Understanding Correlational Research Design in Cognitive Psychology

Hello and welcome to the course basics of experimental design for cognitive psychology. I am Dr. Arkwarma from the

department of cognitive science ID KPUR. This is the second week and we've been talking about descriptive research

design. So uh so far uh but as I said earlier uh I wanted to pre you know present present to us a brief survey of

the other two kinds of research designs as well in some detail before we go on to the experimental research designs. So

in the last three lectures or two lectures probably we saw about different kinds of descriptive research designs.

We talked about case studies, we talked about observational research, we talked about uh survey interviews and

questionnaires. Now we move to a slightly different uh uh you know uh angle and we will start uh with studying

a little bit about correlational research designs. Okay. Now uh as we've seen before

correlational research designs are typically used to search for and describe the relationships between two

variables. Say for example you wanted to study two uh you want to study and note two particular variables. Let us say I

don't know you want to study uh the correlation between weight and height. So what you do uh you can very simply

collect the weights of all the people in your class. You collect the heights of all those all the people in your class

and you perform a statistic. We'll talk about that and it gives you a correlation. The correlation comes out

to be so and so. That correlation will tell you whether height and weight are actually related or not. There could be

other factors as well. There could be any number of things that are contributing here. Okay. Uh another

example uh the one that's been uh you know given in this book by Stanganger is basically this thing of uh you know that

a researcher might be interested in knowing the relationship between let's say family background and career

choices. So uh or say for example between diet and disease what kind of diets lead to what kind of diseases or

say for example the physical attractiveness of a person how beautiful uh you know or uh uh good-looking a

person is and will that relate to the amount of help they will get if they are stranded in a public uh you know in a

public uh sort of place. Okay. So you can ask any kinds of questions. You can collect data and you can compute the

correlation between the two things. Let's say on a scale of 1 to 10, how does physical attractiveness uh vary? On

a scale of 1 to 10, this is where one is least help, 10 is most help. When physical attractiveness is highest, do

you also get the highest amount of help? Or when the physical attractiveness is lowest, do you get no help at all?

Something like that. All right. Now, these variables, whichever you want to study, say for example, can be related

in a variety of ways. There can be variety of kinds of relationships between variables. All right. Uh and

sometimes it could also be the case that there is not only the two variables you are concerned with but there are other

variables in play as well. Okay. So uh let's let's try and see what kinds of relationships exist and uh you know more

detailed discussion can be had there. This is an example uh cited in uh Stanganger. Uh this is the study of Sher

and colleagues in 1994. They basically uh you know collected data from 20 participants uh you know students uh on

two scales. One is the scale of optimism and the other is uh you know reported health behavior. Say for example they

wanted to uh you know so one of the measures is liquid scale measure on optimism how optimistic a person is and

uh on health behavior. What kind of healthy habits are people following? Okay.

Now in this the optim optimism scale varies from 1 to 9. So one you're least optimistic, nine your most optimistic.

So higher numbers indicate a more optimistic personality and the health scale ranges from 1 to 25. So where

higher numbers indicate that the individual reports engaging in more healthy activities you know eating good

food, exercising every day, uh waking up and sleeping at correct time and a bunch of other things. Okay, maybe dietary uh

restrictions and so on and so forth. Now here uh one of the hypothesis let's say that the researchers are probably

testing is that people who are more optimistic about their life might not be following uh extremely healthy habits

because they would think that whatever we eat whatever we do we are going to not have bad consequences in terms of

health outcomes uh and so on. On the other hand, people who are less optimistic and slightly, you know,

conscious about life decisions may probably be uh following more healthy behavior because they constantly have

this fear of let's say having a a diabetes or a cancer or an hypertension and things like that and therefore they

might be following more healthy habits. Okay, again just a hypothesis. I don't even know whether these people actually

went with these hypothesis but just trying to give you a flavor of what might uh you know have been done. So as

the estimate of the relationship between the two variables cannot be made using just raw data because there are too many

scores. So 20 participants on a scale of 1 to 9 somebody would have chosen one somebody should have chosen three or

seven or 9 and you have these different scores and on a 1 to 25 with between 1 to 25 several things must have been

chosen. So let's say there are at least if not more there are 40 values to be analyzed. Okay. And these 40 values on

the uh you know uh face of this is not organized in the best manner. So how do you go ahead? How do you start

organizing this data? One of the ways is to try and have a visual representation about how the values are distributed in

relation to each other. So in the next slide I'll just show you a scatter plot of this data where the x-axis indicates

uh the predictor variable uh you know uh and the y-axis uh has show uh has scores on the outcome variable. Each dot is the

combined score of an individual on both of these scales. Look at this. Okay. So, this is optimism, high optimism,

reported health behaviors. You can see it's it seems to be a linear relationship because this is covered by

a line and it seems to be uh interesting that few people who are optimistic uh extremely optimistic are also following

uh you know good healthy habits. So, let's let's try and analyze this. uh again remember this is not a causal

relationship. It is just a uh associative relationship. We will talk about this in a bit.

