Fundamentals of Experimental Design in Cognitive Psychology Explained

Hello and welcome to the course basics of experiment design for cognitive psychology. I'm Dr. Arkwarma from the

department of cognitive science at ID Kpur. As you know this is the third week and we're talking about uh you know

experimental designs. In this lecture what I will do is I'll take you through the mechanics of experimental design.

Remember in the previous class we adopted a modeling approach which was uh basically proposed by uh Cunningham and

Wal Raven in their book. Uh we sort of going with that uh model and we are trying to understand some of the

fundamental principles in experimental design. Okay. So let's revisit that. The idea was that a model of human behavior

or say for example whatever cognitive function you want to uh study. Let's say you want to study word recognition or

let's say you want to study say for example contrast perception or size perception or orientation perception

anything for that matter uh which are typical subjects of experimental psychological studies uh we basically

have the model M of X is equals to B of X plus EW. Now just to revisit this M of X is the measurement in a measurement

term in a given experiment. It has all the information that there is one trial, single participant, what are the

conditions? Uh what kind of situations are there and everything uh condensed together in this one variable. This is

the measure that you're getting in one uh you know uh trial. What is B of X? B of X is whatever mental functions

perception plus action. Whatever mental functions are sort of involved in producing this measurement. So basically

what is this measurement measuring? This measurement term is measuring the mental functions that are going on inside the

person's uh brain to lead to the given response. All right. So B of X. So that is basically uh and we'll use this term

again and again. This is referred to as the perception action loop. All right. Now you'll see that there is also this

error term in there. What is this error term? Error term basically or error w this one here. This error term is

basically uh you know the error in this uh you know that error that is combined with this perception action loop which

the measurement also uh gets. The idea is that this measurement does not always get the exact uh you know representation

of the perception action loop. There is always some error. Uh what is the source of this error? This could be just random

background neurons firing uh some kind of environmental variables, some kind of subject related variables that are

creating slight variation. Remember we are talking about uh the pointing example that if I want to point at a

specific place in my hand and I'm making this action again and again. Uh it is not you know guaranteed that I will

reach or touch the exact same point and on the hand at every trial. If I want to ensure that then I'll probably need to

uh you know uh be very slow and very conscious in making that uh action movement. So the thing is every time you

do a behavior every time say for example you are let's say you're doing a word recognition experiment. Typical word

recognition experiment is like there is a blank screen there's a fixation cross there's a word you have to tell whether

this is a meaningful word or not. Now uh every time you are making that same decision about different kinds of words.

There are word level characteristics and there are participant level characteristics that will lead the

reaction time to be slightly different every time. Okay. Even if it is the same word that is presented let's say on

trial number 10 and 15 and 20 and 25. Uh you will see that the reaction time might be slightly different. It is not

going to be identical. Let us say 552 second 552 millconds. It'll be probably 552 mconds on one trial. on another

trial it might be 500 milliseconds or another trial it might be 600 milliseconds. All right. So that is

basically what this error term is. Now what are we conducting this experiment for? Just let's uh revisit that we are

conducting this experiment to get a good estimate of the mental processes or the cognitive functions that are involved in

a particular uh decision. So whatever task we're doing. So uh let's say we are doing a reaction time uh experiment to

uh you know a lexical decision reaction time experiment. So m of x is basically the reaction time the measure which is

seemingly capturing what is happening inside behind this response. So the process of flexical access plus let's

say some error. All right. So let's let's go forward and see uh you know how this uh pans out. One of the things that

we basically uh do in experimental design is basically we need to take a number of measures. It's not for the

most part there are no single trial studies. There are single trial studies where you have too many participants you

can have a single trial study. Typically you have few participants and a lot of trials. Why do we need so many trials?

Why do we need say for example for a single measure let's say even if I have a single word to which I want to know

your response whether it is a word or an on word. Why do I need let's say five measurements for it or one measure or

you know 50 measurements for it? Let's try and understand that. So the method for isolating B of X as we've just said

derives from the observation that while this error term EW is different every time uh we measure it our underlying

perception action loop this B of X is constant. So the brain is actually following the same process to arrive at

the decision whether a particular stimulus is a word or non-word. The error term might vary and that is what

is basically creating the uh you know disparity between your responses. So 552, 6002, 752 or even 452 millconds

that error term is changing across every trial and that is what is causing the change in your reaction time. All right.

