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Between and Within Treatment Variability

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Roadmap 0:06
    • Roadmap
  • Experimental Designs 0:51
    • Experimental Designs: Manipulation & Control
  • Two Types of Variability 2:09
    • Between Treatment Variability
    • Within Treatment Variability
  • Updated Goal of Experimental Design 5:47
    • Updated Goal of Experimental Design
  • Example: Drugs and Driving 6:56
    • Example: Drugs and Driving
  • Different Types of Random Assignment 11:27
    • All Experiments
    • Completely Random Design
    • Randomized Block Design
  • Randomized Block Design 15:48
    • Matched Pairs Design
    • Repeated Measures Design
  • Between-subject Variable vs. Within-subject Variable 22:43
    • Completely Randomized Design
    • Repeated Measures Design
  • Example 1: Design a Completely Random, Matched Pair, and Repeated Measures Experiment 26:16
  • Example 2: Block Design 31:41
  • Example 3: Completely Randomized Designs 35:11
  • Example 4: Completely Random, Matched Pairs, or Repeated Measures Experiments? 39:01

Transcription: Between and Within Treatment Variability

Hi and welcome to 0000

Today we are going to be talking about between and within treatment variability. 0002

Here is how we are going to do this.0006

First we are going to talk about all experiments have in common, just recap and then we are going to talk about 2 types of variability within experiments.0010

That is going to be between treatment variability and within treatment variability.0020

Then we are going to reframe the goal of all experiments in terms of variability.0025

We are going to talk about different types of random assignment or different types of control and that will help us control certain kind of variability.0031

Those three different kinds of random assignment IV are completely randomized design, matched pairs design, and repeated measures design.0041

Okay the first thing about experimental designs is that all of them have two things in common. 0051

One is that they have manipulation and control of the treatment variable or we call the IV or the independent variable. 0058

They all have that in common. 0072

Now concretely what that really translates to is that each experimental unit, whatever that unit is, would be a rat or cell or a CD or states or a person.0074

Each experimental unit or case gets assigned to some treatment.0089

This rat gets treatment A, this rat gets treatment B.0097

Everything in this experiment should be alike except for the treatment.0105

Everything else about these rats or states or schools or people should be roughly similar except for the treatment.0112

That is how we isolate the effect of that treatment. 0124

Given that experimental overview, there are really 2 kinds of variability that we need to think about.0129

One is what we call between treatment variability and you can think of it as here are two groups that have 2 different treatments A and B.0138

We know what is the between group variability?0150

How are these two treatments different from each other or three treatments or parts of a treatment?0152

This variability is hopefully caused by the treatment.0158

The impact of the treatment is making on these two different cases were experimental units and that is really caused by the treatment.0164

This is what we think of as the good kind of variability.0178

This is what variability we are interested in.0182

We are looking for this type of variability because if we have a lot of between treatment variability this means they are manipulated variable is quite important. 0187

It makes an impact.0209

That is one kind of variability.0210

The other kind of variability is within treatment variability.0215

That means within an experimental unit they all have the same treatment.0218

It all rats that were exposed to the same hours of sleep.0224

These rats had different hours of sleep.0229

These rats that all have the same hours of sleep there a still some little differences between them.0230

Some rats sleep a little bit more or the other one is active.0239

They have a little bit of within treatment variability that will just come along for the ride.0241

Despite the rigorous experimental methodology, no matter how good your manipulation and control is 0252

They were this some variability that will exists even within a treatment group and that could come from lots of different sources. 0260

Sometimes it does come from experimental mistakes and sloppiness, 0268

Most of the time it just comes from noise or other variables that we are not accounting for.0275

This is what we think of as bad variability, but is not as bad like we want to or if you have it, then oh your terrible experimenter.0281

That is not what it means.0294

It just means that this gets in the way of seeing the good kind of seeing the between treatment variability.0296

Here is the problem.0315

Within treatment variability is very difficult to avoid.0318

They are some techniques to try and avoid it and minimize in as much as possible and we are going to learn about those 0323

Overall even though you try and reduce it probably never completely goes away.0330

Here is the issue with it. 0337

It prevents us from seeing the between treatment variability because sometimes it obscure it.0338

Let me show you what that means in the next slide.0346

Because of these two different kinds of variability we want to update one of the goals of the experimental design. 0354

Not only do we need to have manipulation and control of the IV in order to determine causality.0363

