Design of Experiments

Suppose we want to test alternative movie theater designs using three factors.

**Price**at $10, $13, or $16**Sight**to determine if theater setting should be staggered or not staggered**Food**to determine if we should offer hot dogs and popcorn, gourmet food, or no food at all

The factors to include in the analysis have 3, 2, and 3 levels so we
enter `3`

in the `Max levels`

input.

Here we enter the factors of interest. For example, enter
`price`

as the variable name, $10 as level 1, $13, as level
2, and $16 as level 3. Then click the
icon. This will add
the provided information about the factor to the
`Design factors`

window in the format Radiant needs for
analysis. To remove the last line in the `Design factors`

window click the
icon.

After entering the required information for each of the three factors your screen should look as follows:

You are now ready to create an experimental design by clicking on the
`Create design`

button. This will generate the following
output.

For our example, the ideal design has 18 trials. However, this
implies that the partial and the full factorial are the same size. We’d
like to find out if it is possible to reduce the number of trials. See
`# trials`

below.

This input can be used to control the number of trials to generate.
If left blank Radiant will try to find an appropriate number of trials
using the `optFederov`

function in the
AlgDesign
package.

Lets review the output in `Design efficiency`

. For our
example, the goal is to find a design with less than 18 trials that will
still allow us to estimate the effects we are interested in (e.g., the
main-effects of the different levels of price, sight, and food). Notice
that there are several designs that are considered `balanced`

(i.e., each level is included in the same number of trials). We are
looking for a design that is balanced and has minimal correlation
between factors (e.g., a D-efficiency score above 0.8). You can think of
the D-efficiency score as a measure of how cleanly we will be able to
estimate the effects of interest after running the test/experiment. The
ideal D-efficiency score is 1 but a number above 0.8 is considered
reasonable.

The smallest number of trials with a balanced design is 6. This design is balanced simply because 6 is divisible by 3 and 2 (i.e., the number of levels in our factors). However, the D-efficiency score is rather low (.513). The next smallest balanced design has 12 trials and has a much higher D-efficiency. This design is a reasonable choice if we want to estimate the main-effects of each factor level on movie-theater choice or preference.

To generate the desired partial factorial design enter
`12`

in the `# trials`

input and press
`Create design`

. This will generate the following output.

The `trial`

column in the output shows which profiles have
been selected from the full factorial design. Note that the off-diagonal
elements of the (polychoric) correlation matrix for a partial factorial
design will all be equal to 0 *only* when D-efficiency is equal
to 1. The
polycor
package is used to the estimate the correlations between the
factors.

A partial factorial design may not be unique (i.e., there might be
multiple combinations of trials or profiles that are equally good). By
setting a random seed you ensure the same set of trials will be
generated each time you press `Create design`

. However, to
see alternative partials factorial designs empty the
`Rnd. seed`

box and press `Create design`

a few
times to see how the set of selected trials changes.

Note that we will not be able to estimate all possible interactions
between `price`

, `sight`

, and `food`

if
we use a design with 12 trials. This is the trade-off inherent in
partial factorial designs! In fact, if we do want to estimate even one
interaction (e.g., select `price:sight`

) the appropriate
design has 18 trials (i.e., the number in the full factorial design that
includes all possible combinations of factor levels).

Click on the `Partial`

or the `Full`

button to
download the Partial or Full factorial design in csv format .

To download the list of factors you entered click the
`Download`

button. To upload a previously created set of
factors click the `Upload`

button and browse to find the
desired file.

Add code to
*Report
> Rmd* to (re)create the design by clicking the
icon on the bottom
left of your screen or by pressing `ALT-enter`

on your
keyboard.

For an overview of related R-functions used by Radiant for
experimental design see
*Design
> Design of Experiments*

The key function from the `AlgDesign`

package used in the
`doe`

tool is `optFederov`

.