So this is the fundamental assumption in this research. uh although if you remember uh you know in in one of the

courses I've talked about the central identity theory the type and the token identity theories and so on where people

have argued that is it exactly the same set of mental processes is it is does the brain follow the exact same

algorithm every time it makes a similar decision again that's a debate for another day but let's say that is the

assumption with which we are conducting these reaction time studies also one of the things is that behavior

does change over time so for example on the first trial trial versus on the 50th trial versus on the 100 trial or the 500

trial in the same lexical decision task. Uh I am getting some practice with this. I'm getting uh basically some kind of

learning that okay uh how do I decide whether this is a word or not. Maybe I'm making a strategy. Maybe I'm sort of

just uh referring to the sound whether it is familiar or not. Whether I'm basically just going to oh I know this

word or not. As a participant I can be using any number of strategies. All right. But my strategies will get better

over time and that is why in large scale lexical decision studies you see that there are block effects uh you know

typically participants will start somewhere around 600 700 millconds by the time they sort of are at the 10th

block 50th block 100 block it sort of reduces by around 10 to 15 20%. Okay. So there is effect of learning, there is

effect of practice that is there on behavior. Uh and that is all right. I think uh the mental representations get

sharpened. The response, perception, action loop gets sharpened. All of that happens.

Okay. But the evidence uh of uh you know from current research basically suggests that B of X this perception action loop

broadly remains constant. So the source of this variation or whatever learning uh we are getting uh it does not

drastically change or reorganize the perception action loop. So mx is equals to bx plus ew. This bx for the most part

remains pretty much constant. That's basically why we conduct these experiments hoping that in every

reaction time uh we are actually you know uh indexing that same mental process lexical axis let's say. All

right. So uh evidence suggests that B of X will stay mostly constant over short periods of time. uh which is why it is

suggested to carry out the experiments uh with a limited period of huh so again the practice effects that I was talking

about uh while there is yes there is evidence of the fact that b of x remains typically constant for uh periods of

time but uh if this practice effect if the session is too long if it's something that you're doing for several

hours at once and you're doing it for every day let's say you're learning to play guitar and you're learning to uh

you know you're having your guitar classes 1 hour for every day for continuous uh 30 days or 60 days or 90

days. Now your performance and the mental circuitry that is uh leading to that performance uh from the first day

to the 90th day might change a little bit. In that sense uh that is basically why it is suggested that when you're

doing these experiments don't have too long experiment there are effects of fatigue etc that come in but practice

effects over long periods of time are certainly uh to be avoided and that is why within 1 to two hours this B of X is

least changed and that seems to be the best time to conduct this experiment within all right so this is this is

something that we have this idea of Now error in pointing we let's you remember the pointing experiment we are talking

about. So the pointing experiment is that there is this bullseye and we have asked our participant to come and touch

at the center of the bullseye. The participant has come and touch at the center of the bullseye. On trial one he

was off by 1 mm. In trial two uh he was closer. In trial three suddenly he was off by 5 mm. So we are conducting this

over a number of trials. The idea is that this measure how far off the our participant is from the bullseye that m

that is the me that is the dependent variable that we are saying and that is basically coming out indexing your

mental process plus this error term. So this error can be uh different uh it can be different on every trial say for

example in sometimes it'll be to the left of the intended uh uh midpoint sometimes will be to the right to the

intended midpoint. there is no if there is no constant pattern uh in this error that constantly it is offset by 10 mm to

the left there's nothing to worry about it'll probably you know average out over a number of trials so averaging over

several measurements will typically give us a decent uh estimate of what b of x is all about okay that is by the way why

we were conducting this experiment in the first place okay so just look at this set of equations here if we repeat

this experiment exactly conditions etc being identical over a short period of time then the average pointing accuracy

will give us a good estimate of the underlying pointing ability the underlying mental abilities cognitive

functions that lead to this particular pointing ability. All right. So the same if you want to state it in form of an

equation this basically what these guys have done. So m1x is equals to bx plus ew1. So this is the first error term.

