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Design of Experiments: Variables, Blocking, Factors, and Effects

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Explain the difference between multiple independent variables and multiple levels of independent variables. Which is better? What is blocking and how does it reduce "noise"? What is a disadvantage of blocking? What is a factor? How can the use of factors benefit a design? Explain main effects and interaction effects. How does a covariate reduce noise? Describe and explain three trade-offs present in experiments.

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The solution gives detailed discussion on design of experiments: multiple independent variables and multiple levels of independent variables, blocking, factor, main effects and interaction effects, covariate and trade-offs present in experiments.

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Explain the difference between multiple independent variables and multiple levels of independent variables. Which is better?
In the design of experiment, each researcher must decide the dependent variable and independent variable. We usually have only one dependent variable. But for independent variable, we can have many. Each independent variable can be treated as a parameter. So multiple independent variables mean multiple parameters. For example, if the weight of person is the dependent variable, then the age, sex and feet size can be independent variables. In this case, we have 3 independent variables. However, we can assign multiple level for one independent variables. For the same example, sex can be assigned to male and female and age can be assigned as junior and senior.
In most cases, multiple levels of independent variables is better. There are many reasons to claim this: 1. Usually the more there are independent variables, the more money we spend. 2. Usually the more there are independent variables, the less reliability the model is because we need to test each independent variable first instead ...

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