Soon, so you should see on the slides

the session code if you wanna log in and

also um this slide out event code if

you want to ask a question using slider.

In the meantime, ohh visit the discussion

forum, see whether anybody has asked

any questions there. No, not so far.

And I will also put this slider information.

I'm in the chat.

There we go. The kinds

of people often ask for

OK, I think all sets.

So let's get started from us.

So we've been looking at correlation

in a bit more detail this week. Um,

yeah. If you have any questions,

you can ask them on Slider. Uh,

let's see how we're getting on with that.

Nothing as yet, but I will give

people a little bit of time

so it is all working and ready to

go before we get yes. So what did?

Um. So the other thing to say is

that I have now made the answers. Um

to this week's lab activities

available on the website at Wilton.

So week 12 lab activity answers

are out on the on the website.

The Moodle quiz is also available if you

want to kind of check your understanding.

Um, right, we haven't.

We have a first question.

It says this isn't related to this week,

but is it normal if I'm finding

statistics harder than everything else?

For some people that is certainly the case,

yes, I'm you know, there's of

course everybody's a bit different.

Some people come up with A level

maths to sychology and they

might not find it so difficult.

Other people have not done that

and might find it more difficult.

I'm afraid it is a really

important part of of psychology.

But also it's yeah, it you know,

it is um,

most people will get to grips too with it,

even if it is a bit of hard work.

So I'd say you're definitely not alone

in that there is quite a few people who

didn't necessarily start studying psychology.

With the view of getting into

statistics really deeply.

I'm afraid it's unavoidable.

To understand the knowledge

base of psychology,

you're really also need some understanding

of the statistics that are used.

Otherwise there's no way of telling

whether a study actually finds

something that is that we that we can

trust and that is reliable finding.

Umm so yeah,

trying to trying to stick with it.

Do ask questions.

Do and and don't feel like you

know there might be a question.

Do you feel like ohh you know

it might be a stupid question or

something really not the case at all.

And that's that's whatever

question you might have.

There is at least thirty others

who also have that question.

So,

yeah,

I'd I'd say um that's that's I think that's

probably all I can say about that I'm afraid.

I hope that was helpful.

Um, so looking at this week's

lab activities, we might, uh,

just go through some of them?

If there are no specific questions,

um, I'm just gonna

open things up a bit. Let's get

started. Um,

so first of all,

there were some questions right?

About in the lab activities.

Um, no, no. Let's go to the lab

activity so we can have a look at them.

Ohh, come on.

So we had some questions about, um,

kind of concepts in labour activity one.

As I said, the answers are now here.

Uh, correlation would be an appropriate

form of analysis from researchers

interested in the relationship between and.

And these were the thinking about the the

kind of different types of variables.

And so the the answer would be

B&C because, um, all of those

variables are continuous.

Dog breed and gender are

categorical so that you can't use.

Patients are also payments run as a.

They can't use correlation in

in that sense. Um, go back,

go back and forth too. OK, much.

And when would you use payments rather

instead of patients are sorry when

the data is not normally distributed?

Is there that correct answer?

And looking at these various

histograms and QQ plots,

which of the variables

satisfy advantage assumption?

So remember for just go to

to this QQ plots uh I mean

so here we have this is a QQ plot right?

This is a histogram and in the histograms

we're looking for quite a symmetrical

bell shaped distribution and and in

the QQ plots we are looking for a uh,

we're looking where the data points fall

in relation to this blue line and this kind

of area between these dashed blue lines.

So long as the data points are all

these data points fall close to that

blue line and say that it is the the

variable is normally distributed.

So as you can see that is not the case here.

It's kind of all over the place and here

you can tell from the histogram that it's

not at all um normally distributed and

and you see that in a QQ plot as well.

UH vocabulary on the other hand

is is quite nicely distributed.

So this is,

you would say that that does satisfy the

assumption of normally distributed data.

Um, why should correlation analysis

not be conducted on variables

with a curvilinear relationship?

Um, because, um,

you might conclude that there is a a

relationship between the variables.

Yeah, we we say there isn't because

it is not a linear relationship.

So correlation is as we have

been using it is only for linear

relationships between variables.

So that means that you can

fit a straight line to it.

