Computing a Pearson correlation in
JASP is a simple but rewarding
procedure, so let's learn how to conduct
a simple correlation, how to interpret it,
and how to write it up in APA style. We
will be using the data set about burnout
and job satisfaction called "JobSatisfaction.CSV"
These are data from
200 mental health counselors. The
variables in the data set are job
satisfaction score (how much you like
your job), burnout score, compassion
fatigue, turnover intention (which is your
intention to leave the job),
Gender (coded as male or female), and
compassion satisfaction. Compassion
fatigue is the negative emotional
consequence of helping people who have
been traumatized, or have lived through
something traumatic. It affects people in
the helping professions: first responders,
nurses, counselors, and so on. Compassion
satisfaction, by contrast, is the positive
emotional consequence of helping people
who have been traumatized. So a therapist
who helps others might either become
burned out from vicariously experiencing
the trauma of others, or might feel a
sense of pride and personal satisfaction
from helping.
So both compassion fatigue and
compassion satisfaction can affect job
satisfaction of mental health counselors.
Burnout is a loss of enthusiasm for a
job that can be experienced in any job
setting, not just the helping professions.
But compassion fatigue is theorized to
be a specific form of burnout that is
unique to helpers. What are the
theoretical relationships between
compassion fatigue, compassion
satisfaction, burnout, and job
satisfaction? Let's focus on job
satisfaction.
If a therapist has high levels of
burnout (they hate their job), will job
satisfaction likely be high or low? As
burnout increases, you would expect that
job satisfaction would be lower. There is
an inverse or negative relationship.
What about compassion fatigue? If a
therapist has high levels of compassion
fatigue, you would expect that job
satisfaction would be lower, because
compassion fatigue is theoretically a
form of burnout. Again, there is an
inverse or negative relationship between
these variables. On the other hand, we
would expect that higher levels of
compassion satisfaction would correlate
with increased levels of job
satisfaction. There is a direct or
positive relationship between these
variables. What about the relationship
between compassion fatigue and burnout?
As I said, compassion fatigue is
theorized to be a specific form of
burnout that only affects people in the
helping professions. So, because they are
similar constructs, you would expect that
as compassion fatigue increased, you
would see an increase in burnout. They
should move in the same direction,
because they are kind of the same thing.
At least, that's what the theory says, so
let's find out. Let's walk through the
five steps of hypothesis testing. Step 1:
select the appropriate statistic. We are
measuring the strength and direction of
a relationship between two variables, so
we will use the Pearson correlation. Step 2,
State the null and alternative
hypothesis. The null hypothesis is that
the population correlation is 0 for each
pair, so we write H0: Rho = 0,
where Rho
is the Greek letter for lowercase r. The
alternative hypothesis is H1: Rho
does not equal 0. Step 3: Select a level
of significance. For a two-tailed test,
alpha of 0.05, 198 degrees of freedom,
(that is the number of pairs 200 - 2)
the critical value is 1.98. Now, this is
calculated from a t-table,
just like we used for our t tests. You
will notice that this critical value is
very close to 1.96. Because our sample
size is so very large. So, step 4:
Calculate the statistics. And for that, we
turn to JASP.
[Music]
Begin by placing the data set
"JobSatisfaction.CSV" on your computer
desktop. We open our data set by clicking
on the main menu icon in the upper left
corner - it looks like the stack of
pancakes - and then selecting Open ->
Computer -> Desktop -> "JobSatisfaction.CSV"
and then clicking Open. We will begin
by looking at our data. The variables
imported mostly correctly. I will make
one change to the "Random ID" variable,
which is a String of numbers that serve
as an identifier. It's really a nominal
(or a naming) variable. On the left edge of
the box, we can "click here to change
column type" and set it to Nominal. The
rest of the variables are set to Scale,
which you can see by the yellow ruler
icon next to their names. Both Gender and
Marital status are treated as nominal
variables (or factors), so let's set those
levels. For gender, hover over the name of
the variable and "click here to change
labels". For this research, Male was coded
as 1, and Female was coded as 2. Now click
on Marital. Marital status was coded as 1
equals married, and 2 equals unmarried.
Those are all of the settings that we
need to change. Now we are ready to do
the analysis.
[Music]
To do a Pearson's correlation, begin by
clicking on Regression and then under
Classical choose Correlation. Remember
that correlation is a special case of
regression and that both are part of the
general linear model, in which we model
our data using a straight line. This is
why correlation can be found under
Regression. Move the variables job
satisfaction, burnout, and compassion
fatigue into the variables window. The
option for Pearson correlation is set by
default. In other examples, we would
choose Spearman's Rho or Kendall's tau. The
alternative hypothesis is a two-tailed
test.
It is not positively correlated or
negatively correlated. Significant
correlations in either direction will be
important to us. We want to flag
significant correlations, and sample size
will be important for the APA write-up.
Let's look at the results so far: this
table shows us the correlation of
coefficient for each pair of variables,
and their significance values. What we
see is what we expect we see: that job
satisfaction is negatively correlated to
burnout... as burnout goes up, job
satisfaction goes down. We also see that
burnout is positively correlated to
compassion fatigue: they both increase
together. The relationship between job
satisfaction and compassion fatigue is
also negative, but it is not as strong.
