Understanding Factorial Experimental Designs in Cognitive Psychology

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

Kpur. We are in the fifth week of the course and this is going to be the second lecture. We've talked about in

the previous lecture about uh one-way experimental designs about causality and we basically saw how do the one how do

how does a simple one-way experiment work in both a between participant setup as well as a within participant or a

repeated measure setup. Now let us take it forward and talk about factorial designs.

So let's say typically when you construct a single variable or a you know a simple one-way experiment it is

good it tells you uh about the causal relationship between the two variables but if you look at this uh that in daily

life or in in in everyday uh settings it is not more often than not it is not just a single variable that is causing a

change in a given uh you know behavior. Typically what happens is that there is uh you know more than one variables uh

more than one variable that might be affecting the behavior of interest and in that sense you might want to study

the behavior of interest uh how that is getting affected by more than one variable. So in in those cases what we

need is we need more than one independent variable the effects of which you want to measure on your

dependent variable. So for example, aggressive behavior, we were talking about this, you know, uh example of

watching uh violent uh video games or watching violent uh cartoons. How does it affect aggression? Now, if aggression

is the behavior of interest, aggressive behavior can probably be influenced by the amount of violent television that

the child has watched. Yes, that was your first variable. But it also could be affected by the disciplinary style of

the parent. It could be affected by the uh child's mood state before they came to the experiment. Uh it could be

affected by the soio economic status and any number of things. Now if you're interested in sort of understanding the

behavior of interest in more detail, it might be a better idea to take into account a number of variables at the f

you know in the experiment and all at the same time so that it basically tells you what are the various influences on

this behavior of interest. Okay. Uh another example could be say for example there is this ability to memorize new

information. It could be influenced by both the type of the material let's say easy material difficult material and you

can operationally define easy and difficult but it also uh you know vary on the memory basically your memory

capacity that you have or uh you know other other factors organization of material for example. So if you want if

there is a behavior of interest that you want to study and you want to understand in more detail, typically it is a good

idea to uh you know take into account or to basically uh you know create an experiment that allows for not one but

maybe two or three not many at at the same time but maybe one or two or three uh you know variables at the same time

is possible. You can take that you know and the factorial design basically allows you that kind of manipulation. So

let's let's look at this experimental designs with more than one independent variable are known as factorial designs.

Okay. So uh whether it has two factors, three factors, four factors, all of that is uh you know referred to as a

factorial design experiment. The term factor refers to the each of the manipulated independent variables. So

how many factors you know does a study have? Say for example, if you have you know experimental design that has two

independent variables, it will be a two factor study. If it has three independent variables, it is a three

factor study. If it has four independent variables, it is a four factor study and so on. Now, depending upon the number of

uh you know uh factors that these designs have, you can call your design a two-way design or three-way design or a

four-way design and so on. Also, factorial designs are uh you know described with a notation system that

concisely indicates uh how many factors uh you know your experiment has but also how many levels each factor has. For

example, look at this. If you have a if you say that you you come across a 2 +2 design, 2 + two design basically means

because there are two numbers which are crossed here. So it means two variables and because the number is two, it

basically says each variable has uh you know two conditions. So let us say we were talking about uh you know uh in in

earlier uh examples we were talking about laterality or say let's say in this experiment let's say we are talking

about uh you know uh mood state of the individual and the video game that they have watched. So the type of video game

that they have watched is one factor. It has two levels violent video game nonviolent video game and the type of

mood state frustrated not frustrated happy not happy anything like that can be taken. Okay. So 2 +2 basically means

two factors with two levels each. 2 + 3 basically means two factors. One of the factor has two levels and the other

factor has three levels. That is basically how the notivation works. Now the use of more than one independent

variable in a single experiment increases the amount of information that can be gained from uh from your

experiment that can be gained from the experimental design. It is also more economical uh in the sense that

basically you will now need lesser number of participants and you can basically uh get more information about

these variables their causal role in your dependent variable and the possible interaction between these variables. How

do these variables affect each other uh in bringing about the change in your dependent variable in a single in the

same experiment with fewer participants in hand. Obviously you have to take more measurements and so on but we'll talk

about that going forward. So this happens because factorial designs provide all of the information

