What is a factorial trial? Epidemiology and Psychiatric Sciences

Table Of Content

• 2.5. Graphing the Results of Factorial Experiments¶
• Book traversal links for Lesson 5: Introduction to Factorial Designs
• 5.1. Correlational Studies With Factorial Designs¶
• Advantages of a Factorial Design
• Assigning Participants to Conditions
• How to Analyze a 2×2 Factorial Design
• How to Deal with a 2n Factorial Design

While more research on IC interactions is surely needed, our research has consistently found such interactions (Cook et al., 2016; Fraser et al., 2014; Piper et al., 2016; Schlam et al., 2016). Thus, it might be difficult in many cases to assume conditions that would justify the use of a fractional factorial design. This table reflects the combinations of intervention components (conditions) that is generated by the crossing of two levels of five factors in a factorial design (Schlam et al. 2016). The table shows that the crossing of the five factors generates 32 unique combinations of intervention components; participants in the experiment were randomly assigned to one of these conditions so that approximately 1/32 of the N was assigned to each condition. One of the big advantages of factorial designs is that they allow researchers to look for interactions between independent variables.

2.5. Graphing the Results of Factorial Experiments¶

Suppose that you are looking to study the effects of hours slept (A), hours spent with significant other (B), and hours spent studying (C) on a students exam scores. You are given the following table that relates the combination of these factors and the students scores over the course of a semester. Use the Yates method in order to determine the effect each variable on the students performance in the course.

Book traversal links for Lesson 5: Introduction to Factorial Designs

One might think of this as interventions “competing” for a limit subset of participants who are actually capable of change or improvement; in a sense this subsample would be spread across multiple active intervention components. Using this design, all the possible combinations of factor levels can be investigated in each replication. Although several factors can affect the variable being studied in factorial experiments, this design specifically aims to identify the main effects and the interaction effects among the different factors.

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5.1. Correlational Studies With Factorial Designs¶

All rights are reserved, including those for text and data mining, AI training, and similar technologies. The main effect of a factor can be defined as the change produced as a result of a change in the level of the factor. Onwards, the minus (−) and plus (+) signs will indicate whether the factor is run at a low or high level, respectively. The last four column vectors belong to the A × B interaction, as their entries depend on the values of both factors, and as all four columns are orthogonal to the columns for A and B. Frank Yates made significant contributions, particularly in the analysis of designs, by the Yates analysis.

Advantages of a Factorial Design

In the middle panel, independent variable “B” has a stronger effect at level 1 of independent variable “A” than at level 2. This is like the hypothetical driving example where there was a stronger effect of using a cell phone at night than during the day. In the bottom panel, independent variable “B” again has an effect at both levels of independent variable “A”, but the effects are in opposite directions. One example of a crossover interaction comes from a study by Kathy Gilliland on the effect of caffeine on the verbal test scores of introverts and extraverts [Gil80]. Introverts perform better than extraverts when they have not ingested any caffeine.

Some were negative health-related words (e.g., tumor, coronary), and others were not health related (e.g., election, geometry). The result of this study was that the participants high in hypochondriasis were better than those low in hypochondriasis at recalling the health-related words, but they were no better at recalling the non-health-related words. Since factorial designs have more than one independent variable, it is also possible to manipulate one independent variable between subjects and another within subjects.

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How to Analyze a 2×2 Factorial Design

For example, the entries in the B column follow the same pattern as the middle component of "cell", as can be seen by sorting on B. In the 2 × 3 example, for instance, the pattern of the A column follows the pattern of the levels of factor A, indicated by the first component of each cell. Treatment combinations are denoted by ordered pairs or, more generally, ordered tuples.

For example, one reason that extraversion and the other Big Five operate as separate factors is that they appear to be controlled by different genes [PDMM08]. Main effects occur when the levels of an independent variable cause change in the measurement or dependent variable. There is one possible main effect for each independent variable in the design. When we find that independent variable did influence the dependent variable, then we say there was a main effect. When we find that the independent variable did not influence the dependent variable, then we say there was no main effect.

Another common approach to including multiple dependent variables is to operationalize and measure the same construct, or closely related ones, in different ways. Imagine, for example, that a researcher conducts an experiment on the effect of daily exercise on stress. The dependent variable, stress, is a construct that can be operationalized in different ways. For this reason, the researcher might have participants complete the paper-and-pencil Perceived Stress Scale and also measure their levels of the stress hormone cortisol. If the researcher finds that the different measures are affected by exercise in the same way, then he or she can be confident in the conclusion that exercise affects the more general construct of stress.

We have already seen that factorial experiments can include manipulated independent variables or a combination of manipulated and non-manipulated independent variables. But factorial designs can also consist exclusively of non-manipulated independent variables, in which case they are no longer experiments but correlational studies. Consider a hypothetical study in which a researcher measures two variables. The research then also measure participants’ willingness to have unprotected sexual intercourse. This study can be conceptualized as a 2 x 2 factorial design with mood (positive vs. negative) and self-esteem (high vs. low) as between-subjects factors. This design can be represented in a factorial design table and the results in a bar graph of the sort we have already seen.

Ignoring the first row, look in the last stage and find the variable that has the largest relative number, then that row indicates the MAIN TOTAL EFFECT. The Main Total Effect can be related to input variables by moving along the row and looking at the first column. To get a mean factorial effect, the totals needs to be divided by 2 times the number of replicates, where a replicate is a repeated experiment.