R help - Sep 2015 - Manova: Data similarly generated are significantly different.

Dear R users,

Hi. I don't know if my understanding of Manova test is correct. So I test
with the following code and got strange results.

Any help would be appreciated.

y0, y1, and y2 are independently generated by the same method.

They are each split into 20 groups by the same method.
The summary of the Manova test (stored in variable s) says:

The Pr (>F) value is less than 2.2e-16.

y0 <- runif(100, 0, 1)
y1 <- runif(100, 0, 1)
y2 <- runif(100, 0, 1)

y0 <- c(y0, runif(100, 0, 10) )
y1 <- c(y1, runif(100, 0, 10) )
y2 <- c(y2, runif(100, 0, 10) )

y0=as.numeric(unlist(y0))
y1=as.numeric(unlist(y1))
y2=as.numeric(unlist(y2))

b=10
a=length(y0)/b
g=rep(1:a,rep(b,a))

m1 <- manova(cbind(y0, y1, y2) ~ g)
s=summary(m1, test = "Wilks")

a = s$stats
a = a[11]
s
a

The summary is here:

       Df   Wilks approx F num Df den Df    Pr(>F)
       g           1 0.37069   110.91      3    196 < 2.2e-16 ***
       Residuals 198
       ---
       Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

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On 04/09/2015 5:18 PM, Roger Xu wrote:
> y0 <- runif(100, 0, 1)
> y1 <- runif(100, 0, 1)
> y2 <- runif(100, 0, 1)
> 
> y0 <- c(y0, runif(100, 0, 10) )
> y1 <- c(y1, runif(100, 0, 10) )
> y2 <- c(y2, runif(100, 0, 10) )
> 
> y0=as.numeric(unlist(y0))
> y1=as.numeric(unlist(y1))
> y2=as.numeric(unlist(y2))
> 
> b=10
> a=length(y0)/b
> g=rep(1:a,rep(b,a))
> 
> m1 <- manova(cbind(y0, y1, y2) ~ g)
> s=summary(m1, test = "Wilks")
> 
> a = s$stats
> a = a[11]
> s
> a
If you plot any of the y columns vs g you see a huge effect.  You aren't
testing whether the y's are equal, you are testing whether the triplets
depend on g, and they do.

Duncan Murdoch