We are very interested in causality and experimenter so this is all in order to causality.0375

All so we want to know where as much as possible within treatment variability as much as we possibly can.0381

There can be a couple of different methods for lowering within treatment variability as much as we can.0400

Because that can help us see between treatment differences and that is where we are really interested in, in order to determine causality.0407

Let us look at an example to look at how this variability might impact each other.0419

Here is an example of drugs and driving.0424

Some antihistamines like allergy medicine make people feel drowsy like Benadryl.0428

One danger is that drowsy people are crappy drivers.0433

To check whether an antihistamine makes people worse at driving we wanted to test an antihistamine against the placebo, 0438

Just a sugar pill on people's driving performance in a videogame.0445

Here is the ideal case.0449

In the ideal case in order to determine whether antihistamines cause people to be like crappy drivers. 0454

One thing you might want to look at is let us say the score on the driving performance.0462

Higher score means you are better at driving lower score mean you have more like crashes or swerves, or whatever is right.0468

Maybe we will see if the we draw like a dot plot of the antihistamine people right. 0475

Maybe we will see them all having sort of you know low scores but maybe the placebo group will just tend to get high scores.0483

If we had something like this then we will see that even though there is within treatment variability, there is variability here.0513

There are some within treatment variability here and there are some within treatment variability here too.0521

Basically the means are probably far apart enough where we could probably say all of the antihistamine seems to be different than the placebo group.0527

Between treatment difference is still big enough that we can see it.0540

But the world is not an ideal place.0547

Most of the time we have a sort of noisy world because some people are just better at driving games 0551

and some are better at video game than and some people do not react to antihistamines as strongly as other people.0562

There are lots of other variables that come into play for within treatment variability.0568

We might have been no differences.0576

Maybe we can a lot of spread.0580

We have a lot of spread here and among the placebo group we might also have a whole lot of spread. 0591

In the case is hard see if there is a between treatment difference just because there is a lot of within treatment difference.0602

That is what we mean by a bad kind of variability that gets in our way of really being able to make conclusions from our experiment.0623

What we want to do is reduce that within treatment variability as much as we possibly can. 0631

To conclude that a treatment, some experimental treatment makes a big enough impact, 0639

what you really have to see is that the between treatment variability is overcoming the within treatment variability.0645

The between treatment variability have to come out strong and the within treatment variability have to be some of sort of smaller.0668

When we see that then we can maybe start to have some more confidence and say I think this treatment might make a difference. 0677

In order to reduce within treatment variability as much as possible there are a couple of different types of design for random assignment that we could carry out.0686

All experiments have random assignment of treatments to experimental units or cases.0700

I'm calling them experimental units here because there are so many different things that you could do experiments on.0706

You could do experiments on whole companies and you could do experiments on individual people.0713

I will generally call them units or cases.0719

The one type that we have already talked about before is that we call a completely random design.0722

This means you randomly assigned a treatment to each little experimental unit, gets randomly assigned to a treatment.0729

The only requirement other than is that you keep a number of units that are given each treatment as equal as possible.0741

Treatment A, B, and C all have the same number of experimental units back at each of those.0751

That is the only requirement.0757

The way you can think about this is like that is let us say you have experimental units ABCDEF and you have two treatment groups, treatment 1 and 2.0758

When A comes in you think about it as flipping a coin and whatever they get heads for 1 and 2 for tails, it might be A, B, C, D, E, F.0773

You just randomly assigned them to different treatment groups.0791

That one is really pretty easy and straightforward.0794

The other kinds are what we call generally randomized block design.0799

What we do here is first we have the additional that we place similar units into groups and we call those units blocks.0805

Randomly assigned treatments to use the units within the blocks.0822

Here is the general idea. 0826

Let us say A, B, C, and D are similar for some reason.0828

They are females.0841

Maybe we have E, F, G, H and those are all males.0846

First, we placed similar units into groups of blocks.0854

We have two blocks here.0859

Once we have those blocks, then you randomly assign treatments to the units within the block.0860

Maybe we might get A, B, C, D.0867

We get randomly assigned to the treatments and then also with F, G, H we might get randomly assigned to these treatment groups. 0879

Then you roughly have 2 treatments that have an equal number of females and equal number of males.0892

Whatever similarity you are interested in, you can use that.0901

For instance, if you are interested in whether they are in the same grade level or they have the same major 0908

or sometimes it might be maybe rocks from the same litter because those tend to be similar.0914

