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The research designs we have considered so far have been simple—focusing on a question about one variable or about a statistical relationship between two variables. But in many ways, the complex design of this experiment undertaken by Schnall and her colleagues is more typical of research in psychology. Fortunately, we have already covered the basic elements of such designs in previous chapters. In this chapter, we look closely at how and why researchers combine these basic elements into more complex designs. We start with complex experiments—considering first the inclusion of multiple dependent variables and then the inclusion of multiple independent variables. The main point we want you take away is that factorial designs are extremely useful for determining things that cause effects to change.
5.6 Interaction between Distraction and Reward
I imagine the data could look something the following bar graph. The simplest way to understand a main effect is to pretend that the other independent variables do not exist. If you do this, then you simply have a single-factor design, and you are asking whether that single factor caused change in the measurement. For a 2x2 experiment, you do this twice, once for each independent variable. 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.
8 Real Data
None of the levels were specified as they appear as -1 and 1 for low and high levels, respectively. The following Yates algorithm table was constructed using the data from the interaction effects section. Since the main total factorial effect for AB is non-zero, there are interaction effects. This means that it is impossible to correlate the results with either one factor or another; both factors must be taken into account. In another example, consider how different levels of stress could interact with the type of exercise performed.
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A positive effect means that as RPM increases, the number of theoretical stages increases. Whereas a negative effect indicates that as RPM increases, the wt% methanol in biodiesel decreases. Fortunately for operation with the POD, these are desired results. When choosing operating conditions for the POD, RPM should be maximized to minimize the residual methanol in biodiesel and maximize the number of theoretical stages achieved. Analysis was performed on the DOE study to determine the effects of each factor on the responses. Only first order terms were included in the analysis to create a linear model.
Three Effects
Nature, he suggests, will best respond to "a logical and carefully thought out questionnaire". We showed you how to analyse a repeated measures 2x2 design with paired samples-tests, and what an ANOVA table would look like if you did this in R. We also went through, by hand, the task of calculating an ANOVA table for a 2x2 between subjects design. As a result, the difference in performance (the Stroop effect) should be fairly small (if you have “good” selective attention in this task). They will not ignore the words, causing them to be relatively fast when the word helps, and relatively slow when the word mismatches. In this case, the target information that you need to pay attention to is the color, not the word.
Contrasts are of interest in themselves, and are the building blocks by which main effects and interactions are defined. Other terms for "treatment combinations" are often used, such as runs (of an experiment), points (viewing the combinations as vertices of a graph, and cells (arising as intersections of rows and columns). The Stroop effect is an example of a well-known phenomena.
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Minitab is especially useful for creating and analyzing the results for DOE studies. It is possible to create factorial, response surface, mixture, and taguchi method DOEs in Minitab. The general method for creating factorial DOEs is discussed below. The number of IVs is represented in the number of numbers. You could have just as easily made IV1 the reward and IV2 the Distraction, and the table would still be correct.
5: Simple analysis of 2x2 repeated measures design
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The authors weren’t interested if people are in general faster when they stand. They wanted to know if their selective attention would improve when they stand vs when they sit. They were most interested in whether the size of the Stroop effect (difference between incongruent and congruent performance) would be smaller when people stand, compared to when they sit. To answer this question, we need to look at the interaction effect. The figure shows a big difference in the mean number of difference spotted.
This is less clear because the effect is smaller so it is harder to see. You can look at the red bars first and see that the red bar for no-shoes is slightly smaller than the red bar for shoes. The green bar for no-shoes is slightly smaller than the green bar for shoes. Some questions to ask yourself are 1) can you identify the main effect of wearing shoes in the figure, and 2) can you identify the main effet of wearing hats in the figure. Both of these main effects can be seen in the figure, but they aren’t fully clear. To find the main effect of the shoes manipulation we want to find the mean height in the no shoes condition, and compare it to the mean height of the shoes condition.
Line graphs are also appropriate when representing measurements made over a time interval (also referred to as time series information) on the x-axis. In principle, factorial designs can include any number of independent variables with any number of levels. For example, an experiment could include the type of psychotherapy (cognitive vs. behavioral), the length of the psychotherapy (2 weeks vs. 2 months), and the sex of the psychotherapist (female vs. male). This would be a 2 x 2 x 2 factorial design and would have eight conditions.
When multiple dependent variables are different measures of the same construct - especially if they are measured on the same scale - researchers have the option of combining them into a single measure of that construct. Recall that Schnall and her colleagues were interested in the harshness of people’s moral judgments. To measure this construct, they presented their participants with seven different scenarios describing morally questionable behaviors and asked them to rate the moral acceptability of each one.
Now you should have a good understanding of how to design and conduct a two-by-two factorial experiment, as well as how to statistically analyze the results common to these studies. You’ve also been introduced to several examples where the use of a two-by-two factorial design is beneficial. Perhaps in another situation, a researcher is interested in how students perform on an on-screen versus a written test, whereby participants’ gender may influence performance. Once again, a two-by-two factorial design is necessary for simultaneous examination.
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