Please allow me to rephrase myquery. > 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 > The above is the same as : 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 For reference: > 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 Now I'll explain what is confusing me in the output of summary.lm. Coeff of Intercept = 44.556 = cell mean for A.L. This is the base. Coeff of woolB:L = -16.333 = 28.22222 - 44.556. This is the difference of this cell mean(B:L) from the base. Coeff of woolA:tensionM = -20.556 = 24.000- 44.556. This is the difference of this cell mean (A:M) from the base. Coeff of woolA:tensionH = -20.000 = 24.55556 - 44.556. This is the difference of this cell mean(A:H) from the base. This is where it stops being the difference from the base. Coeff of woolB:tensionM = 21.111 should turn out to be 28.77778 - 44.556 but this is -15.77822 Coeff of woolB:tensionH = 10.556 should turn out to be 18.77778 - 44.556 but this is -25.77822 In the above 2 cases, we can't say that the coefficient = cell mean - base case. Can you tell me what should be the statement to be made ? Best Regards, Ashim PS : My apologies for emailing my query to this list. Can you tell me the names of a few (active) statistics help list ? On Sat, Dec 3, 2016 at 1:33 AM, David Winsemius <dwinsem...@comcast.net> wrote: > > > 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]] > >>>> > >>>> ______________________________________________ > >>>> 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. > >>> > >>> ________________________________ > >>> Tento e-mail a jakékoliv k němu připojené dokumenty jsou důvěrné a jsou > >>> určeny pouze jeho adresátům. > >>> Jestliže jste obdržel(a) tento e-mail omylem, informujte laskavě > >>> neprodleně jeho odesílatele. 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