that would be gained from two separate one-way design experiment. So you can study let's say mood state in a separate

experiment. You can study uh type of violent type of video game watch in a separate experiment. But it al it gives

you that but it also gives you how the mood state will interact with the type of video game that the person has uh

watched or type of video that the person has watched. Factorial designs just like previously one-way designs also begin

with the creation of initial equivalence among the participants across different conditions and these designs help the

researchers draw conclusions about the causal effects of all the independent variables that are involved in the

design. So let's take a simple factorial design to begin with and maybe we can have more

uh in in a you know as we go forward. The simplest factorial design that you can have other than the one-way design

uh which is a separate experiment is a two-way design. So you add just one more independent variable. Now you have a

two-way design. Let's take it with the you know the current example that we have. So our

oneway experiment demonstrated that the children who have viewed violent cartoons subsequently did play more

aggressively than those who had viewed nonviolent cartoons. Now let us say as a researcher we are interested in testing

whether this relationship between viewing of violent versus non-violent cartoons will hold up in all situations

or you know will just be limited to a specific kind of situation. Okay. Say for example you're interested in in this

child who was frustrated when he came to the experiment. You want to test whether this violent uh video watching will add

to the effects of frustration or it will take away from the effects of frustration. What is going to happen?

And so you are now interested in the prior mood state whether the child is frustrated or not and the watching of

the violent video game. So you have two independent variables in play. So the researcher can very simply if if they're

interested in in such a setup they can very easily accomplish such a test by using a two-way factorial design having

two factors to manipulate. The first factor is the same as in the first experiment. So type of vi type of video

watched violent versus nonviolent and the second factor can be the prior state of the participant frustrated versus

non-f frustrated. So you have a 2 +2 design. When you have a 2 +2 design you have four conditions. Okay. So you have

to take care of the fact that the participants are treated to each of the four conditions. We'll talk about that

very shortly. So all of the children in this experiment, what will happen is all of the children are allowed to play with

some relatively uninteresting toys in a play session before they are taken to view the cartoons. However, for half

let's we are seeing how how do we implement this kind of a design. Okay. So now you want to induce frustration in

some way. So what will you do? You'll basically have all of the children, you take them to a playroom and they're

allowed to play with relatively uninteresting, boring, run-of-the-mill toys. Now, half of these children uh in

the frustrated condition, what you do is the experimentter places some really fun, really exciting toys, but disallows

these children to play with those toys. So, that causes a buildup of frustration. Or the other half, these

exciting toys are not even shown. So, they don't know that these toys exist and they will not be frustrated. They

will play with whatever they have. Okay. After this has been done, they will be taken to watch the type of cartoons

violent or nonviolent. And after that has been done, their aggression scores will be measured.

So this is basically the thing. Uh obviously you start with the creation of initially equivalence. Now you have

remember I said 2 + two four conditions. What are the four conditions? Look at it. uh uh prior state frustrated made

them to uh made them watch violent video games. Prior state frustrated made them watch nonviolent video games. Similarly,

prior state non frustrated make them watch uh violent video games. Uh prior state non-f frustrated make them watch

nonviolent video games. So you have four conditions as a result 2 + 2 4. You can see each level of the independent

variable one occurs with each level of the independent variable two. That is why you have four conditions. The

dependent measure dependent variable measurement will go on as it was going on earlier as well. So you add after you

have created these four conditions, you again measure the aggression scores when the children are you know uh in in the

playroom. So in these kinds of factorial designs the conditions are arranged in such a

manner such that each level of each independent variable occurs with each level of the other independent variable.

