In this video we continue the prior video by considering the effects of confounding.

That prior video was all about the technical details behind confounding.

We know that confounding can confuse us but I'll show you how

some knowledge about our systems can be used to recover useful information.

But first right at the beginning of the course,

remember how I always asked you to think how each factor might impact the outcome?

Now you are going to see why I made you do that.

Consider the case where we are treating water and we have three factors.

The first is the chemical added to treat the water.

The second is temperature.

And the third is stirring speed.

A full set of experiments which require eight runs.

But if I can only afford four or five experiments,

I should run a half fraction.

My prior experience with the system might lead me to

believe there will be no significant interaction between temperature and stirring speed.

I would like to get a good estimate of the chemical factor added.

Remember the premise that chemical Q was twice the cost of chemical P?

In that case, I don't want the effects of

the chemical to be confounded with other effects in the system.

So if I would like this good estimate of the chemical added factor,

by that I mean I don't wanted to be confounded with other large effects,

a natural choice is to alias the interaction between any other two factor interaction,

temperature and stirring speed in this case with the chemical effect.

So now when I planned my experiments I could rather assign A as the temperature,

B as the stirring speed,

and factor C--the chemical factor--can be set as A times B.

Notice that I'm free to assign the letters to my factors in any way and I can choose

the assignments that causes the least problems given that I know confounding will occur.

Now factor C, that chemical effect,

will be confounded with the AB interaction.

But I've used my knowledge of the system that I know that

that AB interaction is going to be small so I'm pretty sure that the effect of C,

the chemical effect, will be a good estimate of

that chemical effect and not be confounded with the AB interaction.

Right there is a way I've demonstrated good use

of educated guessing and smart assumptions.

Notice that you may not get this assignment of

letters correct the first time but that's quite okay.

I often tell my students it feels like I spend

more time planning my experiments than actually doing them.

That's because usually we only have one chance to

do them but I have many chances to plan them on paper.

If I don't like the confounding pattern I get the first time,

I can simply reassign my letters and I can do that as many times

as I like until I get the desired confounding pattern.

What's really important to notice here is that at

no points in this video have we used any of the Y values.

What this means is that this analysis can be done before you run any experiments.

You must use your brain and some educated guessing before you start the work.

Remember in the water treatment's example each experiment

costs $10,000 so we can't simply repeat them.

Now back to that tradeoff table.

You might be curious about the other entries and how they were found.

Those entries here are found so that you can minimize the confounding and recover

the most amount of information for a given row and column combination in the table.

So that's a bit of the detail behind half fractions.

We're going to have plenty of practice with these tables coming soon.

Here's one more important point about half fractions.

They are often more suitable than

a full factorial design when you are trying to learn more about a system.

In other words, for that very first set of runs that you're trying.

What if you had four factors to investigate and did the full set of 16 runs?

You do them, you take the samples and you send them to a laboratory for analysis.

A few days later you get the results only to find out

there was a problem with your experimental system. What a waste!

It would've been cheaper to perform just 8 runs,

send the results for analysis to discover the problem,

then you can still spend the remaining budget on

those other eight runs to recover most of your results.

What about the other case?

What if you had done those first eight runs and there was no problem?

Well you haven't lost anything.

You can quickly go do the analysis on

those first eight runs and if you are satisfied you can stop.

If you want, you can go do the other eight runs,

recall those the complimentary half fraction and it's totally

your choice to do that depending on how you want to spend the rest of your money.

Trying to visualize graphically what a half fraction as well as its complementary

half fraction looks like is only feasible for a system of three factors A, B,

and C. First, we would do the runs with open circles and complete

all our analysis to find out which of the factors is

significant and by how much they affect the outcome.

Recall, we would use a Pareto plot for this.

Then let's say things looked promising or there

was too much confounding and you wanted to clear things up.

Then we would get approval to do

the other half fraction and come back and do the runs with closed circles.

This concept extends naturally to a system with 8 plus 8 or 16 experiments.

Or 16 plus 16,

in other words 32 experiments, and so on.

In other words the experiments on the diagonal of the trade off table,

obviously the savings are more impressive for the largest systems.

To end off, half fractions are

a great example of what we call an experimental building block,

a piece of work that we start with and decides to add on top of if we choose.

You should be asking questions about how to use this table. Here's a suggestion.

In the experimental system you've been thinking of all throughout this course,

consider how you would have planned a reduced set of runs for your case.

How would you have used this table for your system?

Make sure you can answer that.