Experimental Design

One-Factor Designs

It is necessary to distinguish between the two-level and multilevel versions of the one-factor design because different statistical procedures are used to analyze their data. Specifically, data from a one-factor, two-level design are analyzed with the t test. The statistical question is whether or not the difference between the means of the two conditions can be explained by chance influences (see Row a of Table 2).

Some version of one-way analysis of variance would have to be used when there are three or more levels to the independent variable (see Row b of Table 2). The statistical question is whether or not the variance based on three or more test conditions is larger than that based on chance.

Table 1 Basic Structure of an Experiment

With quantitative factors (e.g., dosage) as opposed to qualitative factors (e.g., type of drug), [Page 448]one may ascertain trends in the data when a factor has three or more levels (see Row b). Specifically, a minimum of three levels is required for ascertaining a linear trend, and a minimum of four levels for a quadratic trend.

Table 2 Genres of Experimental Designs in Terms of Treatment Combinations

Two-Factor Designs

Suppose that Factors A (e.g., room color) and B (e.g., room size) are used together in an experiment. Factor A has m levels; its two levels are a1 and a2 when m = 2. If Factor B has n levels (and if n = 2), the two levels of B are b1 and b2. The experiment has a factorial design when every level of A is combined with every level of B to define a test condition or treatment combination. The size of the factorial design is m by n; it has m-by-n treatment combinations. This notation may be generalized to reflect factorial design of any size.

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