I am afraid this may turn out to be an elementary statistics lesson, but
here goes, and thanks (and/or apologies) in advance...
When I use Type I sums of squares in a linear model, the sum of squares
of each factor (from summary.aov()) plus the residual add up to the
total sum of squares ([n-1]*s^2 of the response variable. When I use
Type III SS, I get something less than the total sums of squares when I
add up the partial Sums of Squares.... Why?
Example below.
> y2 <- y1 + 50*runif(50)
> y1 <- 1:50
> F1 <- as.factor(c(rep("A",25),rep("B",25)))
> results <- lm(y2 ~ y1 + F1)
> SST <- (50-1) * var(y2)
> SST
[1] 25351.38
> summary.aov(results, ssType=1)
Df Sum of Sq Mean Sq F Value Pr(F)
y1 1 14705.09 14705.09 67.42195 0.0000000
F1 1 395.35 395.35 1.81264 0.1846493
Residuals 47 10250.95 218.11
> summary.aov(results, ssType=3)
Type III Sum of Squares
Df Sum of Sq Mean Sq F Value Pr(F)
y1 1 6055.76 6055.761 27.76531 0.0000034
F1 1 395.35 395.347 1.81264 0.1846493
Residuals 47 10250.95 218.105
>
--
Dr. M. Henry H. Stevens
Postdoctoral Associate
Department of Ecology, Evolution, & Natural Resources
14 College Farm Road
Cook College, Rutgers University
New Brunswick, NJ 08901-8551
email: hstevens@rci.rutgers.edu
phone: 732-932-9631
fax: 732-932-8746
-----------------------------------------------------------------------
This message was distributed by s-news@wubios.wustl.edu. To unsubscribe
send e-mail to s-news-request@wubios.wustl.edu with the BODY of the
message: unsubscribe s-news
|