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.