[R] 2 way repeated measures ANOVA using R: syntax and reportingquestion

[F Z]

Dear Gideon

Unless you are willing to accept uncorrelated measures in time and 
homogeneity of variance I would go for a linear mixed model instead. You 
might be surprised on how diffrent can be your results. Try;
>?lme

I hope that this helps

Francisco


>From: GIDEON WASSERBERG <wasserberg at wisc.edu>
>To: "R-help at lists.R-project.org" <R-help at stat.math.ethz.ch>
>Subject: [R] 2 way repeated measures ANOVA using R: syntax and 
>reportingquestion
>Date: Wed, 26 May 2004 14:03:21 -0500
>
>Dear Friends
>
>I have a technical question about conducting 2 way repeated measures ANOVA 
>analysis using R.
>
>1. Data set: repeated measurement of activity over night (2 hr. intervals)
>repeated (within subject)factor: Hours
>Between subject: Species, Sex
>Dependent variables: specimens
>
>Here is how the data arranged for the analysis:
>
>Subject	Replicate	Hour	Sp.	Specimens
>1	1	       1	a
>2	1	       1	a
>3	1	       1	b
>4	1	       1	b
>5	2	       1	a
>6	2	       1	a
>7	2	       1	b
>8	2	       1	b
>1	1	       2	a
>2	1	       2	a
>3	1	       2	b
>4	1	       2	b
>5	2	       2	a
>6	2	       2	a
>7	2	       2	b
>8	2	       2	b
>
>
>here's the command I used:
>summary(aov(Specimens~Species*Sex*Hours+Error(Subject/Hours),data=SP)).
>
>My question is - is that the correct way to do it??
>
>2. Below is the results output:
>A. I am not sure I understand what is the meaning of the two error terms I 
>get.
>Does the first one show error between subjetcs
>and the second - error within subjects?
>
>Error: Subject -
>         Df  Sum Sq Mean Sq
>Species  1 0.60715 0.60715
>
>Error: Subject:Hours
>       Df Sum Sq Mean Sq
>Hours  1 158.24  158.24
>
>Error: Within
>                     Df Sum Sq Mean Sq F value    Pr(>F)
>Species              2  35.19   17.59 34.3017 2.733e-15 ***
>Sex                  1  18.98   18.98 37.0092 1.493e-09 ***
>Hours                1  40.02   40.02 78.0278 < 2.2e-16 ***
>Species:Sex          2   1.29    0.64  1.2568    0.2849
>Species:Hours        2   9.95    4.97  9.6993 6.530e-05 ***
>Sex:Hours            1   0.66    0.66  1.2778    0.2585
>Species:Sex:Hours    2   1.38    0.69  1.3498    0.2596
>Residuals         1486 762.20    0.51
>---
>B. How do I summarize this information for a report?
>Is the below suggestion acceptable?
>-------------------------------------------------------------------------------
>
>Source	              df	SS	MS	                 F	    P
>-----------------------------------------------------------------------------
>Species	               2	35.19	17.59	                34.3     <0.0001
>Sex          	       1	18.98	18.98	                37.01	  <0.0001
>Species:Sex          	2	1.29	0.64  	               1.2568    0.2849
>Subject(Species)	1	0.60715	0.60715
>Subject(Hours)	       1	158.24  158.24
>Hour	                1	40.02	  40.02	                78.0278	   <0.0001
>Species:Hours        	2	9.95            4.97  	         9.6993	   <0.0001
>Sex:Hours            	1	0.66    	0.66             1.2778    0.2585
>Species:Sex:Hours    	2	1.38    	0.69  	         1.3498	0.2596
>Residuals	     1486	762.20    	0.51
>---------------------------------------------------------------------------------
>Very much obliged for your kind response
>
>Gideon
>
>
>Gideon Wasserberg (Ph.D.)
>Wildlife research unit,
>Department of wildlife ecology,
>University of Wisconsin
>218 Russell labs, 1630 Linden dr.,
>Madison, Wisconsin 53706, USA.
>Tel.:608 265 2130, Fax: 608 262 6099
>
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