Hi, in this video I would like
to talk you through how to check

your assumptions for correlation
analysis in R. How to evaluate

whether there are any issues
with outliers or range

restrictions. Then we'll talk
about how to conduct Spearman's

rho correlation analysis in R
and finally, how to conduct

multiple correlations or inter
correlation in R.

Now first the the assumptions.
On the slide here, you see

the questions that you need
to answer to make sure that

you meet the assumptions
and pick the right type of

analysis for your data.

So the first question that you
have to address is is the data

at interval, ratio or ordinal level
so that refers to the type or

variable that you've got.

So there's nothing to do with
R for that. You need to think

about at what measurement
level your variable was

measured. If they are measured
at the interval or ratio

variable, then

you would use Pearson's
R. If they are measured at the

ordinal level, then you would
use Spearman's rho.

OK, so the second point is that
you need to check whether there

is a data point for each
participant for both variables.

Now that you can look at in
R. So I will navigate here to

my R studio window.

And here you

see my RStudio window, I hope.
I've already set my working

directory and I've loaded in the
packages that we need and I've

also read in here the data file,
the Miller Haden data that we

looked at last time.

So you can see that's that
the table is here.

OK, so that's where we are now.
We want to check whether

there are any missing data

in that file.

Now, because that file isn't
very big, it would be easy. You

could do it by hand, but most
data files are much much bigger

and you cannot do this by hand.
That would be awful and very

prone to errors, so we can use
some R functions to do that.

And the thing to know is that if
there is a missing data point

R kind of write that down as:

capital N capital A, 'not
available\ so there is no data

point in that cell.

So if a participant doesn't have
a score for reading ability,

then there would be a big NA
instead of a number.

Now the way to check whether
you have any missing values

is to use the is.na function.

S, that is basically

asking so you tell it here. OK,
look at this data frame for this

variable. So look in the MH
dataframe at this variable and

tell me whether any of the
cells have an NA.

So if we do that. It tells you
False false false false false

false for each of the 25
participants and false is good

in this case because it tells
you: I can't find any NAs

for that particular variable.

If there are no NAs,
that means that there are

numbers in that cell. That is
excellent. We have a data

point for each of the
participants on this

variable.

Now we can use this function.

I'm using this function here
in the in the slightly kind of.

Different way in that I'm saying
OK, I'm going to combine it with

filter because I want to use
filter to only keep the people

who don't have any NAs
right? So I'm saying here by

using this exclamation mark.

Keep people who don't have any. So for anybody for whom

an NA would be true, they

wouldn't be kept in the next object
and in this function.

I'll say that so I've put that
in a pipe, so what we're essentially

doing is: take the table, mh and then.

send that to the filter

function, and within that
filter function only keep

the people who have

no NAs for reading ability.

And then, because correlation
analysis is with two variables,

you also want them to have a
data point on that other

variable. So then we use the same trick.

To check whether they also have
a value for IQ. So that's what

happens in this line of code.

So send it to the filter
function again and we say OK

only keep the people who don't

have any NAs. So don't is
the exclamation mark.

Is there any not available in

for that particular area?

So that is a neat way of
checking whether both variables

have data points for your

participants. So if you run
that, we've got a new dataframe

where that is the case where
we've only kept those people now

because there were no Na's in
this particular toy kind of demo

datasets, it has the same number
of observations. Here. If in a

real data set you would kind of
see here, OK, there's fewer

observations here. Then it
Had in the original data frame, so

it has thrown out a few people

for not having data points
on both variables.

OK, so much about the missing

data part. So the third
assumption that you need to

check is whether data on both
variables are normally

distributed. Again, we can do
that. We can look at that in R

by making a histogram.

So a histogram plots how many
observations each value of

the scale for a particular value
variable has in the sample. So we use GG plot for

that here. We tell it
which dataframe to used, ones

we've checked for missing
values and we say OK, we want

you to plot reading ability.

Histograms don't
have a y value.

Then be saying use the geom_histogram to do that and there

we go, let's run that.

So here we have. So there's one
observation with 45 for

instance, and there is 4
observations where

participants have a score of 60,
and here you are looking for

something that resembles a
normal distribution. So more

observations in the middle and
fewer on both sides and

hopefully roughly symmetrical.

Now this probably looks about
OK, but it's not always that

easy to see and that is where the
QQ plot comes in really handy.

