### Beyond AP Statistics

#### Probability Basics

#### Small Samples

#### Distributions

#### Power

### Beyond AP Statistics

#### Probability Basics

#### Small Samples

#### Distributions

#### Power

# Experimental Design

The term **experimental design** refers to a plan for
assigning experimental units to
treatment
conditions.

A good experimental design serves three purposes.

**Causation**. It allows the experimenter to make causal inferences about the relationship between independent variables and a dependent variable.**Control**. It allows the experimenter to rule out alternative explanations due to the confounding effects of extraneous variables (i.e., variables other than the independent variables).**Variability**. It reduces variability within treatment conditions, which makes it easier to detect differences in treatment outcomes.

## An Experimental Design Example

Consider the following hypothetical experiment. Acme Medicine is conducting an experiment to test a new vaccine, developed to immunize people against the common cold. To test the vaccine, Acme has 1000 volunteers - 500 men and 500 women. The participants range in age from 21 to 70.

In this lesson, we describe three experimental designs - a completely randomized design, a randomized block design, and a matched pairs design. And we show how each design might be applied by Acme Medicine to understand the effect of the vaccine, while ruling out confounding effects of other factors.

## Completely Randomized Design

The **completely randomized design** is probably the
simplest experimental design, in terms of data analysis and
convenience. With this design, participants are randomly assigned
to treatments. A completely randomized design for the Acme Experiment is
shown in the table below.

Treatment | |
---|---|

Placebo | Vaccine |

500 | 500 |

In this design, the experimenter randomly assigned participants to one of two treatment conditions. They received a placebo or they received the vaccine. The same number of participants (500) were assigned to each treatment condition (although this is not required). The dependent variable is the number of colds reported in each treatment condition. If the vaccine is effective, participants in the "vaccine" condition should report significantly fewer colds than participants in the "placebo" condition.

A completely randomized design relies on
randomization
to control for the effects of **lurking variables** variables. Lurking variables
are potential causal variables that were not included explicitly in the study. By randomly assigning subjects to treatments, the experimenter
assumes that, on averge, lurking variables will affect each treatment
condition equally; so any significant differences between conditions
can fairly be attributed to the independent variable.

## Randomized Block Design

With a **randomized block design**, the experimenter
divides participants into subgroups called **blocks**,
such that the variability within blocks is less than the
variability between blocks. Then, participants within each block are
randomly assigned to treatment conditions. Because this design
reduces variability and potential confounding, it produces a better
estimate of treatment effects. The table below shows a randomized block design for the
Acme experiment.

Gender | Treatment | |
---|---|---|

Placebo | Vaccine | |

Male | 250 | 250 |

Female | 250 | 250 |

Participants are assigned to blocks, based on gender. Then, within each block, participants are randomly assigned to treatments. For this design, 250 men get the placebo, 250 men get the vaccine, 250 women get the placebo, and 250 women get the vaccine.

It is known that men and women are physiologically different and react differently to medication. This design ensures that each treatment condition has an equal proportion of men and women. As a result, differences between treatment conditions cannot be attributed to gender. This randomized block design removes gender as a potential source of variability and as a potential confounding variable.

In this Acme example, the randomized block design is an improvement over the completely randomized design. Both designs use randomization to implicitly guard against confounding. But only the randomized block design explicitly controls for gender.

**Note 1:** In some blocking designs, individual participants may receive
multiple treatments. This is called using the participant
*as his own control*. Using the participant as his own control
is desirable in some experiments (e.g., research on learning or
fatigue). But it can also be a problem (e.g., medical studies where
the medicine used in one treatment might interact with the medicine
used in another treatment).

**Note 2:** Blocks perform a similar function in experimental design as
strata
perform in sampling. Both divide observations into
subgroups. However, they are not the same. Blocking is
associated with experimental design, and stratification is
associated with survey sampling.

## Matched Pairs Design

A **matched pairs design** is a special case of the
randomized block design. It is used when the experiment has
only two treatment conditions; and participants can be grouped
into pairs, based on one or more blocking variables. Then, within each
pair, participants are randomly assigned to different treatments. The table below shows a matched pairs design for the
Acme experiment.

Pair | Treatment | |
---|---|---|

Placebo | Vaccine | |

1 | 1 | 1 |

2 | 1 | 1 |

... | ... | ... |

499 | 1 | 1 |

500 | 1 | 1 |

The 1000 participants are grouped into 500 matched pairs. Each pair is matched on gender and age. For example, Pair 1 might be two women, both age 21. Pair 2 might be two women, both age 22, and so on. This design provides explicit control for two potential lurking variables - age and gender. (And randomization controls for effects of lurking variables that were not included explicitly in the design.)

## Test Your Understanding

**Problem**

Which of the following statements are true?

I. A completely randomized design offers no control for
lurking variables.

II. A randomized block design controls for the placebo effect.

III. In a matched pairs design, participants within each pair receive
the same treatment.

(A) I only

(B) II only

(C) III only

(D) All of the above.

(E) None of the above.

**Solution**

The correct answer is (E). In a
completely randomized design,
experimental units are randomly assigned to treatment conditions.
Randomization
provides some control for
lurking variables.
By itself, a
randomized block design
does not control for the
placebo effect.
To control for the placebo effect, the experimenter must include a
placebo in one of the treatment levels. In a
matched pairs design,
experimental units within each pair are assigned to *different*
treatment levels.

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