> On Dec 2, 2016, at 9:09 AM, David Winsemius <dwinsem...@comcast.net> wrote:
>
>>
>> On Dec 2, 2016, at 6:16 AM, Ashim Kapoor <ashimkap...@gmail.com> wrote:
>>
>> Dear Pikal,
>>
>> All levels except the interactions are compared to the Intercept. I'm a
>> little confused as to what's going on in interaction terms eg. the cell
>> wool B : tension M. It's mean is :
>> 28.78 and 28.78 - 44.56 = -15.78 != 21.111.
>>
>> It's something like 44.56 (intercept) -16.333 (wool B) -.20.556 (tension
>> M) + 21.111 (woolB:tensionM) = 28.782.
>>
>> I don't know how to sum up the above line in terms of differences
>> succinctly.
>
> The aov estimate will not exactly equal the observed mean (this is
> _statistics_ after all). You should be comparing the mean of that cell to the
> estimate:
>
> 44.556 + (-16.33) +(-20.556) + (21.11)
A respected participant advised me to look at this more closely. In this case
(and I think in most such cases) where there are the same number of parameters
as there are means, the model is "saturated" and there is no difference:
with( warpbreaks, tapply( breaks, interaction(wool, tension), mean ) )
A.L B.L A.M B.M A.H B.H
44.55556 28.22222 24.00000 28.77778 24.55556 18.77778
So the B:M estimate is identical up to rounding with the observed mean:
44.556 + (-16.33) +(-20.556) + (21.11)
[1] 28.78
>
> The difference between the observed mean and the estimated mean is known as a
> 'residual'
I've also been privately but gently chided for this misstatement. Residuals are
the difference between data and estimates.
> and the squared sum of the all residuals is what this being minimized ...
> over all the cells including the one implicitly associated with the Intercept.
>
> This isn't really on-topic for Rhelp since you are not having difficulty in
> getting the R program to perform its duties, but are rather in need of
> statistical education. That not what this mailing list is set up for.
>
> --
> David.
>
>>
>>>
>>>> -----Original Message-----
>>>> From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Ashim
>>>> Kapoor
>>>> Sent: Thursday, December 1, 2016 2:48 PM
>>>> To: r-help@r-project.org
>>>> Subject: [R] Interpreting summary.lm for a 2 factor anova
>>>>
>>>> Dear all,
>>>>
>>>> Here is a small example : -
>>>>
>>>>> model <- aov(breaks ~ wool * tension, data = warpbreaks)
>>>>> summary.lm(model)
>>>>
>>>> Call:
>>>> aov(formula = breaks ~ wool * tension, data = warpbreaks)
>>>>
>>>> Residuals:
>>>> Min 1Q Median 3Q Max
>>>> -19.5556 -6.8889 -0.6667 7.1944 25.4444
>>>>
>>>> Coefficients:
>>>> Estimate Std. Error t value Pr(>|t|)
>>>> (Intercept) 44.556 3.647 12.218 2.43e-16 ***
>>>> woolB -16.333 5.157 -3.167 0.002677 **
>>>> tensionM -20.556 5.157 -3.986 0.000228 ***
>>>> tensionH -20.000 5.157 -3.878 0.000320 ***
>>>> woolB:tensionM 21.111 7.294 2.895 0.005698 **
>>>> woolB:tensionH 10.556 7.294 1.447 0.154327
>>>> ---
>>>> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>>>>
>>>> Residual standard error: 10.94 on 48 degrees of freedom
>>>> Multiple R-squared: 0.3778, Adjusted R-squared: 0.3129
>>>> F-statistic: 5.828 on 5 and 48 DF, p-value: 0.0002772
>>>>
>>>>> model.tables(model,"e")
>>>> Tables of effects
>>>>
>>>> wool
>>>> wool
>>>> A B
>>>> 2.8889 -2.8889
>>>>
>>>> tension
>>>> tension
>>>> L M H
>>>> 8.241 -1.759 -6.481
>>>>
>>>> wool:tension
>>>> tension
>>>> wool L M H
>>>> A 5.278 -5.278 0.000
>>>> B -5.278 5.278 0.000
>>>>
>>>>
>>>>> model.tables(model,"m")
>>>> Tables of means
>>>> Grand mean
>>>>
>>>> 28.14815
>>>>
>>>> wool
>>>> wool
>>>> A B
>>>> 31.037 25.259
>>>>
>>>> tension
>>>> tension
>>>> L M H
>>>> 36.39 26.39 21.67
>>>>
>>>> wool:tension
>>>> tension
>>>> wool L M H
>>>> A 44.56 24.00 24.56
>>>> B 28.22 28.78 18.78
>>>>>
>>>>
>>>> I don't follow the output of summary.lm. I understand the output of
>>>> model.tables for effects and means. For instance what does 44.556
>>>> represent ? Is it the grand average ? The grand mean is 28.14815. Can
>>>> someone help me understand the output of summary.lm ?
>>>>
>>>> Best Regards,
>>>> Ashim
>>>>
>>>> [[alternative HTML version deleted]]
>>>>
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>> [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
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>> and provide commented, minimal, self-contained, reproducible code.
>
> David Winsemius
> Alameda, CA, USA
>
> ______________________________________________
> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
David Winsemius
Alameda, CA, USA
______________________________________________
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