient, it is first necessary to construct variational series for each of the compared features. Denote the first row by x and the second row by y. Now we define the average values (M1them2) for each variational series.
- Next, we find the deviations of each numerical value (dxand dy) from the average value of the series.
- Multiply the deviations obtained and put each deviation in the square, then sum up for each row.
- Then you need to substitute all the previously obtained values in the formula and thus find the correlation coefficient: rxy= Ʃ (dx * dy) / (sqrt (Ʃ d2x) * Ʃ d2y).
- If there is a computer technology, the calculation can be made using the following formula, this form of calculation can also be used in programs written in Pascal: rxy= (nƩxy- / Ʃx * Ʃy) / (sqrt ([nƩx2- Ʃx2] - [nƩy2- Ʃy2])).
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