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]]
Hi You probably could get better answer from experts but it has something to do with contrasts. ?contrasts Number 44.556 is mean for wool A and tension L and this is the level to which every other level is compared. Cheers Petr> -----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]] > > ______________________________________________ > R-help at 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 jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a jsou ur?eny pouze jeho adres?t?m. Jestli?e jste obdr?el(a) tento e-mail omylem, informujte laskav? neprodlen? jeho odes?latele. Obsah tohoto emailu i s p??lohami a jeho kopie vyma?te ze sv?ho syst?mu. 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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. Best Regards, Ashim On Fri, Dec 2, 2016 at 5:11 PM, PIKAL Petr <petr.pikal at precheza.cz> wrote:> Hi > > You probably could get better answer from experts but it has something to > do with contrasts. > > ?contrasts > > Number 44.556 is mean for wool A and tension L and this is the level to > which every other level is compared. > > Cheers > Petr > > > -----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]] > > > > ______________________________________________ > > R-help at 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 jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a jsou > ur?eny pouze jeho adres?t?m. > Jestli?e jste obdr?el(a) tento e-mail omylem, informujte laskav? > neprodlen? jeho odes?latele. Obsah tohoto emailu i s p??lohami a jeho kopie > vyma?te ze sv?ho syst?mu. > Nejste-li zam??len?m adres?tem tohoto emailu, nejste opr?vn?ni tento email > jakkoliv u??vat, roz?i?ovat, kop?rovat ?i zve?ej?ovat. > Odes?latel e-mailu neodpov?d? za eventu?ln? ?kodu zp?sobenou modifikacemi > ?i zpo?d?n?m p?enosu e-mailu. > > V p??pad?, ?e je tento e-mail sou??st? obchodn?ho jedn?n?: > - vyhrazuje si odes?latel pr?vo ukon?it kdykoliv jedn?n? o uzav?en? > smlouvy, a to z jak?hokoliv d?vodu i bez uveden? d?vodu. > - a obsahuje-li nab?dku, je adres?t opr?vn?n nab?dku bezodkladn? p?ijmout; > Odes?latel tohoto e-mailu (nab?dky) vylu?uje p?ijet? nab?dky ze strany > p??jemce s dodatkem ?i odchylkou. > - trv? odes?latel na tom, ?e p??slu?n? smlouva je uzav?ena teprve > v?slovn?m dosa?en?m shody na v?ech jej?ch n?le?itostech. > - odes?latel tohoto emailu informuje, ?e nen? opr?vn?n uzav?rat za > spole?nost ??dn? smlouvy s v?jimkou p??pad?, kdy k tomu byl p?semn? zmocn?n > nebo p?semn? pov??en a takov? pov??en? nebo pln? moc byly adres?tovi tohoto > emailu p??padn? osob?, kterou adres?t zastupuje, p?edlo?eny nebo jejich > existence je adres?tovi ?i osob? j?m zastoupen? zn?m?. > > This e-mail and any documents attached to it may be confidential and are > intended only for its intended recipients. > If you received this e-mail by mistake, please immediately inform its > sender. Delete the contents of this e-mail with all attachments and its > copies from your system. > If you are not the intended recipient of this e-mail, you are not > authorized to use, disseminate, copy or disclose this e-mail in any manner. > The sender of this e-mail shall not be liable for any possible damage > caused by modifications of the e-mail or by delay with transfer of the > email. > > In case that this e-mail forms part of business dealings: > - the sender reserves the right to end negotiations about entering into a > contract in any time, for any reason, and without stating any reasoning. > - if the e-mail contains an offer, the recipient is entitled to > immediately accept such offer; The sender of this e-mail (offer) excludes > any acceptance of the offer on the part of the recipient containing any > amendment or variation. > - the sender insists on that the respective contract is concluded only > upon an express mutual agreement on all its aspects. > - the sender of this e-mail informs that he/she is not authorized to enter > into any contracts on behalf of the company except for cases in which > he/she is expressly authorized to do so in writing, and such authorization > or power of attorney is submitted to the recipient or the person > represented by the recipient, or the existence of such authorization is > known to the recipient of the person represented by the recipient. >[[alternative HTML version deleted]]