# Re: [R] simulating the anova

From: <Bill.Venables_at_csiro.au>
Date: Wed, 05 Mar 2008 15:43:10 +1000

Here is one possible way of proceeding:

cohen.f <- 0.25
groups <- 4
between.var <- 19
within.var <- between.var/cohen.f^2
n <- 500

N <- groups*n
sim.means <- rnorm(n = groups, mean = 0, sd = sqrt(between.var)) sim.data <- data.frame(group = gl(groups, 1, length = N),

response = rnorm(N, sim.means, sqrt(within.var))) sim.anova <- aov(response ~ group, sim.data)

## sim.data <- lapply(sim.means, function(mean) rnorm(n = n, mean =
mean, sd =
## sqrt(within.var)))
## sim.anova <- ?

to see the anova table, use summary(sim.anova), for example.

Bill Venables
CSIRO Laboratories
PO Box 120, Cleveland, 4163
AUSTRALIA

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-----Original Message-----
From: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] On Behalf Of Will Holcomb
Sent: Wednesday, 5 March 2008 3:03 PM
To: r-help
Subject: [R] simulating the anova

I have been trying to figure out how to run a simple simulation of the ANOVA
and I'm coming up just a bit short. The code I've got is:

cohen.f = .25
groups = 4
between.var = 19
within.var = between.var / cohen.f ^ 2
n = 500
sim.means = rnorm(n = groups, mean = 0, sd = sqrt(between.var)) sim.data = lapply(sim.means, function(mean) rnorm(n = n, mean = mean, sd =
sqrt(within.var)))
sim.anova = ?

I'm pretty sure I've got data with the between group and within group variances that I want. I don't really know how to run an ANOVA on it though.
All the examples I've been able to find (with aov and anova) require an explicit model. The ANOVA just tests the equivalence of means for a set of
groups, right? Can I not just tell it to give me the likelihood the means
are equal for all the columns without writing an explicit model.

Any help would be appreciated,
Will

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