Hello it's Margriet Groen and in
this video I would like to

talk you through how to
conduct a correlation

analysis in R and how to
report the results

following APA
guidelines.

Now I'll first

give you an overview, using a
few slides of the steps and

different functions to use

So for this example, we'll use
some data that are discussed in

Miller and Haden Chapter 11
about the correlations between

ability, that is reading ability, IQ, how
much children read at home, and

how much they watch TV at home.

In this particular example,
we'll just look at the

correlation between reading
ability and IQ.

So did the null hypothesis would be

that there is no correlation between
these two measures and our

alternative hypothesis would be
that there is a correlation

between reading ability and IQ.

And our expectation might
be that if one goes up, the

other one also goes up, so we
would be looking for a kind of

positive linear relationship.

Before and we go further this example
assumes that you have

downloaded this data set and
you've put it somewhere where

R knows about it. So you've
set your working directory to

whatever folder you have stored
that data file.

So the next thing to do
is to tell R which packages

to use. So we're loading two
libraries, these two and using

these commands. You might have
come across the Tidyverse

library. We'll also use a
library called Broom an it's

really handy because it makes
various outputs from analyses

look a little bit more tidy
and easy, easier to work.

OK. So then we'll read in these
data and will do that using the

read underscore CSV command. In
between the brackets we specify the

name of the data file and we
assign it to a dataframe called

'mh'. I've called it 'mh', you could
call it data or whatever you

like. By just kind of
calling that data frame, it

prints it to the terminal.

Well, you can have a little
look to see what's in there.

That's step one.

Then, as discussed in the other
video on correlation, kind of an

important step in doing a
correlation analysis is plotting

the data using the scatter plot.
So that is what we will do next.

So here we use the ggplot
function. We tell

it to use the MH data frame and
we ask it to map Abil.

Which is the variable
reading ability, to map that to the

to the X axis and map the
variable IQ to the Y axis.

And then we tell it to use the
geom point function to map the

individual data points in the

data set. And so this is what
creates the actual scatter plot.

Then we ask it to add a line
of best fit using this geom smooth

command.

We tell it which methods to
use. There's various options.

I've changed the theme of
what's the scatter plot looks

like, you can play around with
that, and rather than using

this kind of abbreviation of Abil as a label for the for the

X axis, I've decided to use
'reading ability' to make it

clear to whoever is looking at
this scatter plot.

So if you run that, this is what you get.

Reading ability. IQ. The
individual data points for each

participant and a line of best fit.

OK then we come to running the
actual correlation analysis.

So for that we use a function
called cor.test and within

the brackets here you can see
what you need to specify. So we

want to know what the
correlation between reading

ability and IQ is. So we tell it
to look into data frame MH

and then use the variable
Abill and the variable IQ.

Here we show it. Ask here to use
the method for Pearson's R. There are

various options and we'll talk a
bit more about those next week

And it is a 2 sided test.

So that that is kind of the
main function to do the

correlation analysis. Now as I
mentioned it, the output looks a

bit neater if you ask broom, the
package broom, to tidy it up. So

remember, we've loaded the
package broom, so we were piping,

using this command, the
output to a function called

tidy, which will just make the
output look a little bit neater.

And we've assigned kind
of this whole thing to a

dataframe called results.

Here I just ask it to print the results to the console to see

what it looks like.

And this is what
it looks like so.

This is what you get when
you do that.

We are looking at
three most important bits which are

Pearsons R, which is in this
cell here for estimate.

Then we need to know what
the P value is, which is in

this so called P dot value
and we need to report what

the degrees of freedom are
an N -- 2 and that is stored

in the parameter cell. As you might
remember we had 25

participants in this
data set, so N -- 2 is 23

and you need that bit of
information to report

the correlation analysis

properly. And other things in
this output you might be

wondering about what it is and so
here we have what is called the

statistic. Correlation analysis
using Pearson's correlation coefficient

uses a T distribution, and
this is that T value to kind of

check whether it is significant
or not. You don't need to

report it, but that's what it

is. And here we have the
confidence interval around

the correlation coefficient R that is sometimes
useful to report

actually. But it's not standard
APA guidance guidance, so the

confidence interval tells you
how confident you are that this

estimate that this Pearson's R
falls in between these values.

So here it this .07 and .72.

Method

here, it just reminds you
what method it has used to

calculate these things and
that it is a 2 sided test.

OK, but these three things
you definitely need.

And so yes, these are the things
that we need to include. And you

know, you could just read them
off at that kind of output table

that we discussed in the
previous slide. Or if that output

table is a little bit bigger and it's not so easy to

kind of read it out, then you
can use the pull command, the

pull function to pull out these
individual pieces of

information. So here we do that
by saying OK, take the data

frame called results.

and pipe that to the
pull function to pull

out whatever the number is
for estimate.

What is quite handy is then
to pipe that outcome to a

function called round and
tell it to report that number

to two decimals behind the
decimal mark.

Because that is the number of
decimals we use to report a

correlation coefficient.

Similarly for the degrees of
freedom you can

say OK use the dataframe
results, pipe that to the

pull function and give me the
number that is stored in

parameter cell.

And finally we need to know what
the P value is. So again we say

OK take that results dataframe,
pipe it to the pull function and

tell me what's the value is for P

dot value. We can then pipe that
to the round function and say

OK, give me that number
rounded to three decimals.

Because that is how we.

report P values and
sometimes there's many

more digits or decimals

So if you then write up your
reports, you would include

something like this.
Pearson's correlation

coefficient was used to
assess the relationship

between reading ability and
intelligence. There was a

significant positive
correlation.

We've established that from the
from the correlation coefficient

and from the scatter plot of
course, and then you give it

here. So r, opening
brackets. Here you have these

degrees of freedom, 23 = .45
comma, and then you report the P

value equals .024.

And then you give an
interpretation of what that

actually means. And so then you
say in this case, as reading

ability increased, intelligence

increased. That helps the reader to get their head around

how to actually
interpret this number, right?

Now another way to report a
correlation analysis, and in

particular, if you're reporting
more than one correlation. So

you might be looking at like 3
different combinations in in a

data set is a correlation matrix.

So this is what that might look
like. So you'd use a table for

that and you have the variables
of interest across.

The columns here and also across

the rows. And now we're not
interested in the in the

correlation between reading
ability with itself, or

in intelligence with itself, as
that would just be one, right?

But we are interested in these
other cells, so for the correlation

between reading ability and
intelligence you would

put Pearson's R for that

in this cell.

You then use a star. In this case
one star to indicate that

you found this to be significant
at the at the point of five

level and P

Smaller than .25.

You don't also then have to put
it here, because the correlation

between reading ability and
intelligence is identical to the

correlation between intelligence
and reading ability. So he would

just leave that cell open or put
put a sign like that.

So you only fill 1/2 of that
table from below diagonal or

above the diagonal.

So that's useful in
particular when you're

reporting more than one
correlation coefficient.