Solved – Difference Between ANOVA and factorial Design

anovaexperiment-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.

Best Answer

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.

Related Solutions

Solved – Whether to assess normality in a factorial repeated measures ANOVA by looking at distributions within cells

There is a reason that we talk about the normality 'assumption' rather than the normality 'condition'. Whether you are comfortable with the assumption of normality needs to come from knowledge about the science that generated the data, not the data itself.

The tests for normality, when used for justifying the normality assumption, will either give a meaningless answer to a meaningful question (small sample size) or a meaningful answer to a meaningless question (large sample size).

Plots of residuals from an appropriate model (including the repeated measures) can be used along with what you learn by doing your homework about where the data comes from to help you decide if you are comfortable with the normality assumption. But for deciding if the tests and intervals based on the normal are reasonable, dump the formal tests of normality.

Solved – Post hoc test in a 2×3 mixed design ANOVA using SPSS

Answer edited to implement encouraging and constructive comment by @Ferdi

I would like to:

provide an answer with a full contained script
mention one can also test more general custom contrasts using the /TEST command
argue this is necessary in some cases (ie the EMMEANS COMPARE combination is not enough)

I assume to have a database with columns: depV, Group, F1, F2. I implement a 2x2x2 mixed design ANOVA where depV is the dependent variable, F1 and F2 are within subject factors and Group is a between subject factor. I further assume the F test has revealed that the interaction Group*F2 is significant. I therefore need to use post hoc t-tests to understand what drives the interaction.

MIXED depV BY Group F1 F2 
  /FIXED=Group F1 F2 Group*F1 Group*F2 F1*F2 Group*F1*F2 |  SSTYPE(3) 
  /METHOD=REML 
  /RANDOM=INTERCEPT | SUBJECT(Subject) COVTYPE(VC) 
  /EMMEANS=TABLES(Group*F2) COMPARE(Group) ADJ(Bonferroni)
  /TEST(0) = 'depV(F2=1)-depV(F2=0) differs between groups' 
    Group*F2 1/4 -1/4 -1/4 1/4 
    Group*F1*F2 1/8 -1/8 1/8 -1/8 -1/8 1/8 -1/8 1/8 
  /TEST(0) = 'depV(Group1, F2=1)-depV(Group2, F2=1)' Group 1 -1
    Group*F1 1/2 1/2 -1/2 -1/2 
    Group*F2 1 0 -1 0  
    Group*F1*F2 1/2 0 1/2 0 -1/2 0 -1/2 0 .

In particular the second t-test corresponds to the one performed by the EMMEANS command. The EMMEANS comparison could reveal for example that depV was bigger in Group 1 on the condition F2=1.

However the interaction could also be driven by something else, which is verified by the first test: the difference depV(F2=1)-depV(F2=0) differs between groups, and this is a contrast you cannot verify with the EMMEANS command (at least I did not find an easy way).

Now, in models with many factors it is a bit tricky to write down the /TEST line, the sequence of 1/2, 1/4 etc, called L matrix. Typically if you get the error message: "the L matrix is not estimable", you are forgetting some elements. One link that explains the receipt is this one: https://stats.idre.ucla.edu/spss/faq/how-can-i-test-contrasts-and-interaction-contrasts-in-a-mixed-model/

Best Answer

Related Solutions

Solved – Whether to assess normality in a factorial repeated measures ANOVA by looking at distributions within cells

Solved – Post hoc test in a 2×3 mixed design ANOVA using SPSS

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