second error term you summit it over a number of trials you get a decent estimate of you know m of x becomes

almost you know equivalent to the uh the b of x because this error term sort of cancels out over time the more

measurements you take the smaller the error term will tend to become it's getting averaged over time sometimes to

the left sometime in plus sometime in minus and so on now when we have multiple measurements

of multiple trials of this particular term. So M of I given a given a situation X and this X remains constant

across different measurements. Understand this this one very important thing that these measurements will all

not be identical. Okay. And while we've previously previously stated you know we've defined the output uh of B to a

constant let's say there's a constant situation the trial is similar the uh all the other conditions are similar. So

any differences that happen uh across measurements are basically due to variations in this error term. Again

something that I was already saying. Now as mentioned it is very unlikely that this error term will become zero at any

point in time. It will not become zero. It will reduce to a certain negligible thing. Okay. So with two measurements

let's say you have two trials. Trial number one and trial number 20. With two measurements it is more likely that the

average will be close to zero. But this is again still very improbable. it will reduce. If B of X is actually constant

and the situation X is absolutely identical then this variance will be small and then the two measurements

might be enough to isolate the actual mental process that we are after. So that's that basically the idea in these

repeated measurements. Okay. However, you have to understand that it will be extremely difficult to ensure that X is

absolutely identical across trials. What is this X? remember single trial whatever the conditions are whatever the

participants mental state is whatever the uh stimulus etc mental stimulus and other uh you know environmental things

are so obviously there will be some random variations at both ends so it'll be difficult to make it absolutely

identical firstly and there are several reasons of it there are two of which we can point out for example the mere

passage of time between the two trials may mean that the physiological state of the participant will be different okay

when he came he was thinking think about something else. After one or two trials, he's now thinking about something else.

When he came, he was not ready to do the trial. Now he's already motivated. Something has happened. Across trials

also the participant is getting probably more engaged in the task. So they are slightly more alert, slightly more

anticipating and that reaction time is reducing or maybe the task is boring. Towards the end again the participant is

getting fatigued or bored and the reaction times are again increasing. So across measurements it is important to

understand that these things will not be identical. passage of time conditions change that happens. Second is first

trial can essentially be seen as an opportunity to practice this task. So you are going to get slightly better

there will be practice effects there will be order effects. Okay. So uh typically what is done is if I remember

correctly uh a lot of times uh you know when when experiments have a large number of trials it is always a good

idea to basically look how the participants responses have changed over time across trials. So uh something that

used to do uh uh you know a lot is basically you can calculate the split half reliability uh let's say there are

100 trials first 50 last 50 basically uh calculate the correlations so that the responses are not too different from

each other and therefore that's how you can take the overall average and work with that. All right. Now all in all

what really is going to happen is that more measurements will mean a greater likelihood that the error term will be

small negligible and in some sense factor itself out of the equation. Your measure becomes closest to this

perception action loop that you are trying to anyways estimate. All right. And this is basically very common in uh

you know classical psychopysics experiments where tens of thousands of measurements are taken for each

condition and each participant. All right. But in typical experimental psychological studies if you see that

number of trials is is not too many. It's around 20 40 sometimes 60 uh trials per condition. And that's that's broadly

assumed enough. So I I did a lot of literality experiments during my PhD. And the largest number of trials per

condition I had and there were eight conditions. So it is a longish experiment was around 60 trials per

condition. Probably in one experiment I had 80 but 40 to 60 80 is is broadly uh enough. And uh there is something that

also uh you know is important is the effect size. when the effect sizes are large, say for example, when you're

looking for left hemispheric lateralization of uh word processing, then the effect size is typically larger

and then you will need fewer trials to you know get closest to that BFX that you're after. But in cases say for

example when you're looking for symmetry judgment or you're looking for some kind of uh you know right hemisphere task

where you're looking for overall contour judgment things like that where the effect sizes are relatively smaller

compared to uh you know uh left hemispheric uh littleization for words uh then you will probably need a

slightly larger number of trials. There are obviously statistical calculations that allow us that help us to do this

