# [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,
> London W12 ONN
>
> a.mcdonagh at imperial.ac.uk
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
>

--
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

```