Is it possible to test a 2x2x2 design where the first two variables are manipulated high/low categories and the third variable is a measured continuous variable?
Would it be suitable to convert the measured continuous variable to a categorical variable to create a 2x2x2 design?
If so, i would now have 8 categories with multiple high/low combinations.
What test would i use to identify the differences across these groups in a dependent variable if i want to hypothesize that the DV would vary as a function of high/low categorical variable (3rd variable) values?
You probably don't want to dichotomize your continuous measured variable.
Instead, you can include this variable in the model as a continuous variable. This is similar to ancova (analysis of covariance), except you have two categorical variables in your model along with your measured continuous variable.
This is a general linear model. Which is the general model that includes linear regression, anova, and ancova.
The reason why you should uses continuous not categorical is that you will preserve statistical power; if you dichotomise you are throwing a lot of information away. You could do the modelling with continuous and then present the results for two (meaningful) categories by making predictions from the fitted model.
In addition to the loss of power that Kelvyn Jones mentioned, when you carve a quantitative variable into categories, the fitted values are forced to follow an artificial step function. The attached image shows the relationship between age (X) and total cholesterol (Y). Notice that when X is carved into 3 categories, the fitted values are forced to follow a step function. Notice that people near a cut-point who have tiny differences in age have quite large differences in fitted values. And notice that people who fall at opposite ends of an age category have the same fitted value, despite having fairly large age differences. With that in mind, the fitted values from the linear regression model make a lot more sense, I think! HTH.
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2x2x2 Design with Continuous Variable
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it possible to test a 2x2x2 design where the first two variables are manipulated high/low categories and the third variable is a measured continuous variable?
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Yes, it is possible to test a 2x2x2 design where the first two variables are manipulated as high/low categories, and the third variable is a measured continuous variable. In this design, you would have three independent variables:
Variable 1 (Categorical, High/Low)
Variable 2 (Categorical, High/Low)
Variable 3 (Continuous, Measured)
You would have two levels for each of the first two variables (high and low), resulting in a 2x2 design for those variables. This means you would have four experimental conditions in total. You can then measure the continuous variable in each of these conditions to assess its impact or interaction with the categorical variables.
Statistical analysis techniques such as analysis of variance (ANOVA) or regression analysis can be used to analyze the data and assess the effects of these variables on the measured continuous variable. These methods will allow you to determine if there are statistically significant differences or interactions among the variables in your design.