Or plants from the similar elevation level.0922

Whatever those similarities are you want to place them into groups first before assigning them to treatments 0925

so that each group gets equal representation in the two treatments.0932

Actually, there are multiple different kinds of randomized block design.0940

I’m going to show you two of them.0945

Randomized block design have two different ones.0948

The reason that it is called randomized block design is Guy and Fisher, who did a lot of the groundwork for all of the statistics.0952

He wanted to do experiments on meat or some kind of farming thing.0961

What he would do is say I do not want it to be that like one treatment is on the edge, on the west side.0967

What he did was he separated all of the fields into blocks first.0981

Let us say there are like four different treatment what he would do is randomly assign different quadrants into those different treatments.0991

A little bit of each in a place on the field got treatment A.1011

A little bit of each place in the field got treatment B.1022

If you look at all the A, there is an A here, here, and here.1027

If you look at C, there is a C here, here, here, and here,1038

This way he make sure that every part of the field is represented in his little treatment group of C.1044

Back to two different types of block design. 1056

The first type of randomized block design you need to know is what we call matched pairs design.1063

Each block is a pair of similar units and it does not have to be pair.1068

These pairs could be all certain different things. 1077

Maybe they are twins because but at least in different genes they are identical.1080

Once they have these pairs that are the same you randomly assign treatments within pairs.1091

In one entry gets to be in treatment A and one in treatment B.1097

Another example is may be similar companies.1102

If you have big soft drink company like Coca-Cola, maybe it is matched pair is Pepsi company 1106

then you randomly assign Coca-Cola to other thing and Pepsi to another thing.1115

The idea is you have all these little pairs but one gets to be assigned to be in the blue group randomly and one is assigned to be in the red group randomly.1122

These two individuals inside the pair are similar in some important way.1137

You often see matched pairs design, especially in psychology when you have something like different age groups.1144

You want to have age matched controls. 1152

For every 4/2-year-old you have here, you have a 4 ½ year old pair and they are both get assigned to different treatment groups.1155

You might also see this when people do studies with individuals have autism or some brain damage.1163

They might have IQ matched controls.1173

They might have this individual and find somebody who matches them on IQ to be in the control group.1176

That is what we call a matched pairs design.1183

The other type of randomized block design you need to know is what we call a repeated measures design.1188

This one is really nice for reducing within treatment variability because each block now is one case.1196

Like for instance, one person or one lot and each case gets all the different treatments, but in a different random order.1205

Maybe we have case ABCDE.1217

We have all these little people or rats or plants in our study.1225

Let us say plants and they get 3 different kinds of fertilizer, one for each year but in different orders.1231

Maybe A will get fertilizer 1, 2, then 3.1244

Maybe B will get 2, then 3, then 1.1249

Maybe C will get 3, then 1, then 2.1252

And D will get 3, then 2, then 1.1255

E will get 2, and 1, and 3.1258

In this case, each case or experimental unit gets assigned to all the treatment groups.1262

The nice thing about this as well as this design is that you can compare how A does in treatment 1, 2, and 3.1271

You can compare how B does itself in treatment 1, 2, and 3.1282

Also with the match pairs you can look at how their pair does and we could rule out the difference in ages.1286

That is not as important anymore because they're the same age.1299

The nice thing about these is that now we have data to do within treatment comparisons and be able to rule out that source of variability.1303

Let us say plant A just grows a lot faster than all the other plants then they would be different from B because B grows slower than A.1316

Even so does one fertilizer help A grow more even more faster than the other ones?1329

Maybe fertilizer 1 here and 1 here even though B only grows like 3 inches, that is a lot for B, but maybe for A, A grows like 12 inches and that is a lot for A.1337

You can make it relative to A’s performance in the other treatment groups.1355

Often times you might hear the term with between subject variable and within subject variable.1361

This is just a matter of terminology and instead of the word subject feel free to put in the word cases or experimental units.1371

Often times like in social science or medical sciences, you will have between subject persons within subject because we are talking about people and animals.1386

In a between subject variable it just means that this variable whatever it is, like medicine it is being administered between cases or between people.1399

The people who get medicine A do not get medicine B and the people who get medicine B they do not get medicine A.1412

That is what you see in a completely randomized design. 1419

Sometimes you also see that in other designs that are not experiments as well, but when we are talking about experiments, 1423

You will see that primarily in a completely randomized design. 1435

You might also see it in a matched pairs designs but it actually depends on what the pairs are.1439

