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

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

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We know that confounding can confuse
us, but I'll show how some knowledge

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about our systems can be used
to recover useful information.

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But first, right at the beginning of the
course remember how I always asked you to think

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about how each factor might impact the outcome?

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

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

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The first is the chemical
added to treat the water.

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The second is temperature.

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And the third is stirring speed.

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A full set of experiments would require
eight runs, but if I can only afford four

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or five experiments, I should
run a half fraction.

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Prior experience with the system might lead me

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to believe there will be
no significant interaction

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between temperature and stirring speed.

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

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

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In that case, I don't want the effects
of the chemical to be confounded

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with other effects in the system.

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

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by that I mean I don't want it to be confounded
with other large effects, a natural choice is

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to alias the interaction between any
other two factor interaction, temperature

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

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

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B as the stirring speed, and factor C, the
chemical factor, can be set as A times B. Notice

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that I'm free to assign the
letters to my factors in any way,

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and I can choose the assignment
that causes the least problems given

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that I know confounding will occur.

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Now factor C, that chemical effect, will
be confounded with the AB interaction,

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but I've used my knowledge of the system,

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that I know that that AB
interaction is going to be small.

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So I'm pretty sure that the effect of C,
the chemical effect, will be a good estimate

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

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Right there is where I've demonstrated good
use of educated guessing and smart assumptions.

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Notice that you may not get this assignment

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

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I often tell my students, it feels like
I spend more time planning my experiments

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than actually doing them.

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That's because usually we only
have one chance to do them,

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but I've many chances to plan them on paper.

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If I don't like the confounding pattern I get
the first time, I can simply reassign my letters

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and I can do that as many times as I like
until I get the desired confounding pattern.

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What's really important to
notice here is that at no point

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in this video have we used any of the y-values.

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

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

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Remember in the water treatment example,

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

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Now back to that trade-off table.

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

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

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

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

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

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Here's one more important
pointer about half-fractions.

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They are often more suitable
than a full factorial design

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when you are trying to learn
more about a system.

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

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

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

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A few days later you get the results,

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only to find out there was a problem
with your experimental system.

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What a waste.

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It would have been cheaper to perform just
eight runs, send the results for analysis

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to discover the problem, then you
can still spend the remaining budget

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on those other eight runs to
recover most of your results.

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What about the other case?

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

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Well, you haven't lost anything.

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You can quickly go do the
analysis on those first eight runs,

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and if you are satisfied you can stop.

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

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We call those the complementary half fraction,
and it's totally your choice to do that,

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

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Trying to visualize graphically
what a half fraction as well

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as its complementary half fraction looks like is
only feasible for a system of 3 factors: A, B,

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and C. First we would do the runs with the open
circles, and complete all our analysis to find

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out which of the factors is significant,
and my how much they affect the outcome.

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Recall, we would use a Pareto plot for this.

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Then, let's say things looked promising, and
we got approval to do the other half-fraction,

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then you would come back and do
the runs with closed circles.

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This concepts extends naturally to a
system with 8 + 8 = 16 experiments,

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or 16 + 16 = 32 experiments, and so on.

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

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Obviously the savings are more
impressive for the larger systems.

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To end off: half fractions are a great example
of what we call an experimental building block.

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A piece of work that we start with and
decide to add on top of if we choose.

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You should be asking questions
about how to use this table.

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Here's a suggestion, in your the
experimental system you thought of,

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back in an earlier module, consider how you
would have planned a reduced set of runs.

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How would you have used this
table in your system?

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Make sure you can answer that.