Now what is this plot? The scatter plot provided us with a visual depiction of the relationship between variables. For

example, the scatter plot just shown you could see that the points fall in a fairly regular pattern wherein data from

most of the individuals are located in the uh lower left corner this side or in the upper right corner. So there is this

you know straight line this oblique rising line that you saw and this straight line is basically referred to

as the regression line. Okay, this is also referred to as the best fit line as it is the line that minimizes the

squared distance of the points from the line. So it basically says how how distant are each of these data points

from this best fit line. Okay, let's discuss this now. Uh so we will talk about this also. it it tells us uh

something uh extremely important. Okay. Now based on this kind of an example you can work around that there are probably

one or two or three or four different kinds of relationships that are possible between variables. For example linear

relationship if the association between the variables on the scatter plot the one that you just saw seems like it's a

straight line. So it can be called a linear relationship. What more? Sometimes let's say if the straight line

indicates that individuals who have above average values on one variable say optimism also have above average values

on the other variable say healthy habits following and both are sort of increasing in the same direction. That

is what we call a positively linear relationship. All right. So you can look at this graph here. This basically

represents a positively linear relationship. Okay. On the other hand, in some cases,

what you will find is that individuals who have above average uh you know values on one variable but below average

values on another variable, then the relationship could be defined as negatively linear. Okay. From the data

that is collected, we see that it seems very similar to a positively linear relationship. But it could very easily

or in a different set of population could be the opposite. Say for example more optimistic people feel that oh I

will never get a disease I will never uh you know be on the other side of the health and therefore they will be

following minimal healthy habits obviously you know it's just a belief thing so you can find with the same data

across different populations both are possible what is true is basically uh you know reflect in the data when you

collect once you collect the data now relationships between two variables are not always in a linear p in a linear

form Okay, sometimes the relationships cannot be linear or can be nonlinear as well. For example, the relationship uh

for a couple of variables cannot be presented or cannot be summed up by a single straight line. You can see the

graphs here C, D and uh sorry D and E. Okay, here the relationship is curvy linear. In E also you can see the

relationship is curvy linear. What is happening is that values in one variable are changing in response to the changes

in the values of the other variable. But these changes are not best described by a straight line. Okay. So there is some

relationship. It's not that these variables are not related to each other. There is some relationship but this

relationship cannot be uh best understood by a straight line. So these are called curvy linear relationship.

Okay. On the other hand, sometimes there could be no relation whatsoever in the two variables or the values of the two

variables. So you can see here there is no relationship between the variables. Uh that is why there's no discerning

pattern here and that is why this can be called an independent relationship. Changing one variable does not have any

impact on the other variable. Okay. Now you can see some interesting uh things here. This R that is here basically

depicts the uh you know Pearson product moment correlation coefficient and this tells us something about the nature of

the relation. I'll describe this in more detail but let's because we have the figure here let's talk about this now

this R uh is positive in a positive linear relationship is negative in a negative linear relationship is 82 here

and 70 here what does this 82 mean 82 means strong correlation if it were 22 or 16 or 05 then it is weak correlation

okay uh that is one similarly the magnitude on the other side minus.7 70 means strong negative correlation,

moderate to strong strong uh negative correlation. But on the bottom if you see graphs C, D and E uh are basically

showing R is equals to zero which basically tells us when there is no relation the value of R will be towards

zero tending towards zero. Uh and in the other two because the relationship cannot be summed up by a straight line

the R value is coming as zero. other statistics might be able to tell us more about these kinds of relationships. All

right, let's let's talk about uh know some statistical assessment uh uh you know characteristics of

correlations. So as I was saying this R was basically the Pearson correlation coefficient. This is the one that is

normally used to summarize and communicate the strength. So how uh what is the magnitude.20

or 80.20 is weak. 8 0 is strong and the direction plus 2 0 or minus 2 0 + 2 0 is positive - 2 0 is negative. So strength

and direction of the correlation is basically uh depicted by the value of the r or this uh you know uh pearson

correlation coefficient. Okay. So again something that I already told you. So the Pearson correlation

coefficient frequently frequently referred to as the correlation coefficient is described by this letter

R and it is the the number associated with the R indicates both the direction and the magnitude of the association.

The direction is indicated by the sign of the correlation coefficient. So plus or minus tells you whether it is a

negative or a positive relation. The uh strength or the effect size of the linear correlation of this linear

correlation is indexed by the magnitude of the number. So 2060.8 980.90 that way.