This is known as the crossing of factors. I just demonstrated the conditions obviously need to be equated

before the manipulations occur. So that's what you saw the creation of initial equivalence at this side and

this is again typically achieved via random assignment of participants to one of the conditions as we have been

talking about. Now the hypothesis in a factorial design experiment has have to make very specific predictions about the

pattern of means or pattern of measurement that is expected to be observed on your dependent measure. You

know your aggression scores. Here for example the researcher predicts that the effect of viewing violent cartoons would

be reversed for the frustrated children. Okay. The assumption is let's say the intuitive assumption is because for

these children the act of watching the violent cartoons will automatically uh act as a you know catharsis or act as a

way of releasing their frustration and thus eventually it will reduce their subsequent aggressive behavior. Okay. So

uh when they are they frustrated and they watch a violent uh uh cartoon this sort of uh you know aggression gets gets

a release and now when they watch uh when they go to play they will be less aggressive. On the other hand when the

non-aggressive children non- frustrated children will watch the violent cartoon their aggression will build up and that

you will see in the overall dependent uh variable measurement. So let's let's word out this hypothesis. Sanger does it

for non- frustrusted children. Those who view the violent cartoons will behave more aggressively than those who view

the nonviolent cartoons. However, for the frustrated children, those who view the violent cartoons will behave less

aggressively than those who view the nonviolent cartoons. So you you can see there's an interaction that has been uh

hypothesized that has been proposed. Now uh when you have this when you have two variables then you want to look at

the main effects of both of the variables. Okay? in in one way designs you look at the mean effect of one

variable and it basically it's a difference of means it tells you yes the experimental manipulation worked or did

not work you can see here on the top we've basically uh you know summarize our predictions so we are basically

saying in the frustrated condition uh people who are who have watched nonviolent videos uh basically will be

uh you know uh watch the nonviolent videos will be more aggressive than those who have watched the violent

videos in the non- frustrated condition people who have watched the violent ent videos will be more aggressive than

those who watch the nonviolent videos. This is the prediction and this is let us say we've done this experiment. Let

us say some data has come up. Now let's look at the data and see whether our hypothesis have sort of worked or not

worked. Okay, you can see here there are basically condition means. So you can see at the bottom there are these means

for the violent condition versus the nonviolent condition and in the sides here in the right side you can see there

is the means of the frustrated condition as well as the non-f frustrated condition. Okay. So these means show the

aggression score for all. So what what did we really measure? What are these means showing? These means are showing

the uh dependent variable measure that we have which is the aggression score. Now when the means are combined across

the levels of another factor in in in this way they are set to collapse across uh you know or uh basically control for

a given factor. Now when you have uh you know made this summation made this mean across frustrated and non- frustrated uh

you know variable for the violent condition you're basically saying across both frustrated and non- frustrated

condition the mean for the violent condition is this. Across frustrated and non- frustrated condition the mean for

the violent condition is this. Similarly across the violent and nonviolent condition the mean for the frustrated

condition in this. Uh across the violent and nonviolent condition the mean for non-f frustrated condition is this. So

basically what we are seeing is these are basically these are referred to as marginal means. Okay. They tell you the

they tell you about the uh effect of one variable across the other variable. Okay. Now difference on the dependent

measure across the levels of any given factor uh collapsing across other factors is called the main effect. So

the difference between these two means will be referred to as the main effect. Okay. So uh we will do some statistics

later but let's say you know in this experiment the difference between two marginal means these ones appears to be

statistically significant. The children who viewed the violent cartoons actually behaved more aggressively than children

who did not view violent cartoons. So you can see here the mean is 4.5 versus 2.71. Uh we'll do the ANOVA later and

we'll show you that 4.5 uh you know here is statistically significant as compared to 2.71. Similarly, if you look at the

frustrated non-f frustrated condition, you can see here uh people in the frustrated condition were less

aggressive overall as compared to people in the non- frustrated condition. But this difference did not come out to be

statistically significant. Now, uh in factorial designs, not only there are main effects, there are also

interaction effects. Say for example uh how does a frustrated uh uh you know child prior frustrated child uh react to

seeing violent video games compared to nonviolent video games? How does a non- frustrust child react to seeing violent

video games versus nonviolent video games? So you have to basically compare the effect of each independent variable

across the effect of other uh you know other independent variable in the two conditions. Okay. So the two main

effects that we have seen uh in the current experiment they provide the researcher with all the information that

would be that would have been available if you do two one-way experiments. You know you do one with frustration uh

change it uh less aggress less frustration no frustration or less frustration high frustration something

like that. In another experiment as we had done earliestly we earlier we saw seeing violent uh video game or seeing a

violent cartoon versus nonviolent cartoon. The uh benefit of doing a factorial design experiment is basically

that now you can actually see the interaction between these two conditions. Okay. So uh the two main

effects uh will obviously as I said will test the influence of each of the independent variables. But uh in

factorial designs we measure the interaction as well. What is an interaction? An interaction is a pattern

of means that occurs in a factorial design when the influence of one independent variable on the dependent

variable is different for the different levels. Okay. So when watching violent video game affects the frustrated and

non- frustrated uh child differently on the other hand when uh you know uh the effect of say for example frustration

