In today's class, I'm going to show you how
to interpret the results from a very simple experiment.
But before we do that, let's briefly review the previous lesson,
where we introduced some new terminology.
We learned what the word "outcome" means, when talking about experiments.
The word response is also used instead of outcome.
We learned about factors which we sometimes called variables.
Factors, or variables, can either be categorical or numeric,
and we discussed examples of both types.
It might seem strange that I'm showing you how to analyze the results
of the experiment before I even show how I planned the experiment, or designed it.
Sometimes though, it's useful to see the end and then work backwards to the beginning.
The experiment I'm going to describe here has one outcome.
The profit made in one day when selling a specific type of product in a store.
Remember that profit equals income minus expenses.
So when the store owner calculates the total income and then subtracts the total expenses,
that number is called the profit and is the outcome of our experiments.
The objective of this experiment is to increase profit.
We defined what an objective was in the prior class.
Now this experiment has two factors.
The first factor is the amount of light in our store.
We can use a dimmer knob to control just how much light is in the store.
We can put that knob at 50% or at 75%, for example.
This gives a low amount of light or a high amount of light.
It is always good practice to predict what the effect of the factor will be on your outcome.
In this example, do we expect that more lighting will increase the profit?
Maybe more lighting will decrease the profit.
Or do we expect that more lighting really has no effect on the profit at all?
We'll look at the results in a minute.
The second factor we're going to consider in the experiment is the price of the product.
We could sell the product for $7.79 or we could sell the product for $8.49.
This again is a numeric variable.
Try to predict what the effect of price is going to be on the outcome.
Do we expect a higher price to increase the profit?
Do we expect a higher price to maybe decrease the profit?
Or it is quite possible that higher price has no effect on the profit.
Pause the video for a moment and write
down what you predict the outcome will be for changing those two factors.
OK, let's look at those results.
We have to consider all combinations in our experiments.
The easiest way to consider this is with a simple visualization.
Let's start with a horizontal axis for the dimmer amount, where we have a low amount
of light on the left and a high amount of light here on the right.
Then, add a vertical axis for the next factor, price.
We have a low price here at the bottom and then a high price here at the top.
So there are three experiments here so far.
There is actually a fourth experiment we must run.
It is the combination of high amount of light with high prices.
Let's assume you have four days and you could run these four experiments: one per day.
On the first Monday, you run the experiment with high amount of light and low price.
And let's say you get a profit of $570.
Then the next Monday, you run the combination of low amount of light
and high price and the profit is $370.
The following Monday, you have prices that are high and with high amount of light.
And the profit there might be $450.
Then the last Monday you have the final experiment with low light and low prices
and your outcome is a profit of $490.
Here are the results in table form.
We are going to see this format regularly in the course.
I'm going to explain in a future module why we ran the experiments
in a different order to that shown here in the table.
This table order is called standard order.
The simplest way to analyze this data is to use a visual analysis.
No math and no statistics are required to do this.
Start by drawing a square of the four experiments.
As before, we have the lighting factor on the horizontal axis
and pricing factor on the vertical axis.
Next add a minus sign and a plus sign on the axes
to help indicate the low levels and the high levels.
We sometimes also write what the low levels and the high levels are.
Transfer the values of the outcome variable from the table onto the square.
In other words, copy those profit values, the outcome variable, across.
We call this a cube plot.
Later on, when we have three factors, you will see that it really is a cube.
So $490 is written at the bottom left because that was the outcome profit
when we used low lighting and had lower prices.
We add the $570 at the lower right, $370 at the top left and finally $450 at the top right.
Now we are ready to analyze the results.
Let's analyze the effect of lighting amount.
We have two chances to judge the effect of lightning.
The first is to consider the difference between the high level of lighting compared
to the low level of lighting, but keeping prices at their low value.
When we do this, we see the difference is $570 minus $490.
That's a difference of $80.
Now let's look at the difference in lighting when pricing is at the high value.
This time, it's $450 minus $370.
That's a difference of $80 again.
So we can see then, the effect of lighting causes our profit to increase by $80 as we move
from a low level of light to a high level of light.
This effect is consistent both at low prices and at high prices.
Now let's consider the effect of adjusting price.
At low amount of light, we can compare $370 in profit to $490 in profit.
We interpret this as follows.
As prices are increased the profit will, in fact, decrease by $120.
We can also consider the effect of adjusting prices at the high level of lighting.
This time we have $450 minus $570.
That's a decrease of $120 again.
So let's recap.
The effect of lighting is that it increases our outcome variable.
Our profit goes up by $80 when we move from 50% on the dimmer to 75% on the dimmer.
So it's a good thing to use more light in our store.
Pricing though, has an interesting effect.
It shows that our profit decreases by a $120 when we raise prices
from the lower level to the higher level.
This example was in fact quite simple.
Most experiments will not have the same difference in values on the left
and the right hand sides, or on the top side and bottom side of the square.
We will get into more complex examples in the next videos.
Before we end the class I want you to consider what could have gone wrong.
What if, on the day that we did our experiments, there was bad weather
and we had fewer customers come to our store.
What if we repeated the experiment a second time,
would we get the same profit outcome value?
In other words, is our experiment reproducible?
Those are important points we have to bear in mind and we're going
to consider them in the coming classes.
See you next time.