Correlation Matrix

A very useful way to analyze the association between variables is to obtain the correlation matrix, using the coefficients of Pearson, Spearman or Kendall

Pearson Correlation

Example: A company intend to study the relationship between the sales volume during a given period of time by its vendors, considering their experience in an intelligece test. The obtained data are presented in the following table.

^{click here to download the data}

To use the tool Correlation Matix the user must follow these steps:

1. Access the menu:

Action → Basic Statistics → Correlation Matrix

2. The following window will appear;

3. In the field Data Set, we will select the columns that contain the data. If we select the data with the names, we will select the box Columns with names, otherwise we will not select it.

REMARK: In this function, we cannot select just one column, because we are testing the correlation among the variables.

4. If we wish to build the Matrix Scatterplots (where we can see the association between two or more variables) we select the box Matrix Scatterplots ;

5. Select the desired correlation in Type of Correlation. In this example, we will select the correlation matrix through the Pearson's correlation coefficient;

REMARK: Spearman and Kendall correlations are performed in an analogous way: we just need to select the type of desired correlation in the board Type of correlation. The interpretation of the results will also be analogous. But here, there is a remark: the Pearson correlation measures the degree of association between two metric scale (or interval) variables, since the Spearman correlation can be used to the measured variables on ordinal level and in situations where the variable is nominal, we usually use the Kendall correlation coefficient.

7. In the board Show Results, we select between the options Current Cell or New Sheet. We suggest the option New Sheet, because Action does not have the undo command;

REMARK: When choosing the option Current Cell, the results will be printed from the cell where the cursor is. In this case, the user must put the cursor in an appropriate position previously (before step 1).

8. To finish, click Ok.

Results and Interpretation

Once the process is finished, the following results will be shown:

We see that the positive correlation (0.846) between the sales volume and years of experience is significant (proved by the p-value of 0.002, lower than the adopted 5% significance level). It also occurs significant association between the sales volume and the score in the intelligence test and, between years of experience and score.

The p-value is lower or equal to the predetermined significance level α. It means that there is significant correlation between the variables. Otherwise, there will not be association between them..

Complementing the table above through the Scatterplots matrix we see that the three variables under study have a linear association among them, which is also positive. Thus, as a vendor's years of experience increase, his sales volume also tends to be higher. About other associations they will have analogous interpretation.