Introductory Statistics: Concepts, Models, and Applications
David W. Stockburger

## EXPERIMENTAL DESIGNS

Before an experiment is performed, the question of experimental design must be addressed. Experimental design refers to the manner in which the experiment will be set up, specifically the way the treatments were administered to subjects. Treatments will be defined as quantitatively or qualitatively different levels of experience. For example, in an experiment on the effects of caffeine, the treatment levels might be exposure to different amounts of caffeine, from 0 to .0375 mg. In a very simple experiment there are two levels of treatment; none, called the control condition, and some, called the experimental condition.

The type of analysis or hypothesis test used is dependent upon the type of experimental design employed. The two basic types of experimental designs are crossed and nested.

### CROSSED DESIGNS

In a crossed design each subject sees each level of the treatment conditions. In a very simple experiment, such as one that studies the effects of caffeine on alertness, each subject would be exposed to both a caffeine condition and a no caffeine condition. For example, using the members of a statistics class as subjects, the experiment might be conducted as follows. On the first day of the experiment, the class is divided in half with one half of the class getting coffee with caffeine and the other half getting coffee without caffeine. A measure of alertness is taken for each individual, such as the number of yawns during the class period. On the second day the conditions are reversed; that is, the individuals who received coffee with caffeine are now given coffee without and vice-versa. The size of the effect will be the difference of alertness on the days with and without caffeine.

The distinguishing feature of crossed designs is that each individual will have more than one score. The effect occurs within each subject, thus these designs are sometimes referred to as WITHIN SUBJECTS designs.

Crossed designs have two advantages. One, they generally require fewer subjects, because each subject is used a number of times in the experiment. Two, they are more likely to result in a significant effect, given the effects are real.

Crossed designs also have disadvantages. One, the experimenter must be concerned about carry-over effects. For example, individuals not used to caffeine may still feel the effects of caffeine on the second day, even though they did not receive the drug. Two, the first measurements taken may influence the second. For example, if the measurement of interest was score on a statistics test, taking the test once may influence performance the second time the test is taken. Three, the assumptions necessary when more than two treatment levels are employed in a crossed design may be restrictive.

### NESTED DESIGNS

In a nested design, each subject receives one, and only one, treatment condition. The critical difference in the simple experiment described above would be that the experiment would be performed on a single day, with half the individuals receiving coffee with caffeine and half without receiving caffeine. The size of effect in this case is determined by comparing average alertness between the two groups.

The major distinguishing feature of nested designs is that each subject has a single score. The effect, if any, occurs between groups of subjects and thus the name BETWEEN SUBJECTS is given to these designs.

The relative advantages and disadvantages of nested designs are opposite those of crossed designs. First, carry over effects are not a problem, as individuals are measured only once. Second, the number of subjects needed to discover effects is greater than with crossed designs.

Some treatments by their nature are nested. The effect of sex, for example, is necessarily nested. One is either a male or a female, but not both. Current religious preference is another example. Treatment conditions which rely on a pre-existing condition are sometimes called demographic or blocking factors.