[R] Problem with 2-ways ANOVA interactions

Greg Snow Greg.Snow at imail.org
Thu Jan 6 21:40:33 CET 2011

See inline

> From: Frodo Jedi [mailto:frodo.jedi at yahoo.com] 
> Sent: Thursday, January 06, 2011 12:37 PM
> To: Greg Snow; r-help at r-project.org
> Subject: Re: [R] Problem with 2-ways ANOVA interactions
> Dear Greg,
> thanks so much, I think that now I have understood. Please confirm me this reading what follows ;-)
> To summarize from the beginning, the table I analyzed is the result of a simple experiment. Subjects where exposed to some stimuli 
> and they where asked to evaluate the degree of realism of the stimuli on a 7 point scale (i.e., data in column "response").
> Each stimulus was presented in two conditions, "A" and "AH", where AH is the condition A plus another thing (let´s call it "H").
> Before I wrongly thought that if I do the analysis anova(response ~ stimulus*condition) I would have got the comparison between 
> the same stimulus in condition A and in condition AH (e.g. stimulus_1_A, stimulus_1_AH). 
> Instad, apparently, the interaction stimulus:condition means that I find the differences between the stimuli keeping fixed the condition!!
> If this is true then doing the anova with the interaction stimulus:condition is equivalent to do the ONE WAY ANOVA  first on 
> the subset where all the conditions are A and then on the subset where all the conditions are AH? Right?

I think you are closer, but not quite there.  The test on the interaction tests if the difference between A and AH is the same across the different stimuli.  The main effect for condition tests if there is a difference between A and AH.

> So if all before is correct, my final question is: how by means of ANOVA can I track the significative differences between the stimuli 
> presented in A and AH condition whitout passing for the t-test? Indeed my goal was to find in one hand if globally the condition
> AH bring to better results than condition A, and on the other hand I needed to know for which stimuli the condition AH brings
> better results than condition A.
> Finally, Iam burning with curiosity to know the answers to the following two questions:
> 1-  is there a difference between anova(response ~ stimulus*condition) and anova(response ~ condition*stimulus)
> concerning the interaction part?

The interaction part should be identical (with the exception of possible rounding error).

> 2-  doing the anova(response ~ stimulus + condition) give the same results of two ONE WAY ANOVA
> anova(response ~ stimulus) and anova(response ~ condition) but the advantage is that they are presented together in one single output?

Only if there is absolutely no effect in one or more of the terms.  Doing both together allows you to compare the differences in the conditions given the different stimuli.  The one-way anova on condition groups and differences from the different stimuli in with the overall error (in your case that was not much, so you will not see much difference, but in general there can be big differences).

> Looking forward to knowing your response!
> Best regards

Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org

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