If it is not a straight line that fits the

data or the then it don't use correlation.

OK, so that's a lot of activity One line,

activity two.

Ohh, say that I haven't changed

this to the market and script we um,

that's actually in our script

rather than a marked out script.

So we can, I'll.

I'll change that and we'll have

a look at the markdown script.

So, um, let's stop sharing this slide.

I've just realised that that wasn't

very helpful because you couldn't

actually see my screen anyway.

Um,

so let's go to UH,

Don't worry about my turn now

let's go to Lab activity two.

You should now be able to

see my uh Ohh window.

So this is the markdown script,

and your markdown script that

you've created might look

a little bit like that.

So first we do need to load the libraries,

so let's just do that.

Then we're gonna do some work with

it's data on vaping.

So we are going to read in those

data and see what we've got.

Doesn't work. Do not.

Let's check the environment.

Yes, it has credits,

so I've called it that data.

It's not massively informative.

You might want to choose a better name.

Um, so here we can see that

we have 106 observations,

so participants and 8 variables.

So you can click on the blue circle

with the little white triangle and

then you can see what we've got there.

So participants then block three

response times, block 3 accuracy,

block five response times,

and block 5 accuracy.

Now we have vaping questionnaire data.

We have information on sex and on age,

so there was a question for how

many participants do we have data?

As I mentioned,

you can tell that from from

here there's 166 observations.

If you click on that data or on the name,

it will put it into view and

you can see that here as well.

So the answer to question 2A

is there are 166 participants.

Then we do need to do a little

bit of data wrangling because at

the moment we don't have to write

information in the OR we don't have

the the information in the data

frame that we can actually use to

do our correlation analysis. Ohh so

I'm just gonna go

it is useful. It might you might

think oh do I do have to read all

of the background information.

You're doing it. I would recommend

reading it because it then the the data.

This is real data from a real experiment

and it starts making a lot more sense.

So you need to know that block 3 in

the So let's let's go back a bit.

It's all about explicit attitudes and

implicit attitudes towards the vaping.

And explicit attitudes are we're

measured with questionnaires.

So that is, yeah,

the vaping questionnaire,

school and implicit attitudes were

measured through something that's

got an implicit association tests.

So you use images of vaping in one

condition and images of kitchen

utensils in another condition,

and you associate them with positive

and negative words and depending on

how what people's attitudes are and

you should be quicker to respond to

associations that you feel good together.

So if um then then if they do

not go together.

So if you have positive a

positive attitude towards vaping,

you might associate might be

quicker on positive words,

whereas if you have negative

attitude to vaping,

you would be quicker on on in the

condition where vaping images

are paired with negative words.

So you can read more about that

Uh I'll uh there's a link to

the notebook project there.

Um,

so you we need to know that block

3 in the experiment they tested

reaction times and accuracy

towards congruent association.

So pairing positive with kitchen

and negative with vaping and block

5 tested in concrete association so

positive with vaping and negative

with kitchen utensils.

And so we are interested in the

difference in reaction times

to these two blocks.

So if reaction times were longer block 5,

then in block 3 then people are considered

to hold the view that vaping is negative.

Um.

But if UM reaction times were

quicker in block 5 than in block 3,

then we considered them to hold

the view that vaping is positive.

So we need to the difference of UM,

the reaction times.

We also need to do a few other things.

And so we've done all that and we

wanted to do some data cleaning.

So people, um, you know,

accuracy should not go above one.

And uh, you know,

there might be some data entry errors

that we don't want in our analysis.

So we're going to remove

participants who have an accuracy,

created them all and in

either block 3 or block 5.

As we you know we don't.

We can't quite know what's

what's going on there.

We also want data from people

who are paying attention.

So anybody who's average accuracy

school across those two blocks was less

than 80% and we're going to remove now

that you know you could say why 80%.

That is a decision that you make

beforehand and and ideally you

would pre register that so you

would before you've seen the

data you're going to say

what you're how you're going

to handle that cut off so

that you can't be accused of.

I'm kind of throwing out

data that you don't like.

OK, so and then the third thing

that we have to do is, um,

once we've cleaned up the data,

we need to create a new variable with the

kind of the IAT score that we that we want.