I mean you can word it differently in the same way it's a 2 +2 balance design. You can basically say the effect of

frustration on watching violent nonviolent video game sort of effects uh you know in in there. Now when we are

looking at these simple effects when we are basically looking at our hypothesis the effect of one factor over the level

of another factor is called a simple effect. There are main effects uh that are inferred through the marginal means

here uh when you are comparing the marginal means and there are simple effects when you are comparing uh you

know uh across different factors. So if you compare 2.68 with 5.62 or 3.25 with 2.17 we'll talk about this very shortly.

Now now uh the observed means in the four conditions in our experiment actually uh

show that there is indeed an interaction and the frustrate uh you know between the type of cartoons watched and the

factor of prior state. So frustration or non- frustration. Let us zoom in a little bit for the children who had not

been frustrated. Look at this one. And for the children who had not been frustrated uh basically you can see that

uh you know they showed more aggression uh when they viewed violent cartoons as opposed to when they viewed nonviolent

cartoons. You can see 5.62 is being compared to 2.17. So this is non- frustrated condition. Both of these are

non- frustrated. They when they watch violent cartoons show more aggression and these guys when they uh see

nonviolent cartoons show less aggression. Okay. Now this reverses for the children who have been frustrated uh

prior to the experiment. Here you can see for the frustrated children those who had viewed violent cartoons behaved

less aggressively as compared to those who had viewed nonviolent cartoons. So you can see here it is 2.68 versus 3.25.

children who are watching nonviolent cartoons in the frustrated condition are showing more aggression.

Now uh obviously as I said we will compare uh you know we'll carry out ANOVA you basically look at the main

effects of uh you look at the main effects here this is the ANOVA table you look at the main effects of the two

factors cartoon viewed prior state you also look at the interaction so these two are your dependent variables and the

dependent variable is by the way uh aggressively these two are your independent variables. Now you can see

here uh each of these have their own uh f values they have their own degree of freedom they have significance. So you

can see here very quickly cartoon viewed is uh showing a significant effect prior to it is not showing a significant

effect but the interaction is significant. You can visualize this also in terms of these bar charts. You can

see in the non-f frustrated condition people who are uh you know watching uh in a non-f frustrated condition people

who are watching violent video games show are showing more aggression as compared to people who are watching

nonviolent video games. And this effect reverses when you are looking at frustrated condition. People who are

watching nonviolent uh uh video games are more aggressive than people who are watching uh violent video games. So this

is basically what has happened. All right. Now so in the current experiment uh the main effect of cartoon

viewed is significant whereas the main effect of prior state is not. The interaction is also found significant

here. Now having done this analysis, it is also possible to compute say for example the effect sizes of each of the

main effects and the interactions which will basically tell you how big or how strong is the relationship between the

uh you know levels of the dependent and the independent variable. Now let us move on. Let us try and study

interactions. What kind of because there are two variables you can study interactions. You can see how are the

two variables interacting with with each other. Let us try that. As there are many conditions in a factorial design

experiment, it might be beneficial uh you know to visualize the relationships between uh the variables using line

charts. You can see here these are the points uh which basically uh you know are means of violent versus uh violent

condition. So this is violent condition uh frustrated versus non-f frustrated. This is nonviolent condition, frustrated

versus non- frustrated. And you've basically joined them. So uh one has become uh you know uh solid line which

is the frustrated condition. One has become the dash line which is the non- frustrated condition. Towards the you

know uh zero level it is on the on the x-axis one side towards the left is the violent condition. The other side is the

nonviolent condition. Now these lines here are basically telling us what kind of interactions are being observed.

Okay. So let's let's look at this. We know that there is a possibility there is a main effect. We have seen of you

know watching violent video games there is the main effect of prior state is not uh significant and in some cases we see

that there is there seems to be an interaction here and in some cases not. So we will go out and we will basically

measure each of or we will try and interpret these interactions in a uh way.