but we'll talk about them as we go forward. Now we talked about multiple

measurements. Why did we take multiple measurements? But al we also do we also use multiple participants in our

experiments. Why do we need multiple participants? Let's talk about this. So given that if we have multiple

measurements, we can sort of make reliably definitive claims about the specific situation X uh that we are

measuring and a natural part of the measured situation is your participant. So are there error? Is there error

because of the participant participant level characteristics? If you have 1 2 3 4 five participants, each of these five

participants are not going to be exactly identical to each other. Okay? On papers may be the same age, same gender, same

educational qualification, same SCS. Yes. But individuals, they are different people. And because they are different

people, the effect that they will have on the error term is going to be different in your experiments. All

right? So uh if you measure only one person we can talk about only that person's results and that person's uh

perception action loop that B of X that we are talking about but we do measure many people and how is that justified so

uh we have no idea you know within this you remember the specificity versus generality example we have no

information about how other people would perform maybe they will perform in the same manner maybe they'll perform very

differently maybe they'll have other strategies uh and uh you know other personal level factors that will play a

part. So how do we get uh you know around this in our experiments? So measuring more than one person will

typically yield more than one measurement. So you'll have let's say m of x1 and m of x2 something like that.

So it should be possible to basically use these multiple measurements like uh you know rather than repeated

measurements of an identical situation to isolate B of X. What are we after this mental state B of X and we want

multiple measurements across number of people not multiple measurements within. So we're not talking about repeated

measures at this point. We're talking about multiple measurements across different people. Now if this B of X

this mental uh thing this let's say lexical access for word recognition is identical for all people then measuring

one person many times or many people one time is basically the same method because the mental function is pretty

much the same and it is in that sense you can use either of the two. Unfortunately we know that uh you know

in almost no real world case is be of perfectly identical across people. you know people have different experiences,

different uh strategies in which they will do the task uh different uh uh skill sets phenomenal uh things and so

on. So B of X is not is never perfectly identical across people. Okay. So what we do is we can assume that B of X

contains you know some element that is constant across all people and some element that varies across people. Okay.

So in other words what we can do is that we can assume that there is a constant population level perception action loop

and there is a individual level perception action loop. So generally one person's way of uh accessing the

semantic network uh to perform lexical access is this individual strategy and it is obviously if you uh have read

research by Quinnland Quinnland and D uh and some of these Collins and Quillin and those kinds of papers you know that

uh you know semantic networks are basically uh you know affected by personal experiences. So uh one person's

route of reaching a given word may not be obviously identical to other person's root of giving uh you know reaching a

word but across the population there can be a position level perception action loop population level uh mental function

that is basically leading to this successful lexical access and then obviously there are individual level uh

uh processes for lexical access. This is this would be similar to the assumption made for m of x where each

person has an underlying perception action loop and each measurement is a slight deviation from it. So uh m of x

is equals to b of x plus there is a person level error term because that is the one that will be different across

each individual. Okay. So how do we model it? We can model it in two ways. We can basically

look at two kinds of error terms here. The first error term is this original error term ew. This is called the within

participant error term. So within participant uh if uh you compare measurements trial one, trial two, trial

three, trial four and so on, there will be some variation in this error term and that is called EW or within participant

error term. Now obviously we have multiple participants for our experiments that can be introduced by

this error term EB which is this between participant error term. between participant error is broadly difference

in characteristics which are leading to difference in this error term across different individuals. That's broadly.

So now your m of x is equals to uh just look at this m of x is equals to b of x plus these two error terms. Okay. So we

are basically making this assumption rather explicit that there are these two error terms that are independent of each

other and can be linearly combined. You are basically not saying that they are interacting or something. We are saying

one is within participant error, one is between participant error and you can basically combine them to get a overall

idea of how much error there is going to be uh in your measurement m of x. Okay. So uh this new error term will affect

the number of measurements that we will need just as this within participant error term did. Also the larger this

between participant uh noise or error will be the more samples we will need to be sure to have the best approximation

of B of X. Okay. So that's broadly how we we talk about this. So you have M of X is equals to B of X plus E W plus uh

