A factorial design in research involves manipulating two or more independent variables simultaneously to examine their effects on a single outcome measure. This approach allows researchers to study complex relationships where multiple factors may influence a result. A mixed factorial design is a specific structure that incorporates two different methods of participant assignment within the same study. The term “mixed” refers to the inclusion of both independent groups and repeated measures elements in the experimental setup. This structure allows researchers to gain a nuanced understanding of how different types of variables influence behavior or biological processes.
Defining the Design Components
The independent variables manipulated by the researcher are known as factors, and a study must contain at least two factors to be considered a factorial design. Each factor is tested at different values or conditions, which are called levels. For instance, a factor like “drug dosage” might have levels such as 5mg, 10mg, and a placebo.
The notation describing the design is based on the number of factors and the number of levels for each; a “2×3” design has two factors, one with two levels and one with three. The final component is the dependent variable, which represents the outcome measure that the researcher records. This outcome is typically a quantitative score, such as reaction time, blood pressure, or the number of correct answers on a test.
The Combination of Between-Subjects and Within-Subjects Factors
The “mixed” nature of this design comes from how participants are assigned across the levels of the various factors. A mixed factorial design requires at least one between-subjects factor and at least one within-subjects factor. In a between-subjects factor, different, unique individuals are assigned to each level of that factor. For example, if a researcher is comparing two different intervention programs, one group of participants receives Program A, and a separate, independent group receives Program B.
The second component is the within-subjects factor, often called a repeated measures factor, where the same participants are exposed to all levels of that variable. Time is a common within-subjects factor, such as measuring a participant’s performance before an intervention, immediately after, and then three months later. In this case, the same individual acts as their own comparison across the different time points.
Consider a study examining the effectiveness of two teaching methods, Method X and Method Y, on student performance measured across three distinct exams. The teaching method is the between-subjects factor; one group is taught with Method X, and a separate group with Method Y. The three exams (Exam 1, Exam 2, Exam 3) represent the within-subjects factor, as every student takes all three tests. This structure allows the researcher to compare the overall performance of the two groups while tracking how performance changes over time.
Interpreting Main Effects and Interactions
Data from a mixed factorial design is typically analyzed using a specialized statistical test known as a Mixed Analysis of Variance. This analysis breaks down the variability in the dependent variable into three primary results for a two-factor design. The first result is the main effect of the between-subjects factor, which assesses whether there is an overall difference between the groups, averaging across all levels of the repeated measures. This answers the question of whether Method X led to better average performance than Method Y, regardless of which specific exam was taken.
The second result is the main effect of the within-subjects factor, which examines whether there is an overall change across the repeated measures, ignoring which group the participants belonged to. This determines if, across all students, performance significantly changed from Exam 1 to Exam 3. The most informative result is the interaction effect, which shows if the effect of one factor depends on the level of the other factor.
The interaction specifically addresses whether the pattern of change over time (the within-subjects factor) differs between the two groups (the between-subjects factor). For instance, the analysis might reveal that students in the Method X group showed a steep improvement in scores across the three exams, while students in the Method Y group showed little to no change. This suggests that the effect of the exams (time) is not consistent across all levels of the teaching method factor. An interaction finding often qualifies the interpretation of the main effects, showing that one factor’s influence is conditional upon the other.
When to Utilize a Mixed Factorial Design
Researchers choose a mixed factorial design when their research question involves tracking changes over time while simultaneously comparing distinct groups or conditions. The design is suitable for longitudinal studies where an intervention or treatment is applied to one group but not another, such as a drug trial compared against a placebo group. By including a within-subjects factor, researchers can effectively control for the inherent individual differences between participants, which increases the statistical power to detect real effects.
This design is effective when studying populations naturally separated by a fixed characteristic, such as comparing the change in cognitive function over time between a clinical group and a healthy control group. The ability to compare how different groups respond to the same set of repeated conditions, such as multiple training sessions or various stimuli, makes the mixed factorial approach a flexible tool. It allows for the efficient study of both group comparisons and individual change within a single experimental framework.