[R] ANOVA question

[ONKELINX, Thierry]

Dear Robert,

It is easier to use lm instead of aov if you want coefficients for each group. Note that you can use rnorm vectorised.

set.seed(0)
N <- 100 # sample size
MEAN <- c(10, 20, 30, 40, 50)
VAR <- c(20,20,1, 20, 20)
LABELS <- factor(c("A", "B", "C", "D", "E"))

# create a data frame with labels
df <- data.frame(Label=rep(LABELS, each=N))
df$Value <- rnorm(nrow(df), mean = MEAN[df$Label], sd = sqrt(VAR[df$Label]))

mod_aov <- aov(Value ~ Label, data=df)
mod_lm <- lm(Value ~ Label, data = df)
all.equal(anova(mod_aov), anova(mod_lm))

summary(mod_aov)
summary(mod_lm)

summary(mod_lm)$coef
confint(mod_lm)

#without intercept
mod_lm0 <- lm(Value ~ 0 + Label, data = df)
summary(mod_lm0)$coef
confint(mod_lm0)

Best regards,

Thierry


ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx op 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-help-bounces op r-project.org [mailto:r-help-bounces op r-project.org] Namens Robert Latest
Verzonden: vrijdag 11 mei 2012 9:37
Aan: r-help op r-project.org
Onderwerp: [R] ANOVA question

Hello all,

I'm very satisfied to say that my grip on both R and statistics is showing the first hints of firmness, on a very greenhorn level.

I'm faced with a problem that I intend to analyze using ANOVA, and to test my understanding of a primitive, one-way ANOVA I've written the self-contained practice script below. It works as expected.

But here's my question: How can I not only get the values of the coefficients for the different levels of the explanatory factor(s), but also the corresponding standard errors and confidence levels?
Below I have started doing that "on foot" by looping over the levels of my single factor, but I suppose this gets complicated and messy with more complex models. Any ideas?

Thanks,
robert


set.seed(0)

N <- 100 # sample size

MEAN <- c(10, 20, 30, 40, 50)
VAR <- c(20,20,1, 20, 20)
LABELS <- c("A", "B", "C", "D", "E")

# create a data frame with labels
df <- data.frame(Label=rep(LABELS, each=N)) df$Value <- NA # fill in random data for each factor level for (i in 1:length(MEAN)) {
    df$Value[(1+N*(i-1)):(N*i)] <- rnorm(N, MEAN[i], sqrt(VAR[i])) }



par(mfrow=c(2,2))
plot(df)          # Box plot of the data
plot(df$Value)    # scatter plot

mod_aov <- aov(Value ~ Label, data=df)

print(summary(mod_aov))
print(mod_aov$coefficients)

rsd <- mod_aov$residuals

plot(rsd)

# find and print mean() and var() for each level for (l in levels(df$Label)) {
    index <- df$Label == l

    # Method 1: directly from data
    smp <- df$Value[index]  # extract sample for this label
    ssq_smp <-  var(smp)*(length(smp)-1) # sum of squares is variance
                                         # times d.f.
    # Method 2: from ANOVA residuals
    rsd_grp <- rsd[index]                # extract residuals
    ssq_rsd <- sum(rsd_grp **2)          # compute sum of squares

    # print mean, variance, and difference between SSQs from the two
    # methods.
    write(sprintf("%s: mean=%5.1f var=%5.1f (%.2g)", l,
        mean(smp), var(smp),
        ssq_smp-ssq_rsd), "")
# ...and it works like expected! But is there a shortcut that would give me # the same result in a one-liner?
}

______________________________________________
R-help op r-project.org mailing list
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.
* * * * * * * * * * * * * D I S C L A I M E R * * * * * * * * * * * * *
Dit bericht en eventuele bijlagen geven enkel de visie van de schrijver weer en binden het INBO onder geen enkel beding, zolang dit bericht niet bevestigd is door een geldig ondertekend document.
The views expressed in this message and any annex are purely those of the writer and may not be regarded as stating an official position of INBO, as long as the message is not confirmed by a duly signed document.