Yes, but as I fear, the residuals behave badly as soon as the model get a
little bit more complex (e.g., with two covariables or an interactions). The
scope for performing an ANCOVA is thus very limited. That's why I was thinking
about a potential non-parametric model. But I do not want to artificially makes
my data tell something if it cannot.
> Message du 20/10/14 à 16h50
> De : "stephen sefick"
> A : "Martin Weiser"
> Copie à : "V. Coudrain" , "r-sig-ecology"
> Objet : Re: [R-sig-eco] Regression with few observations per factor level
>
> You are more or less preforming an ANOVA/ANCOVA on your data? As pointed out
> earlier, all of the normal theory regression assumptions apply. Assuming all
> of those things are satisfied then if you have large confidence intervals and
> there are significant differences between groups I don't see why you couldn't
> correctly infer something about the treatments. Maybe I am missing something.
> Stephen
> On Mon, Oct 20, 2014 at 8:43 AM, Martin Weiser wrote:
> Hi,
>
> coefficients and their p-values are reliable if your data are OK and you
> do know enough about the process that generated them, so you can choose
> appropriate model. With 4 points per line, it may be really difficult to
> identify bad fit or outliers.
>
> For example: simple linear regression needs constant variance of the
> normal distribution from which residuals are drawn - along the
> regression line - to work properly. With 4 points, you can hardly
> estimate this, but if you know enough about the process that generated
> the data, you are safe. If you do not know, it is not easy to say
> anything about the nature of the process that generated the data.
>
> If you know (or can assume) that there is simple linear relationship,
> you can say: "slope of this relationship is such and such", but if you
> want to estimate both the nature of the relationship ("A *linearly*
> depends on B") and its magnitude ("the slope of this relationship
> is ..."), p-values would not help you much.
>
> Of course, I may be wrong - I am not a statistician, just a user.
>
> Best,
> Martin W.
>
>
> V. Coudrain píše v Po 20. 10. 2014 v 13:37 +0200:
> > Thank you very much. If I get it right, the CI get wider, my test has less
> > power and the probability of getting a significant relation decreases. What
> > about the significant coefficients, are they reliable?
> >
> >
> >
> >
> > > Message du 20/10/14 à 11h30
> > > De : "Roman Luštrik"
> > > A : "V. Coudrain"
> > > Copie à : "r-sig-ecology@r-project.org"
> > > Objet : Re: [R-sig-eco] Regression with few observations per factor level
> > >
> > > I think you can, but the confidence intervals will be rather large due to
> > > number of samples.
> > > Notice how standard errors change for sample size (per group) from 4 to
> > > 30.
> > > > pg <- 4 # pg = per group> my.df <- data.frame(var = c(rnorm(pg, mean =
> > > > 3), rnorm(pg, mean = 1), rnorm(pg, mean = 11), rnorm(pg, mean = 30)), +
> > > > trt = rep(c("trt1", "trt2", "trt3", "trt4"), each =
> > > > pg), + cov = runif(pg*4)) # 4 groups>
> > > > summary(lm(var ~ trt + cov, data = my.df))
> > > Call:lm(formula = var ~ trt + cov, data = my.df)
> > > Residuals: Min 1Q Median 3Q Max -1.63861 -0.46080
> > > 0.03332 0.66380 1.27974
> > > Coefficients: Estimate Std. Error t value Pr(>|t|)
> > > (Intercept) 1.2345 1.0218 1.208 0.252 trttrt2 -0.7759
> > > 0.8667 -0.895 0.390 trttrt3 7.8503 0.8308 9.449
> > > 1.3e-06 ***trttrt4 28.2685 0.9050 31.236 4.3e-12 ***cov
> > > 1.4027 1.1639 1.205 0.253 ---Signif. codes: 0 ‘***’ 0.001
> > > ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> > > Residual standard error: 1.154 on 11 degrees of freedomMultiple
> > > R-squared: 0.9932,Adjusted R-squared: 0.9908 F-statistic: 404.4 on 4
> > > and 11 DF, p-value: 7.467e-12
> > > > > pg <- 30 # pg = per group> my.df <- data.frame(var = c(rnorm(pg, mean
> > > > > = 3), rnorm(pg, mean = 1), rnorm(pg, mean = 11), rnorm(pg, mean =
> > > > > 30)), + trt = rep(c("trt1", "trt2", "trt3",
> > > > > "trt4"), each = pg), + cov = runif(pg*4)) # 4
> > > > > groups> summary(lm(var ~ trt + cov, data = my.df))
> > > Call:lm(formula = var ~ trt + cov, data = my.df)
> > > Residuals: Min 1Q Median 3Q Max -2.5778 -0.6584 -0.0185
> > > 0.6423 3.2077
> > > Coefficients: Estimate Std. Error t value Pr(>|t|)
> > > (Intercept) 2.76961 0.25232 10.977 < 2e-16 ***trttrt2 -1.75490
> > > 0.28546 -6.148 1.17e-08 ***trttrt3 8.40521 0.28251 29.752 <
> > > 2e-16 ***trttrt4 27.04095 0.28286 95.599 < 2e-16 ***cov
> > > 0.05129 0.32523 0.158 0.875 ---Signif. codes: 0 ‘***’ 0.001
> > > ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> > > Residual standard error: 1.094 on 115 degrees of freedomMultiple
> > > R-squared: 0.9913,Adjusted R-squared: 0.991 F-statistic: 3269 on 4 and
> > > 115 DF, p-value: < 2.2e-16
> > > On Mon, Oct 20, 2014 at 10:53 AM, V. Coudrain wrote:
> > > Hi, I would like to test the impact of a treatment of some variable using
> > > regression (e.g. lm(var ~ trt + cov)). However I only have four
> > > observations per factor level. Is it still possible to apply a regression
> > > with such a small sample size. I think that i should be difficult to
> > > correctly estimate variance.Do you think that I rather should compute a
> > > non-parametric test such as Kruskal-Wallis? However I need to include
> > > covariables in my models and I am not sure if basic non-parametric tests
> > > are suitable for this. Thanks for any suggestion.
> > > ___________________________________________________________
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> > >
> > >
> >
> > > --
> > > In God we trust, all others bring data.
> >
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> Stephen Sefick
> **************************************************
> Auburn University
> Biological Sciences
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> **************************************************
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>
> Let's not spend our time and resources thinking about things that are so
> little or so large that all they really do for us is puff us up and make us
> feel like gods. We are mammals, and have not exhausted the annoying little
> problems of being mammals.
>
> -K. Mullis
>
> "A big computer, a complex algorithm and a long time does not equal science."
>
> -Robert Gentleman
>
>
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