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CHAPTER 8: Complex Designs 251The simplest possible experiment involves one independent variable manipulatedat two levels. Similarly, the simplest possible complex design experimentinvolves two independent variables, each with two levels. Complexdesigns are identified by specifying the number of levels of each of the independentvariables in the experiment. A 2 2 (which is read “2 by 2”) design, then,identifies the most basic complex design. Conceptually, there is an unlimitednumber of complex designs because any number of independent variables canbe studied and each independent variable can have any number of levels. Inpractice, however, it is unusual to find experiments involving more than four orfive independent variables, and two or three is more typical. Regardless of thenumber of independent variables, the number of conditions in a complex designcan be determined by multiplying the number of levels of the independentvariables. For example, if there are two independent variables with each havingtwo levels (a 2 2 design), there are four conditions. In a 3 3 design there aretwo independent variables with three levels each, so there are nine conditions.In a 3 4 2 design there are three independent variables with three, four, andtwo levels, respectively, and a total of 24 conditions. The primary advantage ofall complex designs is the opportunity they provide for identifying interactionsbetween independent variables.Understanding the 2 2 design lays a foundation for understanding complexdesigns. The 2 2 design barely scratches the surface, however, when itcomes to tapping the potential of complex designs. Complex designs can beextended beyond the 2 2 design in one of two ways. Researchers can add levelsto one or both of the independent variables in the design, yielding designssuch as the 3 2, the 3 3, the 4 2, the 4 3, and so on. Researchers can alsobuild on the 2 2 design by increasing the number of independent variables inthe same experiment. The number of levels of each variable can range from 2to some unspecified upper limit. The addition of a third or fourth independentvariable yields designs such as the 2 2 2, the 3 3 3, the 2 2 4, the2 3 3 2, and so on.First we will illustrate main effects and interaction effects in the complexdesign by working through an example of a 2 2 design.An Example of a 2 2 DesignThe nature of main effects and interaction effects is essentially the same inall complex designs, but they can be seen most easily in a 2 2 design. Foran example of this design we will draw from the rich literature in the fieldof psychology and law. There are few areas in the legal arena that have goneuntouched by social scientists. Jury selection, the nature and credibility ofeyewitnesses, race of the defendant, jury decision making, and attorney argumentsare only some of the many topics investigated by researchers. Recallthat in Chapter 6 we discussed a research study by Ceci (1993) on children’seyewitness testimony. In the study to be discussed here the researchers lookedat variables that might lead to false confessions from suspects brought in forquestioning.Kassin, Goldstein, and Savitsky (2003) used a 2 2 design to investigatewhether interrogators’ expectations regarding a suspect’s guilt or innocence