EB and you'll need several measurements to uh you know reduce this EB to a smaller more negligible thing. And if

you have enough measurements across enough number of participants, the assumption will be that this M of X will

be very close to B of X. And the EW and the EB error within participants and error across participants will both be

uh sort of uh you know uh neutralized, minimized and sort of rendered out of the equation. All right. Now, uh how do

we know how many participants or what can be used to decide this? There are obviously uh power calculations and

other statistical methods. But what is the concept behind this? Okay, one of the things that people have used a lot

is uh you know historically they look at the literature, they look at the number of similar studies and they use that to

guide uh oneself to the ideal number of participants. More recently however people do uh you know uh best power

calculations and power calculations give you on the basis of effect sizes and confidence intervals the exact number of

participants you need for a given experiment. Okay. uh let's try and understand that conceptually a little

bit although so in many low-level perceptual processes uh basically say for example you want to detect the

processing of line orientation detection of motion detection of contrast those kind of things uh the between

participant error uh variance is found to be very very small it's typically very small uh so as long as we are sure

that we have a good estimate on the uh you know for each specific person you know between within subject error is

less basically by running several trials for one given person, then even a small sample size of four to five people would

be sufficient to yield a reliable estimate of this entire population level perception action loop or this

population level B of X. On the other hand, when you're talking about higher level uh processes that are sort of

affected by individual experiences uh let's say such as the ability to solve math problems, this E of B can actually

be quite large. Okay. Okay. And because it is quite large, you will need more power. You will need many more

participants to be to get closer to this B of X that you want. So as more variance is expected, many more

participants shall be required. As effect sizes are smaller, many more participants are going to be required.

Now this is one of the reasons why uh you know for which many cognitive psychology experiments have hundreds of

participants. Sometimes literality experiments you see that have many participants. Okay. typically and

especially if you're doing right hemisphere functions there are larger number of participants that you need not

few participants will not do because the effect sizes you're typically hunting for are very small and previous studies

will tell you look for this effect size these confidence intervals and nowadays we use GP power it tells you that oh a

large number of sample size is needed also the number of conditions that you need if you have four conditions you

will need adequate number of measurements for each condition that sort of multiplies and basically

increases the amount of partic participants you need. So if we further assume that within this coming back to

this uh if you further assume that the within participant variance EW is similar for all people we can use a

large number of people just with one trial per person in order to estimate the underlying perception action loop

for all people. So that's also one of these ways that you can follow. See again remember the the trade-off is

between number of participants or number of measurements per participant. That's broadly a rule of thumb that one can

follow. Now also it is important to uh note that in some cases the variance between participants EB can be extremely

large which would tend to make it harder for experimenters to precisely measure the effect in which they are interested.

So that basically confounds this a little bit. All right. For instance, it might be the case that the population

has a biodal distribution. That is there are two distinct subpopuls. one of which is very accurate and the other is not.

It'll be helpful then to have an idea of the source of variation. Okay. So what can happen is that uh you have one set

of population extremely proficient, extremely good at the task and they get this done very quickly. Okay. So uh if

we further assume that the within participant error uh term is similar for all people then basically what we can do

is we can use uh you know a large number of people with just one measurement each and that works. Uh but in some cases

this e uh you know this EB this error between participants is quite large and given that it is quite large what will

uh what will happen is that it will become harder for experiments to precisely measure the effect in which

they are interested. Okay. Sometimes you can have very different populations. Say you are doing a language proficiency

task or you're doing a lexical decision task or you're doing a language switching task. Uh you'll get extremely

proficient participants who are very good in uh uh the given language let's say English or Hindi. Uh and you'll get

some participants who are not as good at say for example you're doing an English word who are not as good at that. So

you'll get almost two different distributions. What the idea here is that if you get to the source of the

variation, you can try to control for it. Suppose uh you know in in language switching experiments people get to uh

see that okay the exposure is is the issue the exposure to the second language is the issue. Once they figure

it out, they control and match for the amount of exposure of uh the language that is there and that basically allows

them uh to uh you know uh control for this between uh participants error and keep the sample sizes to uh you know

tractable distance. All right. Now the final thing that we can talk about here is so we've talked about repeated

measures, we've talked about across participants, we should also talk a little bit about different conditions.

