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]]
> 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]] >>> >>> ______________________________________________ >>> 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]] > > ______________________________________________ > 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.David Winsemius Alameda, CA, USA
> On Dec 2, 2016, at 9:09 AM, David Winsemius <dwinsemius at comcast.net> wrote: > >> >> 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)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-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]] >> >> ______________________________________________ >> 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. > > David Winsemius > Alameda, CA, USA > > ______________________________________________ > 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.David Winsemius Alameda, CA, USA