[R] marginality principle / selecting the right type of SS for an interaction hypothesis from Bertolt Meyer on 2008-05-26 (R help archive)

[R] marginality principle / selecting the right type of SS for an interaction hypothesis

From: Bertolt Meyer <bmeyer_at_sozpsy.uzh.ch>
Date: Sun, 25 May 2008 16:50:45 +0200


Hello,

I have a problem with selecting the right type of sums of squares for an ANCOVA for my specific experimental data and hypotheses. I do have a basic understanding of the differences between Type-I, II, and III SSs, have read about the principle of marginality, and read Venable's "Exegeses on Linear Models"
(http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf). I am pretty new to R and a search of the R-help archive did not answer my question (although I found some good pointers).

In brief, leaving my covariates aside, I hypothesize that women (a) generally perform lower then men in a specific task (microworld performance, MWP) and that they (b) perform especially poor if a certain situational condition exists ("stereotype threat"). N = 160, 80 female & 80 male participants, 82 under stereotype threat and 78 not.

I realize that it makes no sense to report/interpret a main effect of stereotype threat in the confirmed presence of the interaction effect GENDER:STTHREAT, because a main effect of stereotype threat would actually be caused by the interaction (an error-bar plot illustrating this can be found here if one scrolls a little downwars: http://myowelt.blogspot.com/2008/05/obtaining-same-anova-results-in-r-as-in.html)

. I thus tend to use Type-II SSs and calculate my ANOVA with

> library(car)
> Anova(lm(MWP ~ GENDER * STTHREAT), type="II")
Anova Table (Type II tests)

Response: MWP

                  Sum Sq  Df F value    Pr(>F)
GENDER           23.939   1 32.3672 6.139e-08 ***
STTHREAT         12.684   1 17.1489 5.644e-05 ***
GENDER:STTHREAT   4.997   1  6.7557   0.01024 *
Residuals       115.380 156
---
Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1

However, it would make sense to report the main effect of GENDER in
the presence of the interaction and thus violate the marginality
principle, because of hypothesis (a) above. Would that mean that Type-
III SSs are desirable for the analysis of the main effect of GENDER,
and Type-II SSs are desirable for the main effect of STTHREAT and the
interaction? Or would it be better to specify a model that only
includes the interaction term and the main effect of gender with Type-
III SSs? Like this:


> options(contrasts=c("contr.sum", "contr.poly"))
> fit <- aov(MWP ~ GENDER:STTHREAT + GENDER)
> drop1(fit,~.,test="F")
Single term deletions Model: MWP ~ GENDER:STTHREAT + GENDER Df Sum of Sq RSS AIC F value Pr(F) <none> 115.380 -44.310 GENDER 1 23.381 138.761 -16.787 31.612 8.475e-08 *** GENDER:STTHREAT 2 17.680 133.061 -25.499 11.952 1.481e-05 *** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 If this has been answered before and I was just too blind to find it, I apologize and would appreciate a link to the post. Another question that arises from the use of Type-III SSs: If every factor is corrected for the other factors, the SSs of all factors plus the RSS do not sum up to the total SS of the model. But doesn't that lead to a situation where the standard way of calculating eta-square for a factor by dividing its SS by the total SS cannot be applied? Regards, Bertolt -- Bertolt Meyer Senior Assistant Psychological Institute, University of Zurich Social Psychology Binzmuehlestr. 14, Box 15 CH-8050 Zurich Switzerland bmeyer_at_sozpsy.uzh.ch tel: +41446357282 fax: +41446357279 ______________________________________________ R-help_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Received on Sun 25 May 2008 - 15:35:18 GMT

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