So for QQ plot we use this
function. It's QQ Capital plot.

Again we just say OK, please
use the MH data set and that

variable to make the QQ plot. So
let's do that.

OK, so here we have our QQ plot
and remember all the

observations need to be kind of
around this line.

The solid line.

So that is good and all that,
and as long as they kind of fall

in between the

dashed lines the blue dashed
lines, here (I just noticed that

you can't actually see my

pointer here)

It is in the bottom right
corner. You can see the plot,

so observations need to fall
between these two blue dashed

lines and ideally as close as
possible to the solid blue

line in the middle of that. If
that's the case, then you can

conclude from the QQ plot.
That the variable is

normally distributed.

Now you would you would do the
same thing for for IQ.

Um? So let's just do that.

We should use that
one, it doesn't really matter in our

case because we didn't have any
missing values, but it is a bit neater.

Here on the right we have the
histogram. For IQ you can see a

roughly. Yeah, it resembles
resembles a normal distribution

to an extent.

I will make a QQ plot.

And then we go and you can
see actually in the top right

corner of the QQ plots and
in the bottom left corner of the

QQ plot you can see some
observations that are quite kind

of just on the outside of the
dashed line, blue line and which

suggests that I would probably
say OK, these data are still

normally distributed, but well,
these observations are something

to watch and if they are further
and would if there would be even

further away from that dashed

line then. It would
have to reconsider.

So if

the data would clearly not be
normally distributed, you would

use Spearman's rho.

OK, then we go on to
the 4th an assumption.

That's about linearity. So does
the relationship between the

variables appear linear. Now for
that we can use a scatter plot.

You already know scatter plots
from last from the last session,

so I'm not going to talk much
about it. This is basically just

using that. Again.

This will make a scatter plot.

Here we are. Here we have a
scatter plot of reading ability

and IQ. I'm not, this looks
like it is a kind of linear

relationship. We don't see
kind of a pattern that has

curves in it.

If.

You know we would have

wanted to. If it would have

decided it is. At any point.

it is nonlinear. Then
you would have to do different

things. Spearman's Rho doesn't
necessarily help there, so more about

that will be covered next year.

The other thing to check in the

scatterplot is the spread

around the line of best fit. An
is the spread roughly kind of

equal across the line, so is it.
Is there as much spread over here as

there is over here and

that looks like that is
the case.

OK, so that is it about

the assumptions. Let me just go
back here and see what comes

next. Yes, of course. The issues
with outliers, an range

restrictions. Again, you would
look at your scatterplot to see

whether there are any
issues with that. So you would

look at it at your scatterplot
to see whether this correlation

would be driven by, you know,
one data point in case of

outliers, or whether there would
be very restricted variation. So

maybe if we.

I only had reading scores kind
of 45 to 65, then the

correlation would have been much
smaller and so that would have

been restricted range.

OK, let's go back to the
presentation.

Intercorrelation Hold on before
we go to intercorrelation. I

just want to show you how to run
Spearman's rho correlation

analysis in the in R. So we go
back to the old window and here

we've got a code example to

do that. Remember you
would do this if you've got

ordinal data or you have the
data breach another

assumption, so it's not.
They're not normally

distributed, for instance.

That a correlation analysis
using Spearman's Rho is very

similar to the one using
Pearson's r. It is basically

displayed here that you change.
It is what's called the method.

So previously it's at Pearson's r
here and now it says Spearman

and that is the only difference.
Other than that we can use this

cor.test function as we did for

Pearson's R. I'm telling it which data
frame to use and which variable

to use, and then we just change
the method, so that's cool.

It is complaining about this
but never don't don't worry

bout that this.

So if we look at the results.

It gives you quite a
similar

correlation so you can read
this in the same way. This is

where you have your Spearman's
rho. This is where you

have your P value and here it
reminds you that it is

Spearman's rho correlation
rather than Pearson's R.

OK, now to

intercorrelation. So what we
want to do is to construct a

matrix of scatterplots because
we want to look at multiple

variables within a data set and
the relationships between them

and a matrix of scatterplots is
then really good idea to get an

overview. Um, and then we want
to conduct multiple

multiple correlations at once
and correct for multiple comparisons using a

Bonferroni correction,
for any adjustment to make sure

we don't have a problem with
type one errors.

So how do we do that?

Let's go back to R.

