A correlation matrix displays the correlation coefficients among numerous variables in a
research study. This type of matrix will appear in hypothesis
testing or exploratory quantitative research studies, which are designed to test the relationships
among variables. In order to interpret this matrix you need
to understand how correlations are measured. Correlation coefficients always range from
-1 to +1. The positive or negative sign tells you the direction of the relationship and
the number tells you the strength of the relationship. The most common way to quantify this relationship
is the Pearson product moment correlation coefficient (Munro, 2005).
Mathematically it is possible to calculate correlations with any level of data. However,
the method of calculating these correlations will differ based on the level of the data.
Although Pearson’s r is the most commonly used correlation coefficient, Person’s r
is only appropriate for correlations between two interval or ratio level variables. When
examining the formula for Person’s r it is evident that part of the calculation relies
on knowing the difference between individual cases and the mean. Since the distance between
values is not known for ordinal data and a mean cannot be calculated, Pearson’s r cannot
be used. Therefore another method must be used.
Most other methods have been derived from Pearson’s. Please note that there are also
other methods for calculating correlations among more than two variables.
Recall that correlations measure the direction and strength of a linear relationship
among variables. The direction of the relationship is indicated by the positive or negative sign
before the number. If the correlation is positive it means that
as one variable increases so does the other one. People who tend to score high for one
variable will also tend to score high for another varriable.
Therefore if there is a positive correlation between hours spent watching course videos
and exam marks it means that people who spend more time watching the videos tend to get
higher marks on the exam. Remember that a positive correlation is like
a positive relationship, both people are moving in the same direction through life together.
If the correlation is negative it means that as one variable increases the other decreases.
People who tend to score high for one variable will tend to score low for another.
Therefore if there is a negative correlation between unmanaged stress and exam marks it
means that people who have more unmanaged stress get lower marks on their exam.
Remember that A negative correlation is like a negative relationship, the people in the
relationship are moving in opposite directions. Remember that The sign (positive or negative)
tells you the direction of the relationship and the number beside it tells you how strong
that relationship is. To judge the strength of the relationship consider the actual value
of the correlation coefficient. Numerous sources provide similar ranges for interpretation
of the relationships that approximate the ranges on the screen. These ranges provide
guidelines for interpretation. If you need to memorize these criteria for a course check
the table your teacher wants you to learn. Of course, the higher the number is the stronger
the relationship is. In practice, researchers are happy with correlations of 0.5 or higher.
Also note that when drawing conclusions from correlations the size of the sample as well
as the statistical significance is considered. Remember that the direction of the relationship
does not affect the strength of the relationship. One of the biggest mistakes people make is
assuming that a negative number is weaker than a positive number. In fact, a correlation
of – 0.80 is just as high or just as strong as a correlation of +0.80.
When comparing the values on the screen a correlation of -0.75 is actually stronger than a correlation
of +0.56. If a researcher was investigating the relationship
between several factors that may influence student marks on an exam the correlation matrix
may look like this. Notice that there are correlations of 1 on
a diagonal line across the table. That is because each variable should correlate perfectly
with itself. Sometimes dashes are used instead of 1s.
In a correlation matrix, typically only one half of the triangle is filled out. That is
because the other half would simply be a mirror image of it.
Examine this correlation matrix and see if you can identify and interpret the correlations.
A great question for an exam would be to give you a correlation matrix and ask you to find
and interpret correlations. What is the correlation between completed
readings and unmanaged stress? What does it mean?
Which coefficient gives you the most precise prediction?
Which correlations are small enough that they would not be of much interest to the researcher?
Which two correlations have the same strength? From looking at these correlations, what could
a student do to get a higher mark on an exam? Comment below to start a conversation.
To generalize conclusions from these correlations researchers need to assume a number of things.
Various measures exist to test these assumptions. To interpret the meaning of correlations researchers
also consider a number of other measures before drawing conclusions.
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