When an experiment test all possible combinations of more than one independent variable it is often referred to as?

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A factorial design contains two or more independent variables and one dependent variable. The independent variables, often called factors, must be categorical. Groups for these variables are often called levels. The dependent variable must be continuous, measured on either an interval or a ratio scale.

Suppose a researcher is interested in determining if two categorical variables (treatment condition and gender) affect a continuous variable (achievement). The researcher decides to use a factorial design because he or she wants to examine population group means. A factorial analysis of variance will allow him or her to answer three questions. One question concerns the main effect of treatment: Do average achievement scores differ significantly across treatment conditions? Another question concerns the main effect of gender: Does the average achievement ...

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Variations on Experimental Designs
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Single-Case Experimental Designs
Single-case experimental design uses experimental methodology to focus on only one subject. This design is distinct from case study methodology, which also focuses on one individual, because single-case experimental designs use the same systematic procedures as other experimental designs. The researcher sets up the study to manipulate an independent variable (or variables) and to measure how a dependent variable responds to changes in the independent variable. This design has the experimental benefit of a controlled comparison, because the individual subject serves as his or her own control by participating in all of the conditions.

In a reversal design, the individual’s behavior of interest is measured at baseline, then the intervention is implemented and the behavior is measured again. Finally, the intervention is withdrawn and the behavior of interest is measured again. This sort of reversal design is sometimes referred to as an ABA design.

The ABAB design offers the same benefits as a reversal design, but involves one additional iteration of the intervention. A multiple baseline design uses a varying time schedule that helps determine if the treatment itself (as opposed to just the passage of time) is actually leading to the change.

Advantages of Single-Case Experimental Designs
Single-case design requires studying only one individual, which is obviously easier and more convenient than assembling a large group of participants. This type of design also retains the powerful advantage of experimental control, allowing you to collect evidence to determine causal relationships.

Disadvantages of Single-Case Experimental Designs
Because single-case designs focus on a single subject, it is difficult (if not impossible) to draw any conclusions about a larger population. Multiple observations and exposures to the intervention itself may also affect the responses of your participant. There are also ethical concerns regarding the withdrawal of treatment in single-case designs.

Quasi-Experimental Designs
A quasi-experimental design is partially experimental; it manipulates an independent variable but perhaps does not have a full set of other experimental controls, such as random assignment. Conversely, a study can be quasi-experimental if it has some experimental controls but does not fully manipulate an independent variable.

Advantages of Quasi-Experimental Designs
Because quasi-experimental methodology does not have as many requirements as a full experimental design, researchers have greater freedom, both in how they set up their methods and in the topics they choose to study. Quasi-experimental research designs offer good options for studying a number of topics that pose practical or ethical constraints preventing full-fledged experimental studies.

Disadvantages of Quasi-Experimental Designs
Quasi-experimental designs will not provide as much clarity about cause-and-effect relations as full experimental designs. In some cases, a quasi-experimental design can be indistinguishable from a correlational design.

Factorial Designs
A factorial design refers to any experimental design that has more than one independent variable. Because a factorial design looks at multiple independent variables simultaneously, it gives you the ability to look not only at the effects of single variables in isolation, but also at the effects of combinations of variables. Therefore, factorial designs allow us to examine the complexity of the real world in an experimental paradigm.

Basic Factorial Designs: The 2 x 2
A 2 x 2 design has four possible conditions. Each condition (often referred to as a cell) represents a unique combination of the levels of the independent variables.

Experimental Independent Variables vs. Participant Variables
Each factor can either be a traditional independent variable that is manipulated by the experimenter, or a participant variable that is not manipulated by the experimenter.

Main Effects and Interactions
A main effect refers to the effect of a single independent variable on a dependent variable. An interaction refers to the joint effect of multiple independent variables considered in combination. Testing for an interaction allows a researcher to examine whether the effects of one variable on another variable (the dependent variable) are conditional on the other remaining variables. Main effects and interactions can occur in a number of combinations. You can have multiple main effects and an interaction; you can have only main effects (or a single main effect) and no interaction; or you can have no main effects but still have an interaction. When significant interactions are present, they substantially modify how one might frame (or think about) the importance of the main effect.

An Example of a Between-Subjects Factorial Design
Michelene Chi’s work, introduced in Chapter 4, is an example of a 2 x 2 between-subjects factorial design. Chi was interested in determining whether age or knowledge (expertise) was the central driving force for cognitive development in the area of memory recall. To determine which was more important, she pitted child chess experts against college-age novices in a task to recall either pieces on a chessboard or a list of numbers. The first factor, memory task, had two levels— either chess pieces or the number list. The second factor, maturation/expertise, also had two levels—either child expert or adult novice. Chi’s findings indicated that child experts performed at a superior level to adult novices when completing the chessboard task, but adult novices outperformed child experts on the number list task. The findings serve as an elegant example of an interaction.

An Example of a Within-Subjects Factorial Design
In contrast to the between-subjects factorial design, within-subjects factorial designs involve conditions where the groups for each level of a factor are not independent of each other, but rather each group is exposed to each level of the factor. Imagine that you are interested in the effects of caffeine dosage (high or low) on two different memory tasks—a visual recall task and an auditory recall task. This could be set up as a 2 (high vs. low caffeine dosage) x 2 (visual vs. auditory memory task) within-subjects design, so that your research subjects participate in both the auditory and visual recall tasks, probably on different days, and are given both high and low dosages of caffeine in combination with the recall tasks.

An Example of a Mixed Factorial Design
In the most basic version of a mixed design, one independent variable is set up as between-subjects, and another is set up as within-subjects. Participants would be randomly assigned to one of the two conditions of the first independent variable (the between-subjects independent variable), and each participant would then be exposed to both conditions of the second independent variable (the within-subjects independent variable). As a researcher you get the benefits of a “within” comparison, and the benefits of a “between” comparison.