Now in the figures we can see that some of the many possible there are obviously different interactions possible. We see

how this is happening. A main effect of the cartoon variable is uh you know cartoon is present when the average

height so you can see here when the average height of these two points is higher than the average height of these

two points when uh in the violent condition the you know the score on aggression is higher as compared to in

the nonviolent condition. It is here also. It is here also. Uh here it is not there. Here also it is sort of uh you

know a main effect of frustration but not of uh you know that. So you can see in conditions where the mean height of

the points in the violent condition are higher than the mean height of the points in the nonviolent condition. We

can infer that there is a main effect of the cartoon variable. What kind of cartoon these kids have watched?

a main effect of the prior state variable is present when the average height of the line the overall you know

solid line versus the dashed line is uh greater than the uh average height of the fr n n n n n n n n n n n n n n n n n

n n non- frustrated line. So here you can see for example in a there is a main effect of you know uh actually there's

there's not effect in that sense if if it were greater or higher if or less than you would see

that there is that effect. So an interaction is present when the two lines are not parallel when they are you

know intersecting or not parallel with each other. It basically tells us that there is a simple effect of watching

cartoons is different in the frustration condition and uh you know as compared to the non- frustrated condition. Now we'll

go on and basically infer each of these uh you know plots. So look at this in figure uh 11.5A there

is only a main effect of the cartoon variable but there is no interaction. the lines are parallel to each other. As

a result, we can see that the proposed research hypothesis in our current experiment is proven to be incorrect.

The children actually showed more aggression irrespective of the frustration or non- frustrust condition.

In 11.5b here, a main effect of prior state is only observed because there is uh you know a lot of difference. A main

effect of prior state is only observed showing that the frustrated children were more aggressive than the non-f

frustrated children. All right. So that is what I was saying. Uh in in A and B and C you can see that there are main

effect of frustration available in 11.5 C. There are both uh main effects. There is the main effect of

violence condition as well as the main effect of the frustration condition. Now let's look at the other three.

There are uh you know where where there are main effects as well as interaction effects. So we can see in 11.5D this one

we there is basically an interaction because the lines are not parallel to each other and they will intersect at

some point. If you look closely you find that the interaction is not exactly as the research hypothesis that we started

with predicts. Only part of this research hypothesis seems to be confirmed. Okay. What is it that we are

finding uh is basically what we are finding is that the viewing of violent cartoons did increase aggression for the

children in the non frustrated condition. You can see that the means are different in the non- frustrated

condition in this dashed line, but they're not affecting the uh aggression levels of the frustrated children. So

there is a main effect. There is I mean we've talked about the main effects. There is an interaction here, but the

interaction is partially affecting only people who are in the non- frustrated condition but not really having an

effect on the participants who are in the frustrated condition. So here you can see that there is a main effect of

the uh prior state variable that is also significant. the solid line is higher than the dashed line. Okay.

Now pattern with main effects and interaction. So we are going to uh talk about these three uh these two figures E

and F. In E you see that the you know it shows basically the pattern that was originally predicted by our research

hypothesis. In this case we see that you know there is a crossover interaction. There is the effect of the simple effect

in one level of the second variable is actually opposite. It's not just different but it is opposite uh from the

simple effect of the other level. So effect of watching violent video games is opposite to the effect of watching is

opposite to the effect of prior state frustration or not frustration. Okay. Uh this is by the way termed as a crossover

interaction. But in F if you see the slightly uh the actual pattern is observed. Let us see what is there. Here

the research hypothesis is supported because the predicted crossover interaction is observed but there's also

an unanticipated main effect of the cartoon factor. Uh that is the mean in the violent cartoon condition. The mean

in the violent cartoon condition here is uh you know slightly uh higher than the mean in the nonviolent cartoon

condition. So when you uh collapse across these two versus these two, you basically find that there is a main

effect of the cartoon factor as well. Okay. So I hope uh you know you were able to visualize and sort of make sense

of how these interactions occur. All right. So I'll stop here. We will continue our discussion with factorial

designs in the next lecture. Thank you.