You know I was just telling you about literality experiments. There are sometimes around four to eight

conditions in these experiments. And uh across condition also there will be some error. So let's see how this uh you know

it it works out. In order to average the number of measurements this m of that we were talking about to approximate this

perception action loop. Every aspect of the situation this x must be identical across samples. Okay. Any difference

from one trial to another will add to the noise. So this random variation from bx this some error term will get added.

For instance, changing the participant from one measurement to the next also alters the situation. Adding this

variance caused by this change of participant as an explicit term EB shall also allow us uh you know to uh isolate

uh this b of x very quickly. Now if we go with this assumption that all other possible changes are also independent of

each other and can be weighted linearly uh you know and added together then what we can do is we can also have an error

term with respect to the different conditions that are there in the experiment. Remember I was saying if we

have more conditions even more measurements are required. All right. So if we go with the assumption that all

other possible changes across conditions uh across participants and so on all other changes are also independent of

each other and can be combined weighted linearly then basically what we can do is we can add this other uh error term

uh across with this measurements and basically uh you know uh work with that. So we can basically uh add more

measurements for this uh condition term as well. So the idea is that your equation will now become m of x is

equals to b of x. You have error between participants, error within participants and error for each condition. So the

number of conditions you have, you will also be adding to the error. But again what you can do is you can keep on

adding the measurements to reduce this error term as well which will get you eventually closer to the B of X that you

are after. Okay. So with reference to the pointing example remember we had this bullseye where the participant is

coming and touching the center of the uh of the target. So with reference to this pointing example we can say that let's

say contrast is different from uh you know one trial to the other. In one trial there is 100% contrast on the

other trial there's a 50% contrast. Now this change of contrast in trial number one and trial number two will cause some

change some additional error uh will be caused and let's say that error is basically represented in this E of C you

know this last the third error term that we have in this equation. Now if we know that a small contrast change does not

really affect performance and it does not cause any additional error. the changes are all small then this contrast

will not really need to show up as an error term here because we know that it is equivalent to zero and it'll go away.

But sometimes what will happen is that we'll need to explicitly control for it because we know that it is going to

cause a difference in the reaction times or difference in the overall performance.

So we will need at least two measurements. Let's say one with a high contrast target M of X and one with a

lower contrast target M of X plus let's say this delta C there's a and this delta is basically the difference

between contrast on first target and contrast on second target. In this case what we will what we end up doing is we

are explicitly varying our stimula along a given dimension and basically what we are doing is we are getting the effect

on B of X of this variance in dimension. Let us say we are talking about word recognition. I was talking about lexical

decision task. Now in this lexical decision task, my words are varying on this dimension of frequency. Some words

have a frequency of 10,000 per million. Some words have a frequency of one lakh per million and some have a frequency of

let's say 100 per million. So I have three levels. Now the thing is in the three trials where these three things

are coming I will need to uh what I'm doing is I'm basically creating frequency as a factor very low frequency

low frequency and high frequency. This different levels of a given dimension are called levels. Factor is frequency.

What is the factor? Factor is frequency. Factor has three levels. Very low frequency, low frequency and high

frequency. In the contrast example what we have? We have the factor is contrast. uh there are two levels low contrast

high contrast. So we have now basically error coming out of these two. This difference in contrast between the two

is probably also creating some difference in the reaction time pattern, some difference in the mental process

that are going on which we are also interested in finding out and measuring and basically this is the one what is

referred to as the variation of or variance in independent v uh variable. Okay. So because it is the uh you know

the only thing that determines the levels of a given factor is the experimentter and because they are

independent of this actual experiment that is why they are referred to as the independent variable. Remember we've

have several other variations of this also. Why is an independent variable called an independent variable? Because

it is independent of the experiment but in control of the experimentter who sort of can vary it independently of

everything else. Okay, remember the underlying assumption in experimental psychology is that the independent

variables are also independent of each other and can be weight as a weighted linear sum. We'll talk about this when

we talk about you know interactions and stuff. Now complete combination of factors uh and levels for any single

trial can be referred to as a condition. So what is a condition? Condition is a high frequency uh condition, low

frequency uh condition. So we can have different things. If there are two factors with two levels each typically

