Hi, I have very simple balanced randomized block design where I total have 48
observations of a measure of weights of a product, the product was manufactured
at 4 sites, so each site has 12 observations. I want to use lme() from nlme
package to estimate the standard error of the product weight.
So the data look like:
MW site
1 54031 1
2 55286 1
3 54396 2
4 52327 2
5 55963 3
6 54893 3
7 57338 4
8 55597 4
:
:
:
The random effect model is: Y = mu + b + e where b is random block effect and e
is model error.
so I fitted a lme model as:
obj<-lme(MW~1, random=~1|site, data=dat)
summary(obj)
Linear mixed-effects model fit by REML
Random effects:
Formula: ~1 | site
(Intercept) Residual
StdDev: 2064.006 1117.567
Fixed effects: MW ~ 1
Value Std.Error DF t-value p-value
(Intercept) 55901.31 1044.534 44 53.51796 0
:
:
Number of Observations: 48
Number of Groups: 4
I also did:
anova(obj)
numDF denDF F-value p-value
(Intercept) 1 44 2864.173 <.0001
I believe my standard error estimate is from "Residual" under "Random Effects"
part of summary(), which is 1117.567.
Now my question is regarding t test under "Fixed effects". I think it's testing
whether the over mean weight is 0 or not, which is not interesting anyway. But
how the standard error of 1044.534 is calculated? I thought it should be
sqrt(MSE)=1117.567 instead. anyone can explain?
Same goes to the F test using anova(obj). The F test statistic is equal to
square of the t test statistic because of 1 df of numerator. But what's the
mean sum of squares of numerator and denominator, where to find them? BTW, I
think denominator mean sum of squares (MSE) should be 1117.567^2, but this is
not consistent to the standard error in the t test (1044.534).
Thanks a lot for any help
John
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