[R] Interpreting summary.lm for a 2 factor anova
David Winsemius
dwinsemius at comcast.net
Fri Dec 2 18:09:28 CET 2016
> On Dec 2, 2016, at 6:16 AM, Ashim Kapoor <ashimkapoor at 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)
The difference between the observed mean and the estimated mean is known as a 'residual' 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-bounces at r-project.org] On Behalf Of Ashim
>>> Kapoor
>>> Sent: Thursday, December 1, 2016 2:48 PM
>>> To: r-help at 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 at 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
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