# Difference Between ANOVA and factorial Design

I was wondering about the difference between ANOVA and factorial design ?

I have applied the factorial design method for studying some models(in fact in is a model with three factors). I used Minitab . In fact it was an application on design of experiments.

Usually during my research ( which I am in the beginning ) I read in several places ( even on this website), asking about ANOVA?

For me, till now, the idea is fully unclear. What is ANOVA ? and what is Factorial design ? how they differ ? When we apply ANOVA, and when we apply Factorial design ?

What I know about ANOVA, Analysis of variance, is that it is may be What I read about the ANOVA decomposition of a function.

Any clarification is highly appreciated.
Thanks.

## 2 Answers

A factorial design is a type of experimental design, i.e. a plan how you create your data.

An ANOVA is a type of statistical analysis that tests for the influence of variables or their interactions.

The connection between the two (if any) is that if you know that you want to do an ANOVA with variables X,Y,Z or a number of their interactions, one would typically apply a (fractional) factorial design - the optimal design can be calculated with various R packages, see CRAN Task View.

• The definition of ANOVA is perhaps a little broad here, but again many statistical people would put it that broadly. Looking at interactions is very common, but not a necessary part of any definition. A factorial design typically leads to an ANOVA, but the converse isn't true. For example, you can report an ANOVA associated with a regression, in which no predictor may be categorical (or a factor, or whatever your terminology), and that's very often done. Conversely you could report a (simple) factorial design in pure regression terms. Commented Jan 21, 2016 at 21:36
• Thank you for answering, may I ask another question: What is precisely experimental design ? Just creating a design from experimental data ?? If yes, then factorial deisgn is just a design of some given data, then when using factorial design in Minitab analysis , what we are doing exactly ? aren't we studying the interation of the factors (parameters) and their effects ? Commented Jan 22, 2016 at 8:39
• Have you googled experimental design, and read a few explanations, e.g. en.wikipedia.org/wiki/Design_of_experiments ? If you have questions remaining, I would suggest that you ask the more specifically as a new question. Commented Jan 22, 2016 at 9:01

As far as I understand with DOE you design your experiments to get your data. In many cases the experiments are expensive and/or time consuming so you want to do only the minimum. DOE helps in that. With ANOVA you use the data you get from your experiments and figure out the mathematical formula for your dependent variables and factors. At least those are my impressions after failing a course twice in the topic. :D