ANOVA Output
The types-of-sums-of-squares issue is FAQ 7.18 and you can find a great deal of discussion in the R help lists. You only need to choose a 'type' if for some reason you need to efficiently produce a table with the results of multiple hypothesis tests. In general I think it is better to think hard about exactly which hypotheses are of interest and and then compare appropriately nested models to conduct the test (via e.g., a LRT). This is covered in many stats books, including many with an R focus. See the books by Venebles and Ripley, Harrell, Faraway, Maindonald, etc... Kingsford Jones On Thu, Nov 13, 2008 at 9:33 AM, Landis, R Matthew
<rlandis at middlebury.edu> wrote:
That's a great point Tyler. It raises the question of what IS a good reference for statistics that treats them the way R does. There has been some discussion of that already, but one book that hasn't been mentioned is that of John Fox, the author of the car package. Fox, John. 1997. Applied regression analysis, linear models, and related methods. Sage Publications. http://books.google.com/books?id=pr2mKvAxXeYC&printsec=frontcover&lr= Although mainly aimed at the social sciences, I found this to be pretty readable, and much more detailed than Crawley's books (admittedly aimed at a higher level). And as for R code, Fox also has "An R and S-Plus Companion to Applied Regression". http://books.google.com/books?id=xWS8kgRjGcAC&printsec=frontcover&lr= If you want to get a detailed understanding of Anova and regression the way R sees them, I think this pair of books is nearly as good as it gets. Matt -----Original Message----- From: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of tyler Sent: Thursday, November 13, 2008 8:52 AM To: r-sig-ecology at r-project.org Subject: Re: [R-sig-eco] ANOVA Output Apologies if I'm beating a dead horse here, but this is exactly the problem I raised in the thread on classical statistics in R. If Katrina is using a textbook like Sokal and Rohlf, it is indeed completely unexpected to find that changing the order of explanatory variables in an anova will produce different results. Thierry points out that this is because R produces Type I SS by default. Unfortunately, nowhere in S&R is this distinction explained, so for this problem a book widely regarded as a comprehensive reference for biologists provides absolutely no help. These questions come up all the time on the r-help list, and I think it's a sign of a real disconnect between the presentation of classical statistics in many undergrad programs and the way the tests are actually implemented in R. Anyways, that's a bigger issue. It may be helpful to know that the 'car' package includes a function Anova (not to be confused with the anova function) that allows you to calculate type II or type III sums of squares. Cheers, Tyler "ONKELINX, Thierry" <Thierry.ONKELINX at inbo.be> writes:
Dear Katrina, The F-value are different because you test different hypotheses since anova yields Type I SS. It looks like you expect Type III SS. HTH, Thierry ------------------------------------------------------------------------ ---- ir. Thierry Onkelinx Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest Cel biometrie, methodologie en kwaliteitszorg / Section biometrics, methodology and quality assurance Gaverstraat 4 9500 Geraardsbergen Belgium tel. + 32 54/436 185 Thierry.Onkelinx at inbo.be www.inbo.be To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher The plural of anecdote is not data. ~ Roger Brinner The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. ~ John Tukey -----Oorspronkelijk bericht----- Van: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] Namens Katrina W. Chu Verzonden: woensdag 12 november 2008 22:27 Aan: r-sig-ecology at r-project.org Onderwerp: [R-sig-eco] ANOVA Output I have a question about my R-output when I run a three-way ANOVA. I just plugged in the interaction term into the formula and presto! ANOVA! But I noticed that if I change the order of the formula (or interaction term), I get slightly different ANOVA outputs. I've pasted the output at the bottom of this message. I didn't think that this should happen, so I would appreciate if anyone had any feedback on this problem. Thanks in advance, Kat.
ANOVA <- aov(Chlorophyll.a~Treatment*SamplingPeriod*Site) summary(ANOVA)
Df Sum Sq Mean Sq F value Pr(>F) Treatment 3 356.5 118.8 4.2878 0.005276 ** SamplingPeriod 3 374.7 124.9 4.5069 0.003911 ** Site 1 1016.5 1016.5 36.6791 2.629e-09 *** Treatment:SamplingPeriod 9 467.6 52.0 1.8747 0.053284 . Treatment:Site 3 167.8 55.9 2.0176 0.110424 SamplingPeriod:Site 3 1670.2 556.7 20.0884 2.383e-12 *** Treatment:SamplingPeriod:Site 9 277.2 30.8 1.1115 0.352455 Residuals 534 14799.5 27.7 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ANOVA <- aov(Chlorophyll.a~SamplingPeriod*Treatment*Site) summary(ANOVA)
Df Sum Sq Mean Sq F value Pr(>F) SamplingPeriod 3 369.5 123.2 4.4437 0.004264 ** Treatment 3 361.8 120.6 4.3510 0.004840 ** Site 1 1016.5 1016.5 36.6791 2.629e-09 *** SamplingPeriod:Treatment 9 467.6 52.0 1.8747 0.053284 . SamplingPeriod:Site 3 1662.0 554.0 19.9894 2.718e-12 *** Treatment:Site 3 176.0 58.7 2.1166 0.097111 . SamplingPeriod:Treatment:Site 9 277.2 30.8 1.1115 0.352455 Residuals 534 14799.5 27.7 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
ANOVA <- aov(Chlorophyll.a~Site*SamplingPeriod*Treatment) summary(ANOVA)
Df Sum Sq Mean Sq F value Pr(>F) Site 1 1008.9 1008.9 36.4050 2.998e-09 *** SamplingPeriod 3 374.1 124.7 4.4990 0.003953 ** Treatment 3 364.8 121.6 4.3871 0.004607 ** Site:SamplingPeriod 3 1654.8 551.6 19.9026 3.050e-12 *** Site:Treatment 3 172.6 57.5 2.0761 0.102364 SamplingPeriod:Treatment 9 478.2 53.1 1.9172 0.047282 * Site:SamplingPeriod:Treatment 9 277.2 30.8 1.1115 0.352455 Residuals 534 14799.5 27.7 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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