Now how do you interpret R? It's is fairly simple. The calculation of the correlation coefficient will be

discussed again. We'll talk about that more in more detail. But basically what you do is you also carry out some kind

of significance testing and the sign and whether the correlations are significant. Let's say P less than 05 or

01. Uh we'll talk about this in more detail later. But the significant values basically tell us whether we can

seriously take this relationship or not. whether we can seriously interpret that these variables are actually related to

each other or not. And this will be extremely helpful in when you're trying to predict uh the change in values of

variable B uh based on the change in variable uh change in values of the variable A. Okay. So significant R

indicates that there is a linear association between the variables and thus there is a linear association

between the variables uh you know which is this is the knowledge that you will be able to use about a person's score in

order to predict the changes in the value of the other variable. So for example as optimism and health

behavior remember shares example are significantly positively correlated we can use optimism to predict health

behavior. So maybe uh what comes out of this is more optimistic people follow more healthy habits. Good. So the extent

to which however the extent to which we can predict uh this is indexed by the effect size of the correlation 040.60

and so on and uh yeah so which is the value of R. Now each test statistic as we know also

has an associated statistic that indicates the proportion of variance that this R can account for in the data.

Okay. So that is basically for example for R it is the R square and it is referred to as the coefficient of

determination how much data this particular thing is explaining. Okay. Now when the

correlation coefficient is not statistically significant, this indicates that there is no positive or

linear or negative linear relationship between the variables. So this has to be also you know in the range of uh you

know p value being significant. Now if the r is non-significant does that mean that the data is not useful and we

should discard the data? No. The non-significant R does not necessarily mean that there is no systematic

relationship between the variables. It might sometimes indicate that although one variable can be used to can not be

used to predict uh the other the Pearson correlation coefficient is is not able to provide a good estimate to the extent

to which it is possible. Okay. So if the relationship is not significant it does not say that there's no relation but the

strength is not there the effect size is is much smaller. This again it represents a limitation of the

correlation coefficient because also because it is very common in curvy linear relationship. So other statistics

are followed there. Now uh this can occur in other various ways also. For example, sometimes uh the

data on one of the variables is in a very restricted range. Okay. So the size of the correlation may be reduced if

there is a restriction of the range of variables being correlated. Okay. Let's take an example the one that the book

has Tanganger's book. Uh this could occur for example when the sample under study does not cover the full range of

the variable. So the example was uh the values on the SAT test as predictor of college performance. Now uh it turned

out that the SAT scores and measures of college performance such as gradepoint average

the relationship is almost is only 30 which basically uh you know depicts a uh weaker correlation. Why is this uh

coming out as a weaker correlation? because probably uh you know the size of the coalition is is basically reduced

because students only with the highest uh you know with very high SAT scores anyways get admitted to college. So when

you are uh you know looking at SAT scores distribution and you're looking at GPA distribution the SAT score

distribution will be in a very limited range because this is in a very limited range its ability to predict this one

will not be as much. Okay. So when there is a smaller than normal range or one or both of the measured variables, the

value of the correlation coefficient will automatically be reduced and this will not really represent an accurate

picture of the true relationship between uh variables. So before you are planning to conduct a correlational study, we

should have a very good idea about the distributions of the variable in the population and choose the one which

basically uh carries a wide range of values. Typically that's why you see correlational only studies typically

have a larger sample size uh because they don't handpick their participants. They'll collect a large range of

participants. So it used to happen a lot in bilingualism research when the idea was that you divide people into uh low

proficient and high proficient bilingual. Uh there could be this threshold let's say threshold of 70 on a

particular test under 70 and below 70 and then you you know are carrying out your experiment and data. At some point

somebody suggested that okay we should treat this as a as you know values of one variable across a continuum. So now

what you could do is you could actually dump all of this data together and basically look at proficiency having

this range. So now the number of participants increases. Earlier there were let's say 60 in each group. Now you

have 120 on the same continuum and in that sense it basically you know allowed the people to understand the effect of

language proficiency on other variables much better. Okay, they get this here. Okay, uh the

correlation between high school GPA and college across students is about point uh across all students is 80. However,

since only the students with high school GPA with high school GPA uh about 2.5 are admitted to college, the data are

only available for on both variables for the students who fall within this circled area. Within this circled area,

you can see that the correlation is typically much lower. It comes down to 30. Okay, so this is in that sense

interesting. Now how do we report correlations? We just talking about this. So when the

research hypothesis involves uh testing or presenting the relationship between two quantitative variables, the best way

to report is the R statistic. Okay. So if the null hypothesis is that the variables are independent, then R should

be equals to zero. If the research hypothesis is that the variables are not independent, then it should have some

value either more than zero or less than zero. Some magnitude will be there. In some cases, the correlation between the

variables can be reported in the text of the research board. For example, as predicted by the research hypothesis,

the variables of optimism and reported health behavior were significantly positively correlated in the sample. Uh

you can see here uh we've indicated the sample size for R. We've indicated the value of R and we've basically also

indicated whether this is a significant value or not. All right. Now sometimes there are many correlation

many variables involved. Okay, when there are many variables involved then how do you present the correlations?