what we will have is 2 +2 we have four uh conditions. Okay let's say uh I was looking at the I want to look at the

lateralization of tools. Now I have two kinds of stimula tools non-tools. How will I test lateralization? I will use

lateralized presentation to the left visual field and to the right visual field. So one factor is uh stimulus it

has two levels tools non-tools. Another factor is visual field. It has two uh levels left visual field, right visual

field. 2 +2 we have now four conditions. Each of these conditions will have their own error term. And we will need an

adequate number of measurements in each of these conditions to basically get closer to the B of X that we want. All

right. So some changes across conditions will be trivial and will not affect our measurement. and to determine the

question of which changes will be important and which are not. That's basically what we try and handle in

experiment design. Okay. Now our a priority hunches about what changes will affect our experiment will not always be

accurate and hence without knowing beforehand which factor will play a role and which will not. The best strategy is

to make all trials as identical as possible along all dimensions. Even things like apparatus, room in which the

experiment is being conducted, noise levels etc. So you don't measure different conditions in and different uh

conditions here. These you know these four conditions you don't measure them differently. You measure them within the

same experiment with all things being equal. Only the thing that is different is say for example uh tool versus

non-tool tool in left hemisphere tool in left visual field right visual field non-tool in left visual field right

visual field. So what we try and do is that the only difference will be the one that you are actually varying all the

other things are to be kept equal. Okay. So let's let's look at this in terms of this uh pointing experiment. So going

back to this pointing experiment that we started with pointing to a high or a low contrast target. We have one factor with

two levels. What is the factor? The factor is contrast. What are the levels? High and low. Note that the two

conditions are broadly identical with the sole exception of the fact that just the contrast is different. This

difference can be represented by saying that one of these conditions is a baseline and the other is the

experimental condition. So let's say we say uh 100% contrast is the baseline condition and 50% contrast is the

experimental condition. We are studying the effect of lowering contrast levels that can be done. Okay. So equation wise

just to sort of make uh you know sense of this in the model that we're talking about MX is equals to BX plus error

within participant error between participant. Now we uh what we do is both sides we have a delta C the error

because of condition and this side also we have error because of condition. Now what we have uh you know this whole

equation if you take the difference between first and three what you basically get is you can get closer to

the effect of condition effect of contrast change in this specific example which is your B of

delta C. What is basically happening in the brain in the mind whatever you want to use with respect to this conditional

change and this is what uh we are after in experiments. So error between participant yes error within participant

yes but what are you after when you are having these multiple conditions you are looking at the effect of the condition

on the mental process that is what B of delta C is all right so you basically that's basically what we are after now

how much of this effect say for example when you go from 50% contrast to 100% contrast how much change happens let's

say the reaction time changes by 50 millconds or 100 milliseconds remember Sternber's example of search uh you know

thing every single term that you are adding in memory it was basically leading to 40 millisecond uh increase in

the reaction time. All right. So this uh you know this difference in conditions that is happening in the

uh brain or the mind is basically referred to as effect. That is the very broad slightly loose definition. When

there's a large effect it would basically refer to a large difference in performance between the two conditions.

Say for example difference between word and a non-word. So status if wordness wordness is the factor then word and

non-word reaction times are very different the reaction times are faster for words how much faster is your effect

size. Okay. However if B delta C is large then it will be easier to detect. If it is small it'll be difficult to

detect and you'll need more measurements. That's what we were talking about. So a large value of this

B delta C can be detected even with an imprecise uh you know estimate of the error terms EW and EB and small effect

sizes will basically get masked by large error terms. So basically when you're looking for small effect sizes you want

the error terms to be even more negligible and minimal and that is what will make you have more and more

measurements. Okay. So conceptually obviously a lot of us as uh you know a lot of people as students will just

enter uh you know what is the effect size you're looking for confidence etc in the g power thing and get your values

out but this is the conceptual uh you know uh underlying principle that why do you need the error terms to be small why

do you need uh you know the effect size to be large that is basically what we are trying to talk about so this is

broad idea of how and what are the fundamental principles in experimental design within in a modeling perspective.

We will talk about uh uh you know we'll extend this example to uh other uh uh domains in the next lecture. Thank you.