# [R] How to obtain the coefficients from a summary of aov ?

David Winsemius dwinsemius at comcast.net
Wed Apr 21 18:36:16 CEST 2010

```On Apr 21, 2010, at 12:09 PM, Andrea Bernasconi DG wrote:

> Thank you David,
>
> but how to get the value of 0.015939 present in s.npk.aov, and not
> given by s.npk.aov\$coef["block","Pr(>F)"] ?

??? That's not a coefficient. It's a p-value.
>
> On the other, the procedure to extract coefficients from a summary
> of lm or aov should be the same.

I think one generally extracts the coefficients from the model, rather
than from summary(model):

> coef(npk.aov)
(Intercept)      block2      block3      block4      block5
block6          N1
51.8250000   3.4250000   6.7500000  -3.9000000  -3.5000000
2.3250000   9.8500000
P1          K1       N1:P1       N1:K1       P1:K1
0.4166667  -1.9166667  -3.7666667  -4.7000000   0.5666667

> coef(npk.lm)
(Intercept)      block2      block3      block4      block5
block6          N1
51.8250000   3.4250000   6.7500000  -3.9000000  -3.5000000
2.3250000   9.8500000
P1          K1       N1:P1       N1:K1       P1:K1    N1:P1:K1
0.4166667  -1.9166667  -3.7666667  -4.7000000   0.5666667          NA

>
> Andrea
>
> On 21 Apr, 2010, at 3:20 PM, David Winsemius wrote:
>
>>
>> On Apr 21, 2010, at 8:37 AM, Andrea Bernasconi DG wrote:
>>
>>>
>>> I am able to obtain the coefficients from a 'summary' of 'lm', but
>>> NOT from a 'summary' of 'aov'.
>>> The following example shows my steps.
>>>
>>> ## Initialize
>>> rm(list = ls()) # remove (almost) everything in the working
>>> environment
>>
>> @#\$%^&*() DON'T DO THAT.... luckily I left off the "l" when I
>> copied and pasted but otherwise this would have trashed my workspace.
>>
>>> utils::data(npk, package="MASS") # get data
>>> model <- yield ~ block + N*P*K
>>>
>>> ## Using lm
>>> npk.lm <- lm(model, npk)
>>> ( s.npk.lm <- summary(npk.lm) )
>>>
>>> ...
>>>          Estimate Std. Error t value Pr(>|t|)
>>> (Intercept)  54.8750     0.8021  68.415  < 2e-16 ***
>>> block1        1.7125     1.3893   1.233  0.24131
>>> block2        1.6792     0.8021   2.093  0.05822 .
>>> block3       -1.8229     0.5672  -3.214  0.00744 **
>>> ...
>>>
>>> s.npk.lm\$coef["block1","Pr(>|t|)"] # this works
>>> [1] 0.2413061
>>>
>>> ## Using aov
>>> npk.aov <- aov(model, npk)
>>
>> str(npk.aov)
>>
>>> npk.aov\$coefficients
>> (Intercept)      block2      block3      block4      block5
>> block6          N1
>> 51.8250000   3.4250000   6.7500000  -3.9000000  -3.5000000
>> 2.3250000   9.8500000
>>        P1          K1       N1:P1       N1:K1       P1:K1    N1:P1:K1
>> 0.4166667  -1.9166667  -3.7666667  -4.7000000   0.5666667          NA
>>
>> Or reading the help pages one might have tried, although I will
>> admit that the differences in parametrization confounded my efforts
>> at describing a linear combination of those results to create the
>> simpler result offered above:
>>
>> ?model.tables
>>> model.tables(npk.aov, "effects")
>> Tables of effects
>>
>> block
>> block
>>    1      2      3      4      5      6
>> -0.850  2.575  5.900 -4.750 -4.350  1.475
>>
>> N
>> N
>>     0       1
>> -2.8083  2.8083
>>
>> P
>> P
>>     0       1
>> 0.5917 -0.5917
>>
>> K
>> K
>>     0       1
>> 1.9917 -1.9917
>>
>> N:P
>>  P
>> N   0       1
>> 0 -0.9417  0.9417
>> 1  0.9417 -0.9417
>>
>> N:K
>>  K
>> N   0      1
>> 0 -1.175  1.175
>> 1  1.175 -1.175
>>
>> P:K
>>  K
>> P   0        1
>> 0  0.14167 -0.14167
>> 1 -0.14167  0.14167
>>
>>>
>>> ( s.npk.aov <- summary(npk.aov) )
>>>
>>> ...
>>>          Df Sum Sq Mean Sq F value   Pr(>F)
>>> block        5 343.29  68.659  4.4467 0.015939 *
>>> N            1 189.28 189.282 12.2587 0.004372 **
>>> P            1   8.40   8.402  0.5441 0.474904
>>> ...
>>>
>>> s.npk.aov\$coef["block","Pr(>F)"] # this does NOT works
>>>
>>> ...
>>> NULL
>>> ...
>>>
>>> How to obtain the coefficients from a 'summary'  of 'aov' ?
>>>
>>>
>>> Sincerely, Andrea Bernasconi
>>>
>>> mobile: +41 79 621 74 07
>>> URL: http://web.me.com/andrea.bernasconi.dg/Andrea_Bernasconi_DG_home_page/HOME.html
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> and provide commented, minimal, self-contained, reproducible code.
>>
>> David Winsemius, MD
>> West Hartford, CT
>>
>
> mobile: +41 79 621 74 07
>
>
>
>
>
>

David Winsemius, MD
West Hartford, CT

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