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Analysis of Variance is a statistical procedure much beloved and revered in psychology. In its most revered form it involves more than one variable with two or more levels of each variable. The simplest version of this most esteemed form is shown below where we have two independent variables, A and B. For each of these variables we have two values, A1 and A2 and B1 and B2. These are completely crossed yielding four experimental groups. Now, since we need to add, square and do similar violence to our dependent measure, it is most advisable to believe that your dependent variable is measuring something that has the same properties as a well-behaved domain such as the real numbers or at least the integers. In the case of the mental chronometry work, we are presumably in fine shape because the reaction time measure is a measure of good old physical time just like the physicists measure. We also should assume that the response measure has a random component associated with it; and this random component should have a more or less Gaussian distribution. If is also nice if real numbers (or at least integers) can be used to describe the levels of the independent variables. This is because we are going to use these values in the equations below....the terms such as ai and bj. All of these assumptions are probably rarely met in psychological experiments, but no one seems too really much care. Now notice in the figure below we have written a bunch of formulae and done some algebra on these formulae. In these formulae, Rij refers to the dependent variable or response to the treatment combination AiBj of the independent variables. If in our analysis of experimental data, the main effects for A and B are significant as well as the interaction of A and B, then all of the terms in these formula contribute to the prediction of the response. The terms in red represent the interaction terms. Intuitively, the interaction terms reflect the possibility that the response is influenced by the particular combination of values of the independent variables. |
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| But, if the interaction is non-significant, then these terms drop out and we are left with the table shown below. Here, the interactive terms have been dropped and you can see that a simple linear equation describes the way in which the response depends on the values of the independent variables. | ||
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| What is called the Additive Factors Method is simply the use of this feature of the analysis of variance model to test for statistical independence. That is, if the interaction terms are not significant, then the response does not depend on the particular combination of values of the independent variables. Thus, there is in a weak sense, now a method for testing the independence required by the subtractive method rather than simply assuming that independence holds. Namely, if the investigator has identified two stages of a mental processes; and, if the investigator believes that two independent variables have been idntified which affect the stages independently, then if an experiment establishes this statistical indpendence then the investigator has more confidence that the two stages are in fact independent stages of a mental process. | ||
Experimental Decomposition of Mental Processes |
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| © Charles F. Schmidt | ||