Question

What is the purpose of ONEWAY ANOVA test? Give an example with three treatment levels.

What is the relationship between factorial design and TWO-WAY ANOVA? Give an example

What is Factorial Design? Provide an example indicating the variables and possible interaction effects?

Answer 1

The one-way analysis of variance (ANOVA) is used to determine whether there are any statistically significant differences between the means of two or more independent (unrelated) groups (although you tend to only see it used when there are a minimum of three, rather than two groups).

Basically, you’re testing groups to see if there’s a difference between them. Examples of when you might want to test different groups:

• A group of psychiatric patients are trying three different therapies: counseling, medication and biofeedback. You want to see if one therapy is better than the others.
• A manufacturer has two different processes to make light bulbs. They want to know if one process is better than the other.
• Students from different colleges take the same exam. You want to see if one college outperforms the other.

A factorial ANOVA compares means across two or more independent variables. Again, a one-way ANOVA has one independent variable that splits the sample into two or more groups, whereas the factorial ANOVA has two or more independent variables that split the sample in four or more groups.

Factorial design involves having more than one independent variable, or factor, in a study. Factorial designs allow researchers to look at how multiple factors affect a dependent variable, both independently and together. A study with two factors that each have two levels, for example, is called a 2x2 factorial design.

When two or more independent variables are involved in a research design, there is more to consider than simply the "main effect" of each of the independent variables (also termed "factors"). That is, the effect of one independent variable on the dependent variable of interest may not be the same at all levels of the other independent variable. Another way to put this is that the effect of one independent variable may depend on the level of the other independent variable.