This table is called a "correlation
matrix" because each variable correlates
with itself at a positive one (and this
is not very interesting because every
variable correlates with itself as a
positive one) those correlations are not
reported. Instead, we see only a line. We
also see blank spaces
in the upper-right, rather than reporting
the same correlations twice. So the only
correlations we need are in the lower
left. This table is the traditional
correlation matrix, but JASP gives us a
more elegant display, as well. Click on
Display Pairwise. We now see each pair of
variables correlated... the same
information as the previous matrix, but
more simply displayed. You can use either
table, but I prefer this one. In either
view, if a correlation is statistically
significant, JASP will flag that
correlation and notate it with one, two,
or three asterisks. The number of
asterisks indicates the level of
significance. It will also include a note
under the table as to what those
asterisks mean. In this case, three
asterisks means this correlation is
significant at a p < .001
for a two-tailed test. But you
know what we need? We need some visuals!
Let's get some scatter plots by clicking
on scatter plots under Plots. Nice Plots,
right? Remember that one of the features
of JASP is progressive disclosure. You
can click on other options to see what
they do, and then un-click them. Nothing
that you click will mess up your
analysis, and this is a really good way
to learn about the features in the
software. For example, untick the display
pairwise option. The scatter plots now
change to a matrix. I don't care for this
display. I like the separate plots, so I
would tick Display Pairwise and I would
be able to see the plots separately. I
can change the size of the plots
individually and
I can copy a scatterplot to the
clipboard and then later on paste it
into my research article.
The variables are listed by their names,
so if I wanted to change the plot labels,
I would have to go back to my original
data set, edit it, and then rename them
there. I might also want to know about
the 95% confidence intervals around
these estimations, and I could ask for
the Vovk-Sellke maximum p-ratio. So, what
is this? All p-values are not created
equal.
The Vovk-Sellke maximum p-ratio gives us
a way to assess the diagnosticity of
our p-value. It helps us to interpret the
correlation. I would like to make a
standalone video about this, but I'm
still learning about it myself, and I'm
working on explaining it to others. So in
the meantime, I've included a link to a
cartoon explanation of the procedure in
the video description. We can also get
more information about our plots. Add the
densities for variables. This adds
histograms that show us the distribution
of each variable pair. The Statistics
option shows us the correlations for
each pair. The Heatmap again shows us a
simple correlation matrix with
correlations indicated by color, based
upon their relative strength: blue colors
correspond to positive correlation
coefficients, red colors correspond to
negative correlation coefficients, the
saturation of the colors reflects the
absolute value of the correlation
coefficient. Look at these options to see
what they do, and then when you're done,
untick the additional options and go
back to our original settings. And,
finally, remember that if you ever need
information about what each of these
options does you can click on the blue "i"
to
"Show info for analysis".
Returning to our five steps of
hypothesis testing, we are ready to
calculate the statistics, but because we
have so many correlations, these will go
better in a table. We will be able to
copy this table directly from JASP.
Step 5 is to make the decision, but again,
some correlations may be significant,
while other correlations are not, so we
will want to write up the correlations
that are most important for our research
question. We would report the results in
APA style like this: we would mention the
type of test, and the purpose of the
research.
Notice that in APA style, you do not
capitalize the names of the variables.
Next, we would report important
correlations, including our degrees of
freedom in parentheses, the coefficient
and its significance value. The degrees
of freedom is n - 2, where n is the
number of pairs for that correlation.
Each of our correlations was for 200
pairs, so the degrees of freedom are 198.
Because I was interested in the
relationship between
Burnout and the other two variables, I
reported only those correlations, but I
included a table with all of the other
correlations, and I will create a scatter
plot for burnout and job satisfaction.
This would be a good time to remind you
that the APA publication manual states
that no single correlation is worthy of
a publication all by itself. In other
words, if you correlate only two
variables, don't expect to publish that.
It is a good exercise for a class, but
not important enough to advance the
science in your field. The solution is to
make your research design more robust
and measure more than just two variables.
Returning to the interpretation, I might
also mention what some findings suggest,
something I will explore further when I
write up the discussion section. And
mention the effect sizes in the form of
r-squared.
I would also explain what those effect
sizes imply. I have two options for
tables: I can create an APA style table
out of the correlation matrix, like this.
Because every variable correlates with
itself at a positive 1, use a 1 or a
dash in those spaces... or just leave them
blank, which is what I did here. Also,
report each correlation only once. That
is why the boxes on the lower left of
the table are all blank. In this example,
I used abbreviations for the variables
in the column headers, but defined
them with the variable names. You could
also simply repeat the names of the
variables in the headers, use numbers, or
use abbreviations, and then define them
in a note below the table. Finally, I used
the JASP convention of three asterisks
for correlations significant at the
.001 level, and I included
the meaning of the asterisks in a note
below the table.
My second option is to report the
pairwise correlations in a single APA
style table like this. One of the really
handy features in JASP is the ability to
create publication-ready tables and
figures. I would copy the scatterplot
from the results window and paste it
into my report. And that is how we
compute and report a Pearson correlation
in JASP.
[Music]