In a completely randomized design what you'll end up having is 2 treatment groups.1443

You will have in the treatment group 1 or however many treatment you have, you could have three or four.1452

Treatment group 2.1460

You have different people in each of those.1462

You know you will have ABCDEF and so A is only in treatment 1 when they are not in treatment 2.1465

This treatment variable treatment is a between subject variable because it occurs between subjects.1476

It is not like inside of one subject that you have the different values of that variable inside it is between subjects.1495

In a repeated measures design this is a case where we have ABCDEF.1504

We have the same subjects here, but instead they might get 2 treatments.1513

Here everybody gets both the treatment.1521

Within subject A they hold both the treatment 1 and treatment 2.1536

Because of that treatment in this case, treatment here is a within subject variable.1546

Because the variable varies within a subject inside of one subject. 1565

Inside of one subject. 1569

Let us go into some examples.1571

Here is example 1, We want to know whether sitting or standing affects our heart rate.1579

Design a completely random experiment, as well as a matched pair and repeated measures experiment.1584

In order to have a completely random experiment let us say we start off with 20 people, maybe in your statistics class 1590

and maybe one thing you might do is assign 10 of those people random like to split the coin or something 1603

and assigned 10 of those people to the sitting condition treatment and assign half of the people to the standing treatment.1612

Here is sit, stand, sit, stand, sit, stand.1622

Actually the other way I’m going to write it, let me write sit in red and stand in blue.1633

It might be sit, sit, sit, sit, sit, we will do 10 of those.1648

Maybe stand, stand, stand, stand, 10 of those.1656

Then you will get you know people ABCDEFGH and then the other half you might pu FGHIJ.1666

That will make it easier and make it 10 people because it makes me easier to draw.1684

In this way you might have 5 people standing, 5 people sitting, and they have been randomly assign and then you might get everybody's heart rate.1691

Whatever their heart rates are.1706

58, 52 so on and so forth.1710

That might be one experiment, and you will compare these numbers to these numbers.1714

A matched pair design might go something like this.1720

Let us say we have those same 10 people, but maybe we want to match them based on something.1726

Everybody already has a different heart rate.1733

Some people have faster heart rate and some people slower and so maybe we take everyone's heart rate first.1737

Everyone who has the same heart rate we will put them as a pair.1743

These people might have a resting heart rate of 58 and one person, one of these people gets to be in this standing condition.1748

And one of these people get to be in the sitting condition.1766

We might do that for 5 pairs.1770

A, B, C, D, E, F, G, H, I, J.1779

In this way they are paired according to their resting heart rate.1796

And then one person continues to sit and then one person to sit and take the heart rate again.1803

But one person stands up and they are now taking their heart rates standing up.1808

We could compare these two people because we know that they started off with the same resting heart rate.1815

This is the A matched pair design.1823

Finally the repeated measures design we might do something like this.1827

Let us say we have A, B, C, D, E, F, G, H, I, J.1832

We have our 10 people and some of them have to sit and take their heart rate first and then stand and take their heart rate.1842

Sit, sit, sit, sit, sit.1855

Stand, stand, stand, stand, stand. 1860

In this way, person A will have to sit and take heart rate and then stand then take the heart rate.1866

Person B will have to stand first and take their heart rate and sit then take heart rate.1874

Everyone gets both treatments and the treatment is the within subject variable.1879

It is within each subject, but they each have in a different order. 1885

So, roughly half of our participants should be in the sit- stand order and the other half should be in the stand-sit order.1891

Example 2, why is blocking sometimes a desirable feature of the design?1901

Given example where blocking might be better idea than completely randomized.1908

Blocking might be important if there's some variable that you know of ahead of time that might impact your dependent variable.1912

Like standing heart rate might be influenced by your sitting heart rate.1922

For whatever your baseline is it is going to affect what your standing heart rate is.1930

Sometimes you want to like rule out variation that comes from that variable that you know might be important. 1936

Let us think of an example. 1946

Maybe we want to see how fast people learn to play tennis.1950

How quickly people learn to play tennis?1956

What are some things that might affect their ability to learn to play tennis?1967

Maybe our racquet ball experience?1972

Maybe, previous tennis experience.1975

Maybe their age.1988

Maybe younger people might be able to learn faster than older people.1992

Anyone of these variables might be important.1996

Let us just pick one athletic experience.2001

We will just ask people how many years of athletic experience.2003

We might want to the experienced athletes in one block and the less experienced athletes in another block.2007