So by subtracting block 3 reaction times,

flock from block 5 reaction times.

Now I will just check to see

whether there are any questions.

No. Um. So let's see.

We can do that all in one pipe, right?

Um. You might remember that um.

So the pipe symbol is this thing, right?

The percentage symbol?

Um, a bigger than UH symbol and

another percentage UH symbol, um.

So we use our data frame that

we've called that and here we

are actually overwriting it.

It's in I I tend not to do that,

but I I clearly hear I have done that.

So you might want to want to give

this a different name than that one

that you don't overwrite a data frame.

So you know you might say debt

clean or something.

So we're using that this data

frame and first of all we're going

to philtre out and go only keep

the participants with accuracy.

Schools that are kind of below 1

so that are actually possible um.

So accuracy scores for block

three are in this variable.

So we say philtre and then keep the

participants where accuracy is below 1.

Um,

then we do the same thing four block 5.

Um. Then we compute a new variable here,

and we calculate the average accuracy

on the IT across block 3 and block 5.

So you know this is just take that the

accuracy from book three and the accuracy

from block 5 and divide that by two.

You could also have used the function

to do that, just doing it by hand here,

and that is going to be in a new variable.

And then we say, OK, use that new

variable and throw it to anybody who is.

Or keep the people who have an

accuracy above .8, so 80% UM.

And then finally we calculate our

new variable, here the I18RT.

So here we subtract the reaction

times before block three from

the reaction times in block 5.

So let's run that thing and

let's see what it does there.

And so now that has 104

observations and 10 variables.

So that does make sense, right?

Because we added two variables and.

You can see those here on the end.

So here accuracy and I TRT which is

the difference between reaction time

look 5.3 UM and we kicked out a few

UH participants right UH because they

didn't quite fit these UH criteria.

Um,

keep your questions

coming in if you have any.

Umm just regularly check slider for that.

So for how many participants do we have

data now that we have cleaned them up?

104 participants We could actually Yeah,

I'm not gonna go into that.

Let's stick with that for now.

So Dan, question 3B used the information

in the background description to understand

how the schools related attitudes, right?

So what does a positive score on the ITRT?

Mean What does a negative score mean?

Etcetera. So people with a positive IE

TRT score are considered to hold to the

implicit view that vaping is negative, right?

Because they the quicker to respond to

concurrent associations and then to

incoherent associations and people with

a negative ITRT score opportunity to hold

the implicit views that vaping is positive.

And then we have the questionnaire,

So um higher scores indicated a positive

explicit attitude towards vaping on

and this other variable, this one,

the vaping questionnaire school,

which is kind of the explicit matches

the explicit attitudes.

Now we do want some descriptives for

all of these, so let's do that here.

Umm, I haven't called them here,

so let's do that.

I don't know, Daniel.

I'd like to see in the console

as well, but it doesn't do that.

There we go. So the mean accuracy is .9,

which is quite high of course,

but we've thrown out anybody who

was bad kind of worse than .8,

so it's not that surprising.

And on average people seem to have a

positive score on the UH I TRT variable.

So that suggests that Ohh average

people have a negative implicit

attitudes towards vaping.

And the score on the explicit

questionnaire is, um,

62 points something.

Um, so you know, just a question

about why these things are useful.

It is always worth worth

thinking about the averages.

So and some averages are are more

informative than others, so the

so did UM.

I guess what I'm asking here is to think

about what the numbers actually mean.

And it depends on how the questions

students are asked, right?

So the the implicit measure we

know how to how to interpret the

explicit questionnaire score.

It might be informative, but we don't,

we don't have a lot of information about

what that school actually is, right?

So is that what is the maximum possible

support said out of 100 or out of of 63?

If it is, you know out of 63 than it

is is very high that average word.

If if it's out of 100 it's not so high.

So we need a bit more information

and we also don't know what kind

of skill they were answering on.

So it's this basically is the question

is that to illustrate that we don't

have all the information to interpret

their means that we get at the moment.

OK, so then we're gonna do

some assumption checking. Um,

so we need to think a little bit about

our the types of comparables, right?

So are they continuous?

Well, the reaction time measure

is certainly a continuous variable

and and for now we're going to

consider the vaping questionnaire

score also a continuous variable.