Then you typically present them in a correlation matrix. You can see here there are four variables and basically

they are all related to each other as well. Uh so this is basically how they are reported. The one with the asterisk

are the ones that are significant. Okay. All correlations are based into n is equals to 155. here is also uh you know

a correlation matrix that comes out as an output in the IBM SPSS uh you know software. I'm sure everybody knows about

it. Now this is one way you can present a correlational matrix. But sometimes you

are interested in knowing what are the different variables that are playing a part. So we carry out multiple

regression. As we know that the primary objective of correlational research is to investigate the relationship between

variables. It is also possible to study the relationship among many variables, okay? Or more variables. For example, if

the researcher's objective were to predict the GPA of a sample of college students and the scientist decides to

use three uh predictor variables, perceived social support, number of study hours per week and the SAT score.

So now there are three variables that the person is interested in. Now in such a research design where there is more

than one predict uh you know where there are more than one predictor variable then what you are conducting is called a

multiple regression. It can be multiple predictors and a single outcome and either ways. Okay. So multiple uh

regression is basically a statistical technique based on the Pearson correlation uh coefficient and basically

what it does is it correlation coefficients are calculated uh between each of the predictor variables and the

outcome variable and among the predictor variables as well. Okay, so there are several predictor variables and there is

one outcome variable. All of these are trying to predict how does college performance uh fare in terms of

perceived social support in terms of number of study uh uh hours per week and terms of sat score that they had

initially obtained. Look at this. There are different predictors and there is one outcome variable and you can see the

correlational uh sort of uh values that are here. Okay. So uh social support.14

study hours.19 and sad score is 21. So this is broadly what we are getting. Uh this one is not significant and these

two are significant. Now typically uh you know because there are so many of these correlations to

compute it is typically done using softwares and computers. But two important informations are are

information pieces of information are very important. First the ability of all the predictive variables to uh predict

together the outcome variable. So this is indicated by what is called the multiple regression coefficient the

capital R. And just as uh the small uh R had R square. Uh there's also a uh you know capital R which is basically uh the

amount of uh variation the proportion of variation that is uh explained in this data. Okay. So there is the R square. R

square is the proportion of variance measure uh and both can be directly compared to R and R square because it's

broadly these are just correlations. Okay. Second is that the regression analysis may show that statistics

indicate the relationship between each of the predictors as well. So that's why in the correlation matrix you can also

write down correlation values between variable A, B and C also. Okay. So these are called uh regression coefficients or

beta weights. Okay. Now each regression coefficient can be tested for statistical significance. So you can say

these these these are significant. The others are not significant. So that is why P values are indicated by means of

an asterisk on the correlation matrix. You can see here. Okay. So this one is not significant. This one is

significant. This one is. So you can basically uh you know see uh you can when you're putting this in the paper

you or in a table you will mark a star here and a star here and this is the uh regression coefficients. Also understand

the regression coefficients are not exactly same as the zeroorder correlations because they represent the

effects of each of the predictor measures in the regression analysis holding constant for or controlling for

others. So remember because you are doing performing a multiple regression these B values here are not the same as

the value of R that we have seen earlier uh this B the this value of B is uh arrived at controlling for this one and

this one. So this is the overall contribution of social support when you have controlled for study hours and SAT

scores. This one here is the contribution of the study hours controlling for social support and SAT

score. uh uh you know uh predict the outcome variable is GPA and this one is the contribution of stat score in GPA

controlling for study hours and social support. So I think that should be clear that's why the uh beta uh weight is

written there. So that's why the B is there. Okay. Uh the result is that regression coefficients can be used to

indicate the relative contributions of each of the specific variables. For instance, the regression coefficient of

I should have written B. B is equals to 0.1 N indicates the relationship between

study hours and college GPA controlling for both social support and SAT. That's what I was telling you. Okay. In this

case, you can see uh that the regression coefficient was statistically significant and the relevant conclusion

that you can make is that estimated study hours do have uh you know a power or propensity to uh predict the GPA in

the college. All right. So this is a little bit about the correlation uh uh style of research

that we uh that I wanted to talk about. I'll continue this in the next lecture. Thank you.