= SIMPLE MAIN EFFECTS =

Click [[http://www-01.ibm.com/support/docview.wss?uid=swg21475404|here]]

to find out how to use EMMEANS (Estimated Marginal Means) in GLM to test simple main effects. You can additionally also add ADJ(BONFERRONI) or ADJ(SIDAK) to the /EMMEANS subcommand line to correct for multiple t-tests and use /EMMEANS for designs involving only between subjects factors (see some examples [[http://www.ats.ucla.edu/stat/spss/seminars/Repeated_Measures/default.htm|here]] and in Field, (2005), in Chapter 11 on Repeated Measures designs.) /EMMEANS correct for the number of comparisons within each level of an effect but not across levels e.g. for 3 trials and 2 groups in a trial by group interaction the only correction performed would be for comparing trials within each group with the correction for the three pairwise trial comparisons made within each group. Since there are only 2 groups there would be no adjustment comparing groups at each trial as there is only one pairwise comparison (the group difference) for each trial. 

/EMMEANS can also compare groups adjusted for covariates in repeated measures, For example the below syntax compares the average change over time in each of two groups adjusted for age differences between the groups.

{{{
GLM time1 time2 BY group WITH age
  /WSFACTOR=time 2 Polynomial 
  /METHOD=SSTYPE(3)
  /EMMEANS=TABLES(group) WITH(age=MEAN)COMPARE ADJ(SIDAK)
 /EMMEANS TABLES(time*group) WITH(age=MEAN)COMPARE(factor1) 
  /CRITERIA=ALPHA(.05)
  /WSDESIGN= time
  /DESIGN= group age group*age.
}}}

Simple effects involving between subject factors can also be specified in SPSS using the [[attachment:lmatrix.pdf|/LMATRIX subcommand]] and the /MMATRIX subcommand for within subjects factors
or [[http://listserv.uga.edu/cgi-bin/wa?A2=ind0107&L=spssx-l&P=13210|combinations of the two]]. [[http://www.nicholasgibson.com/lmatrix.html|See also.]]

MANOVA can also be used to compare pairs of within subjects factor levels in each group separately using the overall Mean Square Error which was used for testing the original interaction which was computed using ''all'' the groups. For example to decompose the Time x A interaction separately into the differences in times in groups 1 and 2 we can use the below. Further details are available [[http://support.spss.com/ProductsExt/SPSS/Documentation/Statistics/articles/simple.htm|here.]]

{{{
MANOVA V1 V2 BY GROUP(1,2)
 /WSFACTORS=TIME(2)
 /DESIGN=MWITHIN GROUP(1), MWITHIN GROUP(2).
}}}


See David Nichols's illustrations using the above SPSS syntax for explaining all types of interactions [[attachment:simple.txt|here.]] There are also illustrations of simple effects in the [[http://imaging.mrc-cbu.cam.ac.uk/statswiki/StatsCourse2006|ANOVA Grad talk]] and [[attachment:lmat.sps|some SPSS syntax here for two-way interactions.]]

The ''multcompare'' procedure in MATLAB also works out and compares pairs of estimated marginal means using the Tukey-Kramer test.

 * [[FAQ/wwsimple| How /EMMEANS works our standard error for simple effect for repeated measures factors]]

__Reference__

Field, A (2005). Discovering statistics using SPSS. Second Edition. Sage:London.

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These pages are maintained by [[mailto:ian.nimmo-smith@mrc-cbu.cam.ac.uk|Ian Nimmo-Smith]] and [[mailto:peter.watson@mrc-cbu.cam.ac.uk|Peter Watson]]

~-[Last updated on 14 April, 2004]-~