Use the Pearson correlation coefficient to examine the strength and direction of the linear relationship between two continuous variables.
The correlation coefficient can range in value from −1 to +1. The larger the absolute value of the coefficient, the stronger the relationship between the variables.
For the Pearson correlation, an absolute value of 1 indicates a perfect linear relationship. A correlation close to 0 indicates no linear relationship between the variables.The sign of the coefficient indicates the direction of the relationship. If both variables tend to increase or decrease together, the coefficient is positive, and the line that represents the correlation slopes upward. If one variable tends to increase as the other decreases, the coefficient is negative, and the line that represents the correlation slopes downward.
The following plots show data with specific correlation values to illustrate different patterns in the strength and direction of the relationships between variables.
 
 

In these results, the Pearson correlation between porosity and hydrogen is about 0.624783, which indicates that there is a moderate positive relationship between the variables. The Pearson correlation between strength and hydrogen is about 0.790146, and between strength and porosity is about 0.527459. The relationship between these variables is negative, which indicates that, as hydrogen and porosity increase, strength decreases.
 
 

In these results, the pvalues for the correlation between porosity and hydrogen and between strength and hydrogen are both less than the significance level of 0.05, which indicates that the correlation coefficients are significant. The pvalue between strength and porosity is 0.0526. Because the pvalue is greater than the significance level of 0.05, there is inconclusive evidence about the significance of the association between the variables.
Use the Spearman correlation coefficient to examine the strength and direction of the monotonic relationship between two continuous or ordinal variables. In a monotonic relationship, the variables tend to move in the same relative direction, but not necessarily at a constant rate. To calculate the Spearman correlation, Minitab ranks the raw data. Then, Minitab calculates the correlation coefficient on the ranked data.
The correlation coefficient can range in value from −1 to +1. The larger the absolute value of the coefficient, the stronger the relationship between the variables.
For the Spearman correlation, an absolute value of 1 indicates that the rankordered data are perfectly linear. For example, a Spearman correlation of −1 means that the highest value for Variable A is associated with the lowest value for Variable B, the second highest value for Variable A is associated with the second lowest value for Variable B, and so on.
The sign of the coefficient indicates the direction of the relationship. If both variables tend to increase or decrease together, the coefficient is positive, and the line that represents the correlation slopes upward. If one variable tends to increase as the other decreases, the coefficient is negative, and the line that represents the correlation slopes downward.
The following plots show data with specific Spearman correlation coefficient values to illustrate different patterns in the strength and direction of the relationships between variables.
It is never appropriate to conclude that changes in one variable cause changes in another based on correlation alone. Only properly controlled experiments enable you to determine whether a relationship is causal.
 
 

In these results, the Spearman correlation between porosity and hydrogen is 0.590058, which indicates that there is a positive relationship between the variables. The Spearman correlation between strength and hydrogen is 0.858728 and between strength and porosity is 0.675468. The relationship between these variables is negative, which indicates that as hydrogen and porosity increase, strength decreases.