Now all the we we might want to check

whether there's any missing data.

So that's what we do next,

and we can use.

This is dot and a function,

so it is not an A function basically. Um

tells you whether there are

values that are called NA not

available in the data frame.

And if you philtre for exclamation

mark is not an, A is not a,

then you keeping everybody who

does not have missing data.

So if we do that, we, you see,

you can see here that we

now have 96 participants.

So there were some people in there with

missing data who we've now thrown out.

Um, ah, I can see your question here.

Um, sorry, I missed that.

What is the difference between using

the pipe symbol and the plus symbol

for continuing code in the new line?

It's a really good question because

they're highly similar and they're

just used in different contexts.

It might seem like why

not be more consistent?

That is in the nature of our being an

open source code programming language,

and people have contributed

different packages.

And for everything in reply,

R or actually everything in the

tiny verse uses this pipe symbol.

And so it's actually not that one.

It is and percentage sign rightward

error or bigger than size percentage.

So kind of slightly different from that.

I'll type it in the chat,

but it's meant to be.

It will allow me

teams not being very fast. So

that symbol, um, that's in there,

check now that is called the pipe and that is

used in all functions that come from dplyr.

The plus symbol is what you use

when you create graphs in ggplot.

I'm not 100% sure, but pretty sure

that that 4th in particular what for

the kind of functions that you use,

that's the only place that

you would use a plus sign.

So when you create a figure,

think of it as adding layers one at a time.

So plus another layer plus

another layer plus another layer.

When you are cleaning data,

working with data,

it is the arrow kind of thing with

the percentage signs around it where

you link data from one function to

another function to another function.

So I hope that makes sense.

Let me know if it doesn't.

Right.

So we were checking assumptions, right?

So we've kicked out people who had

missing data for one of the variables and

then we are going to check normality,

other variables normally distributed.

So we can do that by creating some plots.

Um, and we're doing that in

the codes that comes next.

So here we have a a histogram for

the Vaping Questionnaire School that

looks pretty nicely distributed, doesn't it?

It's never going to be perfect in real life.

And so if we look at the

QQ plot for that variable,

you can see that almost all,

I mean this and that.

There's two data points here that are

little bit there's a lot in here,

the extreme that are outside of

this blue shaded area,

but the rest is all kind of

close to that blue line.

So that umm,

from those two graphs together,

the histogram and QQ plot,

we can conclude that the vaping

questionnaire score variable is

normally distributed and the same

holds for the IATR variables.

So here is the histogram.

Again,

it doesn't look perfect.

Ideally you would have you know in the

real real bell shaped form you might

have that thing would be more in the middle,

but it is close enough as you

can tell from the Q plots,

so that is uh,

So yes,

both histograms resembling normal

distribution and the open source and QQ

plot all within the blue striped lines.

So yes,

we're happy with the normality assumption,

right?

Then we will create a

scatter plot um.

This will tell us whether um,

so two things. And we can,

we can look at homoscedasticity

of data and we can also look at

the linearity and the direction

and strength of the relationship.

So if you look at this,

here we have explicit attitude, right?

And here we have implicit

attitudes and and here we have it.

It's basically a cloud of data, right?

Um. We can see that the well that

suggested the relationship might be weak.

And in terms of linearity,

this catapult doesn't suggest

any curvilinear relationships,

which is, you know,

something like that

in terms of variance or constant variance.

Whether or not that is constant,

that's the same thing as whether

the data share almost capacity.

It seems quite constant,

but there there is a few there's fewer

people with a negative ITT, right?

So here we don't quite have the

same range of people here on

the left of the of the graph.

So um, yeah, that it called.

It's not perfect,

but I would say it's OK for now.

Let's check whether anybody has

questions about assumptions, No.

OK, then we're actually going

to do the correlation analysis.

So you might remember, you know,

but this is the code to do

that and then we can pull out

those the numbers that we need.

So let's do that.

Um. And here we've got our SO correlation

coefficient is in the estimate cell and

as you can see it is awfully close to 0,

so and and you can see that in the pin

value as well that is way larger than .5,

so it's not significant.

So it suggests that there's not a significant

correlation between these two variables.

Now this is how you would write this up.

