[R] interpreting anova summary tables - newbie
Prof Brian Ripley
ripley at stats.ox.ac.uk
Thu Apr 6 17:59:51 CEST 2006
On Thu, 6 Apr 2006, Andrew McDonagh wrote:
My question relates to the meaning of the p-values. Do the p-values
relate to
a) the confidence in the estimate
or
b)the confidence that the non-intercept categories are different to the
intercept
Both (given a loose interpretation of your words and some assumptions
that a newbie is using the default settings of e.g. contrasts).
The estimates are of the difference in intercept from the reference
category, I guess Mutant.IDA. The p-values refer to the test that the
particular (population) difference is zero.
However, the p-values are for a test done in isolation. Here you are
doing 41 tests (ignoring the intercept), and I think you should be making
some allowance for multiple comparisone. See e.g. the package multcomp.
My preference (and it is widely shared) would be to present confidence
intervals for the estimated differences you are interested in (which might
be all the differences from the reference category, or something else
as, just guessing, you might be interested to know if there is a
difference between IDG and IDH).
On Thu, 6 Apr 2006, Andrew McDonagh wrote:
> Hello,
>
> Apologies if this is the wrong list, I am a first-time poster here. I
> have an experiment in which an output is measured in response to 42
> different categories.
> I am only interested which of the categories is significantly different
> from a reference category.
>
> Here is the summary of the results:
>
> summary(simple.fit)
>
> Call:
> lm(formula = as.numeric(as.vector(TNFa)) ~ Mutant.ID, data =
> imputed.data)
>
> Residuals:
> Min 1Q Median 3Q Max
> -238.459 -25.261 -0.868 25.660 309.496
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 49.0479 10.5971 4.628 5.08e-06 ***
> Mutant.IDB 149.8070 23.1632 6.467 3.09e-10 ***
> Mutant.IDC 98.7443 23.1632 4.263 2.55e-05 ***
> Mutant.IDD 97.2203 23.1632 4.197 3.37e-05 ***
> Mutant.IDE 118.9820 23.1632 5.137 4.49e-07 ***
> Mutant.IDF 241.8537 23.1632 10.441 < 2e-16 ***
> Mutant.IDG 107.4883 23.1632 4.640 4.80e-06 ***
> Mutant.IDH 105.7664 23.1632 4.566 6.74e-06 ***
> Mutant.IDI 517.4650 23.1632 22.340 < 2e-16 ***
> Mutant.IDJ 19.7777 23.1632 0.854 0.393735
> Mutant.IDK 47.4240 23.1632 2.047 0.041313 *
> Mutant.IDL 3.2542 23.1632 0.140 0.888347
> Mutant.IDM 180.9638 23.1632 7.813 5.63e-14 ***
> Mutant.IDN 19.0582 23.1632 0.823 0.411155
> Mutant.IDO 61.8684 23.1632 2.671 0.007891 **
> Mutant.IDP -0.5306 23.1632 -0.023 0.981738
> Mutant.IDQ -10.6972 23.1632 -0.462 0.644478
> Mutant.IDR 1.5377 23.1632 0.066 0.947107
> Mutant.IDS 14.6333 23.1632 0.632 0.527934
> Mutant.IDT 48.8900 23.1632 2.111 0.035458 *
> Mutant.IDU 58.9597 23.1632 2.545 0.011313 *
> Mutant.IDV 81.7657 23.1632 3.530 0.000467 ***
> Mutant.IDW 82.9576 23.1632 3.581 0.000386 ***
> Mutant.IDY 49.1926 23.1632 2.124 0.034343 *
> Mutant.IDZ 51.0381 23.1632 2.203 0.028170 *
> Mutant.IDZA 116.0487 23.1632 5.010 8.38e-07 ***
> Mutant.IDZB 56.4402 23.1632 2.437 0.015287 *
> Mutant.IDZC -14.5305 23.1632 -0.627 0.530838
> Mutant.IDZD -5.0069 23.1632 -0.216 0.828983
> Mutant.IDZE 9.1176 23.1632 0.394 0.694080
> Mutant.IDZF 232.2879 23.1632 10.028 < 2e-16 ***
> Mutant.IDZG -27.1671 23.1632 -1.173 0.241595
> Mutant.IDZH 0.8757 23.1632 0.038 0.969862
> Mutant.IDZI 4.7952 23.1632 0.207 0.836108
> Mutant.IDZJ -5.5859 23.1632 -0.241 0.809568
> Mutant.IDZK -12.9263 23.1632 -0.558 0.577138
> Mutant.IDZL 38.8621 23.1632 1.678 0.094224 .
> Mutant.IDZM 39.2643 23.1632 1.695 0.090880 .
> Mutant.IDZN 73.8419 23.1632 3.188 0.001553 **
> Mutant.IDZO 147.7804 23.1632 6.380 5.20e-10 ***
> Mutant.IDZP 0.5654 23.1632 0.024 0.980540
> Mutant.IDZQ 50.5117 23.1632 2.181 0.029824 *
> Mutant.IDZR 217.6824 23.1632 9.398 < 2e-16 ***
> Mutant.IDZS 237.3227 23.1632 10.246 < 2e-16 ***
> ---
> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Residual standard error: 61.79 on 377 degrees of freedom
> Multiple R-Squared: 0.7351, Adjusted R-squared: 0.7049
> F-statistic: 24.33 on 43 and 377 DF, p-value: < 2.2e-16
>
> >
>
> My question relates to the meaning of the p-values. Do the p-values
> relate to
> a) the confidence in the estimate
> or
> b)the confidence that the non-intercept categories are different to the
> intercept
>
> Somebody mentioned to me that the p-value for the intercept is the
> confidence in the estimate of the intercept, whereas the remaining
> entries are the confidence in each strain being different from the
> reference / intercept
>
> Note the contrasts setting is contr.treatment.
>
> Any help would be appreciated
>
> Andrew McDonagh,
> PhD Candidate,
> Department of Infectious Diseases,
> Commonwealth Building,
> Hammersmith Hospital,
> Du Cane Road,
> London W12 ONN
>
> a.mcdonagh at imperial.ac.uk
>
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>
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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