So again, we will
use the MH data

and I will use
this function called pairs and

what that does it basically
creates a matrix, right?

So.

Technically, we should really be
using that, alright? Because

here we checked for missing
values, so we have four very

full variables and participant
number. Now we don't want the

correlation between the
participant number and reading

ability, because that would be
meaningless. So before we use

the pairs function to create a

matrix. We say OK, we use select
to say, get rid of

that. T

So I will say
matrix.

So what I'm doing is taking the

table we checked
for missing values and I'm piping

that to the select function and
I'm using here this minus sign

to say OK keep everything except
the participants variable and

I'm sticking that in a new

object called mh_matrix. So

there we go.

So here you can see I will

click. But so this one you
can see it has five variables

because participants is still
in there and this one now has

four variables here, because
a participant is not there

anymore.

OK, so then we can run
the pairs function too.

I create this matrix now. This
is really tiny because my R

window has to be quite small to
fit into the window that I'm

using to make the video
recordings. So I would say try

this code in your own screen and
then you can actually see that

it is quite helpful, but I'll
talk you through it

Oh, hold on.

I think participant is still
there. That is wrong, but

that's because I'm using the
wrong dataframe. There we

go.

So here we are. We've got
ability, IQ, home and TV.

This basically shows
you the relationships between all the variables.

This is the scatter plot for
ability on one axis and IQ on

the other axis and this one. I'm
sorry I keep forgetting that you

can't see my

pointer so let me try and talk
you through that without using

my pointer. So you can see the
different variables across the

diagonal in this graph: ability,
IQ, home and TV and then if you

kind of go down from ability and
then you are to the left of IQ

that is the scatter plot that
plots those two variables. So if

you go down one more you have

reading ability
on one variable and home on

the other variable.

So to the left of home and kind
of below IQ sits the scatter

plot that plots IQ on one
and home on the other

axis, etc etc.

So it is a bit small on

this screen, but that's
because of the recording, so try

it on your own screen. Then you
can see that you get a lot of

scatterplots all in one go.

That's the main thing I'm trying to

say. So how do we then? So
that's the scatter plots, but we

want the correlation
coefficient as well, of course.

So how do you run that?

Then you first have to tell

it. That's well over writing it
in this case.

That you're treating this as a
dataframe. Don't worry too much

about it. Well, there's do that.

And then. It's just, well, I can
say something about it. So that

you know what you're doing.

Previously these functions store
this as what is called a

tibble. It's just a sort of type
of specific type of table in

R. But the function that we will
be using in a minute needs it as

a data frame, which is also a
table, but it has slightly

different properties. So that's
what you're doing here. You just

saying OK. In anticipation of

this function we need

the input as a dataframe. We say

OK. Take my table and make it
into a take my table here and

make it into a data frame and
we are just overwriting it.

So we've done that. I think I'll
just do it again.

And then we use the function

correlate to create this
correlation matrix, so we have

to tell it what data frame to
use. I've been changing that

during the video.

So here is our data here we say

yes, please compute P values.
Here is the method.

So quite similar to the cor.test
function that we used

previously. We're using Pearson's
here. You could change that to

Spearman if you need to. And
here we have to adjustment

method that we're using. So here
we're using Bonferroni. There are

ones that you can learn about at
some point in time.

So we're using that to create a
correlation matrix and storing

that in an object called interior results. So let's do that.

So here we've got it. We can
look at that that way, but we

can also just do it
here.

So now in the console you've got
this, you can have a look at the

correlation matrix. So here we
have this matrix setup again. So

across the diagonal correlations

with itself. So if I say here I
mean in the console window at

the bottom. So across the
diagonal you have to correlation

with itself, so they not interesting, that's why

these cells are empty, and then
we have the correlations between

reading ability and IQ, reading
ability and home, reading ability

and TV and then the next
column you have IQ and Home and

IQ and TV.

ETC etc here in the top half
kind of above the diagonal

you have the same values as
we discussed previously. You

only need to report 1/2 for
that reason.

So that's all the correlation
coefficients And then

here we have the P values.
So if you're going to scroll

down, you'll see the P
values for all those

combinations and these are
adjusted for multiple

comparisons using the

Bonferroni correction. So
here you can see which ones

are significant and they
have already been corrected.

And finally, there is a table
with the sample sizes where

yeah, where you can just double
check how many

participants are there
for each correlation.

OK.

And that is it for now.
Thank you very much.