Testing the hypothesis of

relationship between implicit and

explicit attitudes towards vaping,

piercing correlation coefficient,

The patient correlation found no

significant relationship between IT.

Reaction times implicit attitude and answers.

All vaping questionnaire explicit

attitudes and here you have that

and this is how you write it.

Uh, kind of the report,

those, those numbers, right.

So they all value it.

This, you might wonder why this

is an extra exists because I'm

writing it in our lock down here

and that makes it in italics.

If I need this document in a minute we

can see that the degrees of freedom

you need to report here and then

we'll report the actual value for it.

And then here we have the P value.

Overall,

this suggests that there is no direct

relationship between implicit and experts.

Attitudes were forgotten safely and as

such our hypothesis was not supported.

We can not reject the null hypothesis.

So there we go.

So let's see what I can knit this.

And then you can see that there's

things that are in asterixis

are actually turned into,

um,

things that are in italics.

It's just getting there. Some 88%. No,

there we go.

I'm I'm not sure you can now

see that, so let me share my

full screen.

There we go. So by knitting

this ARM markdown document,

you've got kind of a summary of of

various things and the write up is just,

you know, put in all the graphs.

It puts in all the text

that I've written there,

and so any notes that you make. Um,

and here we are. So this is what I

wanted to show you here because that

in our markdown I've put asterisks

around that R it puts it in italics.

That's what I I was trying to show you.

So I've now knitted it to an HTML document,

but I could also limit it to a

Word document or to PDF document.

And so you can write up and the result,

you know the your analysis in our

using an our markdown script and

then knit it to a Word document and

you've got everything you need for

your report without having to copy and

paste individual values or individual

tables or figures or anything.

OK. So any question about the

correlation analysis here,

it doesn't look like it.

So we'll just continue.

And then the last bit we've just looked

at something called intercorrelation

where you basically look at multiple

correlations at the same time.

So we made matrix of scatter plots.

It's you know,

you could have made them individually.

This is quite a neat way of making

multiple scatter plots at the same time.

And the way to read this is.

So we have 3 variables here.

Um, this is the scatter plot we saw earlier,

right? Between So yes,

situation between implicit

and explicit attitudes.

But now we want to see whether either

of them correlated with age as well.

So if so,

if you want to look at the scatter

plots with age on one axis and the

implicit attitudes on the other axis,

then you would end up here and age and

explicit aptitude is is over here and

and above the diagonal it's the same,

right?

So H implicit attitudes H explicit attitude.

So you can just kind of navigate like that.

Um, so the scatterplot with age,

it really suggests highly skewed,

with only a few participants older than 25.

Looks like they did this study

with undergraduate students.

And you know, we have one person

who's quite a bit older than the rest,

so we don't have a good

spreads in high schools.

So we'll therefore calculate experiments,

right rather than pieces are

right because this doesn't look,

look normally distributed whatsoever.

Yeah, you, you know,

if you were analysing those things

for a research project that you

would look at it more closely and,

you know, look at the histogram,

look QQ plot, et cetera,

or you would actually collect more data.

This was really the question

that you wanted to answer of

different ages to have more data

points of people older than 25.

So here we have the code to um

hmm it can't find something.

Ohh, that's because I haven't run this.

So we need to do a few things before

you can do, uh, run this code.

It needs the data frame in a

particular way and and that's.

Then it will all come out fine.

So when you run this function

correlate it will give you 3 tables,

one with the correlations,

one with the P values and one with the

sample sizes from which you can the decide

what the degrees of freedoms are right?

So it's a little bit slightly different

output from when you run 1 coronation.

So here you can see the

correlations with HR quite small.

Um, and indeed not significant.

So you've got significant correlation.

Was found for with H for

item measure of attitudes.

OK, so that is the lab activities.

Um, I will see whether there's

any other questions anywhere.

I don't see any.

That's OK.

If all is clear then and everybody

is happy then that is great.

So next week we will be working.

Materials are all on the website.

We'll be looking at linear regression.

So simple linear regression,

which is quite it,

It's related to correlation,

but it is kind of a stepping stone

for more complex or aggressions

that you'll do later on.

So thank you everybody for attending

today and good luck with that and I

look forward to seeing you next week.

All right. Bye. Bye.