Factorial Experiment Design¶

SweetPea is a domain-specific programming language for creating factorial experimental designs. Our goal is to make it easy to specify and set up all of the factors and levels needed for your experiment.

Hint

There’s a glossary at the bottom of this page for a brief overview of the most important terms.

Wikipedia gives a decent introductory definition of a factorial experiment:

In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or “levels”, and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.

Factors¶

A factor is an independent variable in your experiment. In simple experiments, there may be only one factor — in which case SweetPea is definitely overkill for you! But experiments can be successfully run with multiple factors without issue, and SweetPea will help you plan this out.

Fun Fact

The term factorial likely first appeared in the 1935 text The Design of Experiments by Ronald Fisher. The book is also credited with introducing the concept of the null hypothesis.

Levels¶

In a factorial experimental design, each factor can take on one of a finite number of discrete possible values, called levels. To make this more concrete, consider a simple example.

Example¶

Imagine we are conducting an experiment to observe the Stroop effect. In a simple Stroop experiment, we show a participant the name of a color, and we render the text of that word in a color other than that which was named. For this experiment, we identify our factors and levels:

Factor	Levels
Color Name	red, blue, green, yellow
Text Color	red, blue, green, yellow

If this is a full factorial experiment (also said that the experiment is fully crossed), then we must conduct one trial for each possible combination of factors and levels. In other words, we must have \(4 \times 4 = 16\) distinct trials to fully cross the above example experiment.

Derivations¶

A derivation (or derived level) is a new level produced by combining other levels. This combination of levels can be directly constructed with sweetpea.primitives.DerivedLevel().

Derivations can also be constrained by derivation windows, which allow for specifying specific manners in which different levels from multiple factors can interact across trial boundaries. There are three kinds of derivation windows:

Basic windows, from which other windows are made.
Transition windows, which constrain derivations across trial transition points.
Within-trial windows, which provide windows that look only within a single given trial.

These are explained more below.

Basic Windows¶

A basic derivation window (sweetpea.primitives.DerivationWindow) creates a level that is selected depending on a combination of levels from other factors in the current trial and zero or more preceding trials.

Transition Windows¶

A transition window (sweetpea.primitives.TransitionDerivationWindow) describes a level that is selected depending on a combination of levels from other factors in the current trial and the immediately preceding trial.

Within-Trial Windows¶

The within-trial windows (sweetpea.primitives.WithinTrialDerivationWindow) describe a level that is selected depending on levels from other factors, all within the same trial.

Glossary¶

derivation¶: An artificial level that results from the combination of other levels. Also called a derived level.
derivation window¶: A window constraining a derivation that depends on a combination of levels from other factors in the current trial and zero or more preceding trials.
derivation window, transition¶: A derivation window that depends on a combination of levels from other factors in the current trial and the immediately preceding trial.
derivation window, within-trial¶: A derivation window that depends on levels from other factors, all within the same trial.
derived level¶: See derivation.
factor¶: An independent variable in a factorial experiment, composed of finitely many levels.
factorial experiment¶: An experimental design measuring multiple independent variables (called factors) consisting of finitely many discrete possible values (called levels). A factorial experiment can either be classified as a full factorial experiment or a fractional factorial experiment.
fractional factorial experiment¶: A factorial experiment consisting of a specific subset of possible trials that together expose meaningful information about important features of the problem without the resources or redundancy of a full factorial experiment. An experiment of this nature is said to only be partially crossed.
full factorial experiment¶: A factorial experiment consisting of enough distinct trials to independently observe each possible combination of factors and levels. An experiment of this nature is said to be fully crossed. Contrasts with a fractional factorial experiment.
fully crossed¶: A factorial experiment run with enough distinct trials to be able to distinguish the effects of each factor and level from one another.
level¶: A discrete possible value that a factor can have.
partially crossed¶: See fractional factorial experiment.
transition window¶: See derivation window, transition.
trial¶: An individual repetition of an experiment. A minimum number of trials must be run to obtain sufficient evidence to draw conclusions, and this number is determined in part by the number of factors and levels.
window¶: See derivation window.
within-trial derivation¶: See derivation window, within-trial.