Implementing Clinical Research Using Factorial Designs: A Primer PMC

Table Of Content

• Effects and Interaction Plots
• Estimation of Factors Effects (in the Yates tradition)
• Contrasts, main effects and interactions
• Minitab Example for Centrifugal Contactor Analysis
• Selecting the Right Factors and Components in a Factorial Design: Design and Clinical Considerations
• Selecting Factors: Factor and Intervention Component Compatibility

You would measure combination effects of \(A\) and \(B\) (a1b1, a1b2, a2b1, a2b2). Since we have two factors, each of which has two levels, we say that we have a 2 x 2 or a 22 factorial design. Typically, when performing factorial design, there will be two levels, and n different factors. A main effects situation is when there exists a consistent trend among the different levels of a factor.

Effects and Interaction Plots

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For example, a researcher might choose to treat cell phone use as a within-subjects factor by testing the same participants both while using a cell phone and while not using a cell phone (while counterbalancing the order of these two conditions). But he or she might choose to treat time of day as a between-subjects factor by testing each participant either during the day or during the night (perhaps because this only requires them to come in for testing once). In general, when dummy coding is used, the effects corresponding to main effects in a standard ANOVA are similar to simple effects, i.e., the effect of a variable when all other variables in the model are set to the level coded as zero. For instance, in the design depicted in Table 1, the effect of Extended Medication would be reflected by the average effect of all Extended Medication conditions (1–16) versus the average effect of all Standard Medication conditions (17–32). With effect coding, when the experimental conditions have equal (or nearly equal) numbers of participants, the main effect of a factor does not reflect the effects of interaction effects that may be present in the data. Observing the effects of at least two independent variables is a more practical and economical approach.

Estimation of Factors Effects (in the Yates tradition)

So, there is an effect of 3 units for being tired in the 5 hour condition. Clearly, the size of the effect for being tired depends on the levels of the time since last meal variable. To continue with more examples, let’s consider an imaginary experiment examining what makes people hangry. It’s when you become highly irritated and angry because you are very hungry…hangry. I will propose an experiment to measure conditions that are required to produce hangriness. The pretend experiment will measure hangriness (we ask people how hangry they are on a scale from 1-10, with 10 being most hangry, and 0 being not hangry at all).

Contrasts, main effects and interactions

One nice feature of the Yates notation is that every column has an equal number of pluses and minuses so these columns are contrasts of the observations. This column has four pluses and four minuses, therefore, the A effect is a contrast. Since this is a first order, linear model, the coefficients can be combined with the operating parameters to determine equations.

Minitab Example for Centrifugal Contactor Analysis

Even if you are primarily interested in the relationship between an independent variable and one primary dependent variable, there are usually several more questions that you can answer easily by including multiple dependent variables. Factorial design is a type of research methodology that allows for the investigation of the main and interaction effects between two or more independent variables and on one or more outcome variable(s). Higher order interactions can reflect complex patterns that defy easy interpretation. However, they also reveal information that is unique and of potentially great value. Further, this problem is reduced if factorial designs are used as screening experiments, whose purpose is not to identify the single best combination of ICs (Collins et al., 2009).

Types of Factorial Designs

This averts the need to expend time and resources for separate experiments. Furthermore, collecting data for different combinations of conditions enables researchers to make a variety of assessments, including main and interaction effects. First, non-manipulated independent variables are usually participant background variables (self-esteem, gender, and so on), and as such, they are by definition between-subjects factors. For example, people are either low in self-esteem or high in self-esteem; they cannot be tested in both of these conditions.

In other words, sunlight and watering frequency do not affect plant growth independently. Rather, there is an interaction effect between the two independent variables. We've used Minitab to create the factorial design and added the data from the experiment into the Minitab worksheet. First, we will produce a normal probability plot of the effects for this data with all terms included in a full model.

By doing this, psychologists can see if changing the independent variable results in some type of change in the dependent variable. This framework can be generalized to, e.g., designing three replicates for three level factors, etc. The columns for A, B and C represent the corresponding main effects, as the entries in each column depend only on the level of the corresponding factor. 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. A contrast in cell means is a linear combination of cell means in which the coefficients sum to 0. Contrasts are of interest in themselves, and are the building blocks by which main effects and interactions are defined.

Although she found that creativity was unaffected by the ambient odor, she found that people’s moods were lower in the dimethyl sulfide condition, and that their perceived health was greater in the lemon condition. Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level.

For instance, to examine the main effect for food category, the favorability ratings of ice cream would be compared against soup. Experiments that include more than one independent variable in which each level of one independent variable is combined with each level of the others to produce all possible combinations. But the two 2-way interactions effects combined are no longer significant, and individually, the interactions are not significant here either. So, the log transformation which improved the unequal variances pulled the higher responses down more than the lower values and therefore resulted in more of a parallel shape.

Recall that in a between-subjects single factor design, each participant is tested in only one condition. In sum, unless the investigator has access to clearly relevant data (preferably from factorial experiments) s/he should have strong concerns about how the elements in a treatment (the ICs) might interact. However, factorial experiments do not permit strong inferences about how well a particular grouping of components (occurring as levels of different factors) will work as an integrated treatment as compared to a control. After all, only a small portion of a sample in a factorial experiment will get a particular set of components (e.g., in the design depicted in Table 1 only 1/32 of the N will get a particular combination of components).

Introverts perform better than extraverts when they have not ingested any caffeine. But extraverts perform better than introverts when they have ingested 4 mg of caffeine per kilogram of body weight. Chakraborty et al., (Chakraborty et al., 2009) noted that factorial designs may not perform optimally for intervention selection in cases where there are weak main effects, but relatively strong interaction effects. Unfortunately, this situation may be a fairly common occurrence in factorial experiments of clinical interventions (e.g., Cook et al., 2016; Piper et al., 2016; Schlam et al., 2016).