Stat > Basic Statistics > Correlation

A correlation coefficient measures the extent to which two variables tend to change together. Minitab offers two different correlation analyses:

·    Pearson product moment correlation - The Pearson correlation evaluates the linear relationship between two continuous variables. A relationship is linear when a change in one variable is associated with a proportional change in the other.

For example, you might use a Pearson correlation to evaluate whether increases in temperature at your production facility are associated with decreasing thickness of your chocolate coating.

·    Spearman rank-order correlation (also called Spearman's rho) - The Spearman correlation evaluates the monotonic relationship between two continuous or ordinal variables. In a monotonic relationship, the variables tend to change together, but not necessarily at a constant rate. The Spearman correlation coefficient is based on the ranked values for each variable rather than the raw data.

Spearman correlation is often used to evaluate relationships involving ordinal variables. For example, you might use a Spearman correlation to evaluate whether the order in which employees complete a test exercise is related to the number of months they have been employed.

There are a few points to keep in mind when performing or interpreting a correlational analysis:

·    It is always a good idea to examine the relationship between variables with a scatterplot. Correlation coefficients only measure linear (Pearson) or monotonic (Spearman) relationships. Other relationships are possible.

·    It is never appropriate to conclude that changes in one variable cause changes in another based on a correlation alone. Only properly controlled experiments allow you to determine if a relationship is causal.

·    The Pearson correlation coefficient is very sensitive to extreme values. A single value that is very different from the others in a data set can change the value of the coefficient a great deal.

## Dialog box items

Variables: Choose the columns containing the variables you want to correlate. When you list two columns, Minitab calculates the correlation coefficient for the pair. When you list more than two columns, Minitab calculates the correlation for every possible pair, and displays the lower triangle of the correlation matrix (in blocks if there is insufficient room to fit across a page).

Method

Pearson correlation: Calculate the linear correlation coefficient for each pair of variables.

Spearman rho: Calculate the rank-order correlation coefficient for each pair of variables.

Display p-values: Check to display p-values for the hypothesis test. For a coefficient, r, the hypothesis are: H0: r = 0  versus  H1: r ≠ 0.

Store matrix (display nothing): Check to store the correlation matrix. Minitab does not display the correlation matrix when you choose this option. To display the matrix, choose Data > Display Data.