# [R] Estimated Effects Not Balanced

Bert Gunter bgunter.4567 at gmail.com
Tue Aug 23 00:32:55 CEST 2016

```Thanks, Rich. I didn't notice that!

-- Bert
Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Mon, Aug 22, 2016 at 1:43 PM, Richard M. Heiberger <rmh at temple.edu> wrote:
> The problem is that you have 12 observations and 1+2+10=13 degrees of freedom.
> There should be 1 + 2 + 8 = 11 degrees of freedom.
> Probably one of your variables is masked by something else in you workspace.
> Protect yourself by using a data.frame
>
>> tmp <- data.frame(A=factor(c(1,1,1,1,1,1,2,2,2,2,2,2)),
> + B=factor(c(1,1,2,2,3,3,1,1,2,2,3,3)),
> + y=rnorm(12))
>> mod <- aov(y ~ A+B, data=tmp)
>> summary(mod)
>             Df Sum Sq Mean Sq F value Pr(>F)
> A            1  1.553   1.553   1.334  0.281
> B            2  3.158   1.579   1.357  0.311
> Residuals    8  9.311   1.164
>
> On Mon, Aug 22, 2016 at 11:15 AM, Justin Thong <justinthong93 at gmail.com> wrote:
>> Something does not make sense in R. It has to do with the question of
>> balance and unbalance.
>>
>> *A<-factor(c(1,1,1,1,1,1,2,2,2,2,2,2))*
>> *B<-factor(c(1,1,2,2,3,3,1,1,2,2,3,3))*
>> *y<-rnorm(12)*
>> *mod<-aov(y~A+B)*
>>
>> I was under the impression that the design is balanced ie order does not
>> effect the sums of squares. However, when I compute the anova R reports
>> that the Estimated Effects are Unbalanced. I thought that when all
>> combinations of levels of A and B have equal replications then the design
>> is called balanced. But, R tends to think that when not all levels of A and
>> levels of B have equal replication, then the "Estimated Effects are
>> unbalanced".... Is this the same as the design being unbalanced? Because
>> for the example below, where the error occured, the order does not matter
>> (which make me think that the design is balanced).
>>
>>
>> *Call:*
>> *   aov(formula = y ~ A + B)*
>>
>> *Terms:*
>> *                        A         B Residuals*
>> *Sum of Squares   0.872572  0.025604 16.805706*
>> *Deg. of Freedom         1         2        10*
>>
>> *Residual standard error: 1.296368*
>> *Estimated effects may be unbalanced*
>> --
>> Yours sincerely,
>> Justin
>>
>> *I check my email at 9AM and 4PM everyday*
>> *If you have an EMERGENCY, contact me at +447938674419(UK) or
>> +60125056192(Malaysia)*
>>
>>         [[alternative HTML version deleted]]
>>
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