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The correlation coefficient can be used to measure the correlation between the two variables, and different correlation coefficients are selected for calculation and analysis according to the different conditions satisfied by the data.

Two commonly used correlation coefficients: Pearson person and Spelman spearman.

Population and sample:

Pearson correlation coefficient: (data are required to be in accordance with normal distribution, and the data should be linearly correlated)

The linear correlation between the two variables must be confirmed first (the sample scatter diagram is first observed to see if it is linear), and then this coefficient can tell them the degree of correlation. If the calculated correlation coefficient is 0, it can only indicate the nonlinear correlation.

It cannot be said that the two variables with large covariance are more related than the two variables with small covariance, because the influence of the dimension of the variable is not eliminated. Pearson correlation coefficient is the result of eliminating the dimension of covariance.

Sample Pearson correlation coefficient and population Pearson correlation coefficient:

Since Pearson's correlation coefficient only measures the degree of correlation between two variables that are known to be linearly related, other cases do not apply:

Explanation of the magnitude of the correlation:

According to the specific analysis, there is no standard size threshold. We pay more attention to its significance than the correlation coefficient. (hypothesis test)

Carry on the hypothesis test to the Pearson correlation coefficient:

For example, find out the correlation coefficient r _ (0.3) and ask if there is a significant difference between it and 0 (non-linear correlation)?

If there is a significant difference between 03 and 0 through the hypothesis test, it can show that the correlation of the variable is significant; if there is no significant difference between 0.3 and 0, it shows that the variable is not related and the correlation coefficient is not significant.

Steps:

By constructing statistical variables for Pearson correlation coefficients and knowing the distribution of statistics, we can draw the probability density function of statistical variables. Bring the calculated Pillman correlation coefficient into the statistical variable, get a test value, draw the acceptance domain and rejection domain of the statistical variable according to the confidence level, and see whether the test value falls in the acceptance domain.

In addition to finding the critical value of the reject field according to the table, a more useful method is:

The conditions for testing the Pearson correlation coefficient hypothesis:

Verify that the data is normally distributed:

① JB Inspection:

② Shapiro-Wilke test

③ QQ diagram (requires a very large amount of data)

Spelman correlation coefficient:

Small sample size:

Large sample situation:

Summary:

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