We have a whole bunch of experience. 2015

Maybe we have moderately experienced.2018

A little bit experienced and then little to no experience and within each block, maybe we give them two different ways of learning tennis.2022

Method A and method B.2036

Here some people get method A in red.2039

Some people get method A.2047

For each of these people there is another person in their group that gets method B.2053

In this way, we have a mix of people who have experience who get method A and less experienced people who have a lot experience get method B.2067

That is the same across all these different levels of experience.2087

That might be an example if blocking is better because then you reduce the within treatment variability 2092

so that you could maybe see more clearly between treatment variabilities.2098

The real difference between treatment A and treatment B. 2108

Why our completely randomized designs, also called between subjects designs popular?2109

Given example where this is a better design than randomized block design.2118

One of the real problems with randomized block design is that sometimes you do not know you what might be important.2122

There might be a lot of variables that you need to control for and it is probably really hard to control for all of those things. 2132

Maybe in something like grade at school.2139

Many things important grades at school that it might be better off to have a completely randomized design than to have a randomized block design.2145

Or if you do have a randomized block design maybe you could only do it with a limited number of variables like one variable.2158

In that case, our completely randomized design might be more important. 2165

In example of something like this and you know, let us also modify this question to why it might be better than with subjective design.2170

The one kind we learned about is the repeated measures design.2188

Sometimes it is hard to assign one single experimental unit to multiple treatments.2200

For example, some medications last in your body for a long time and so it would be really hard to give one group of rats the medication 2207

and then give them a placebo later because that medication is still in their body.2221

Sometimes it might be very difficult to assign different treatment levels to the same individual.2227

And there might be some carryover effects.2236

Things like the drugs staying in their body or maybe we are looking at two different teaching methods for statistics. 2239

Maybe we are trying within treatment A versus treatment B or teaching method A versus B.2248

And they might have learned a lot from whatever teaching method came first.2256

And because of that the second one may not look as effective, but maybe it is just that whichever one came first.2260

Sometimes it is going to be really hard to deal within subject design, but you have to do between subjects design.2268

In a completely randomized design this actually a sort of easier. 2275

It is an easy way of doing experiments because you do not have to do as much planning ahead of time.2281

In the case where maybe you do not know who your subjects or cases might be.2289

Maybe it is good to have a completely randomized design.2296

That is it.2300

An example might be maybe we are looking at how volunteers at a supermarket case test some jams.2307

Maybe where looking at if they taste it plastic spoons versus metal spoons.2316

Does it make an impact?2326

We do not know who's coming at.2327

We can randomly assign them to blocks first.2329

We might just a clever confident and randomly assign them to one group or the other.2333

That might be an example.2339

Example 4, are the following designs completely random?2342

Matched pairs or repeated measures experiments?2346

A college health service wanted to test whether putting antibacterial soap in the dorm bathrooms will reduce visits to the infirmary.2351

They kept track of how many students from which dorms visited the infirmary per semester.2359

They assigned 10 randomly picked alarms to get antibacterial soap and the other 10 get regular soap.2364

It is helpful to know what are the experimental units here.2370

You might think it is the people, the students going to the infirmary. 2376

Actually, that is not.2380

That is the dependent variable.2382

How many students?2384

The case is the experimental units are actually the dorms.2385

The dorms had been randomly selected into one group or the other. 2389

The antibacterial soap group or the regular soap group.2395

This one looks like a completely random design.2398

The other way they could have done that is that five large dorms that have 200 students 2406

and 5 small dorms only have 40 students received antibacterial soap.2413

Then another 5 large dorms and 5 small dorms received regular soap.2418

The largeness of the dorms might matter because maybe in a larger dorms things are crazier and messier.2423

Maybe it is easier to cast disease in a larger dorm.2431

Maybe they wanted to make sure half of the time that the size of the dorm isn't what causing the difference in the variability.2437

In order to control for that day they have an equal number of large dorms and small dorms in each of the treatment conditions, 2448

the antibacterial soap and regular soap groups.2456

That looks like sort of a matched pairs. 2460

It is a block design. 2462

For every large dorm you have another large dorm here and it is like a pair on the other side.2464

For every small dorms you have a small dorm, on the other side. So they have a matched pair.2477

That is the end of within and between treatment variability.2482

Thanks for using