# [R] Difference between two-way ANOVA and (two-way) ANCOVA

syrvn mentor_ at gmx.net
Wed Jul 4 15:20:17 CEST 2012

```Hi!

as my subject says I am struggling with the different of a two-way ANOVA and
a (two-way) ANCOVA.

I found the following examples from this webpage:

http://www.statmethods.net/stats/anova.html

# One Way Anova (Completely Randomized Design)
fit <- aov(y ~ A, data=mydataframe)

# Randomized Block Design (B is the blocking factor)
fit <- aov(y ~ A + B, data=mydataframe)

# Two Way Factorial Design
fit <- aov(y ~ A + B + A:B, data=mydataframe)
fit <- aov(y ~ A*B, data=mydataframe) # same thing

# Analysis of Covariance
fit <- aov(y ~ A + x, data=mydataframe)

I) The 1. example is pretty clear. A simple on way ANOVA.

II) Is it correct to say that example 2. (which is called a Randomized Block
Design) is a two way ANOVA?

III) Example 3 is like example 2. (in case I was right in II) )  a two way
ANOVA but including an interaction term. That's why
they call it here a Factorial Design.

So far so good.

IV) For me, the ANCOVA (last example) looks like a two-way ANOVA. So in what
way is the variable "x" different to variable "B" so that it is called an
ANCOVA and not an ANOVA??? I presume that from the type of data R knows
whether to perform an ANCOVA or an ANOVA.

V) Is it right to say that the ANCOVA example is a two-way ANCOVA? Or can a
one-way ANCOVA actually exists?

You see I am a bit confused especially how R distinguishes between the
ANCOVA and the two-way ANOVA?

I hope to find some useful answers here.

Cheers!

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