# ANALYSIS OF VARIANCE AND REGRESSION TESTS

Much of psychological research depends upon the general linear model to describe the statistical relationship between a dependent variable and one or more predictor variables. ANOVA and regression analyses are variations of this model. Underlying these analyses is the expectation that a large part of the variability observed in the dependent variable should be explained or accounted for by the predictor variables.

Within this statistical framework, one can ask a number of important questions about the relationships among the variables of interest. In particular, one can estimate to what extent the dependent variable is influenced by changes in the predictor variables. Workload can serve as either the dependent variable or a predictor variable, depending upon the research questions of interest.

In most cases, workload on any task is expected to be a single number that characterizes an individual’s response to a task. It is usually estimated by the mean ICA computed over all seconds of the task.

**Simple analyses.** A simple study would involve two independent groups of subjects who are expected to be different on some factor of interest. For example, the subjects might be novices and experts in a specified domain. Each subject would respond to the same identical task, and the mean ICA would be computed across the duration of the task for each one. A statistical test for this case would be a t-test or a one-way ANOVA to determine if the two groups had different levels of workload.

Several variations of this study are possible. One variation looks at the workload of just a single group of subjects across two or more tasks. All subjects respond to the same tasks, with mean ICA computed for each subject on each task. The statistical analysis is a one-factor repeated measures analysis of variance to determine whether workload varied by task.

The most common variation is based on both multiple groups and multiple tasks. In this case, several independent groups of subjects respond to a set of tasks. The mean ICA is computed for each subject on each task. The statistical analysis is now a mixed model analysis of variance, with a between-subjects factor of group and a within-subjects factor of task. Three statistical tests yield a test of the main effect of group, the main effect of task, and the interaction between group and task.

**Analyses with multiple predictor variables.** When more factors are to be included in the analysis, you may want to use a regression approach. For instance, you might want to include variables such as experience, age, education, or gender. These variables could be categorical or continuous.

A simple study here would be based on a single cognitive task. All subjects perform the same task. Each subject has a number of different characteristics (i.e., the predictor variables) which will be part of the analysis. A multiple regression analysis would determine the extent to which cognitive workload (i.e., ICA) can be predicted individually or collectively by all the other variables included in the model.

A variation of this study would be to designate the ICA as one of the predictor variables rather than as the dependent variable. For example, you might want to see whether overall measured task performance could be explained by a number of different variables, including the measured cognitive workload of the individual on the task. In this case, the multiple regression analysis would regress performance across all the variables of interest. Each variable would be assessed for its unique contribution to the analysis, and the overall R² would indicate how much of the variance observed in performance could be attributed to the predictor variables.

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