However, the term “independent variable” refers to the relationship between the manipulated variable and the measured variable. Remember, “independent variables” are manipulated independently from the measured variable. Specifically, the levels of any independent variable do not change because we take measurements. Instead, the experimenter changes the levels of the independent variable and then observes possible changes in the measures. Interactions occur when the effect of an independent variable depends on the levels of the other independent variable.
2 Purpose of Factorial Designs
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. Remember, the posture main effect collapses over the means in the congruency condition. We are measuring a general effect of sitting vs standing on overall reaction time. The table shows that people were a little faster overall when they were standing, compared to when they were sitting.
x 3 designs
But there are also plausible third variables that could explain this relationship. It could be, for example, that people who are lower in SES tend to be more religious and that it is their greater religiosity that causes them to be more generous. Or it could be that people who are lower in SES tend to come from certain ethnic groups that emphasize generosity more than other ethnic groups.
Interaction Effects
Instead, let's find the pairwise mean differences, and compare them to a critical value of 14.86; any mean differences that have an absolute value larger than 14.86 are statistically significantly different. This is important because, as always, one must be cautious about inferring causality from correlational studies because of the directionality and third-variable problems. For example, a main effect of participants’ moods on their willingness to have unprotected sex might be caused by any other variable that happens to be correlated with their moods. Main effects occur when the levels of an independent variable cause change in the measurement or dependent variable.
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5 Simple analysis of 2x2 repeated measures design
Hedonic products tended to gain more favorable attitudes when a wide shot image was accompanied by emotion inducing advertisements. Inverse findings were observed for utilitarian products in this 2 x 2 x 2 Factorial ANOVA, otherwise known as a three-way ANOVA. We'll complete an ANOVA Summary to whether the differences in the means are likely or unlikely to be due to chance.
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Two additional points about factor analysis are worth making here. Factor analysis does not tell us that people are either extraverted or conscientious or that they like either “reflective and complex” music or “intense and rebellious” music. Instead, factors are constructs that operate independently of each other. So people who are high in extraversion might be high or low in conscientiousness, and people who like reflective and complex music might or might not also like intense and rebellious music.
1.1 2x2 Designs
We could write this in reverse, and ask if the effect of IV1 (whether there is a difference between the levels of IV1) changes across the levels of IV2. However, just because we can write this two ways, does not mean there are two interactions. We’ll see in a bit, that no matter how do the calculation to see if the difference scores–measure of effect for one IV– change across the levels of the other IV, we always get the same answer. Similarly, there is only one interaction for a 3x3, because there again we only have two IVs (each with three levels). Only when we get up to designs with more than 2 IVs, do we find more possible interactions. If the IVs are labelled A, B, and C, then we have three 2-way interactions (AB, AC, and BC), and one three-way interaction (ABC).
Notice we didn’t say the dependent variables they are measuring, we are now talking about something called effects. Effects are the change in a measure caused by a manipulation. You get an effect, any time one IV causes a change in a DV.
Note that only four experiments were required in factorial designs to solve for the eight values in A and B. A main effects situation is when there exists a consistent trend among the different levels of a factor. From the example above, suppose you find that as dosage increases, the percentage of people who suffer from seizures increases as well. You also notice that age does not play a role; both 20 and 40 year olds suffer the same percentage of seizures for a given amount of CureAll. From this information, you can conclude that the chance of a patient suffering a seizure is minimized at lower dosages of the drug (5 mg). The second graph illustrates that with increased drug dosage there is an increased percentage of seizures, while the first graph illustrates that with increased age there is no change in the percentage of seizures.
They predicted smaller Stroop effects when people were standing up and doing the task, compared to when they were sitting down and doing the task. Overall now, we are thinking of our distraction effect (the difference in performance between the two conditions) as the important thing we want to measure. We then might want to know how to make people better at ignoring distracting things.
People found 5 differences on average when they were distracted, and 10 differences when they were not distracted. We labelled the figure, “The distraction effect”, because it shows a big effect of distraction. The effect of distraction is a mean of 5 spot the differences.
But a multiple regression analysis including both income and happiness as independent variables would show whether each one makes a contribution to happiness when the other is taken into account. Research like this, by the way, has shown both income and health make extremely small contributions to happiness except in the case of severe poverty or illness [Die00]. When an experiment includes multiple dependent variables, there is again a possibility of carryover effects. So the order in which multiple dependent variables are measured becomes an issue. One approach is to measure them in the same order for all participants—usually with the most important one first so that it cannot be affected by measuring the others. Another approach is to counterbalance, or systematically vary, the order in which the dependent variables are measured.
In many studies, the primary research question is about an interaction. The study by Brown and her colleagues was inspired by the idea that people with hypochondriasis are especially attentive to any negative health-related information. 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.
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