Skip to content

Difference between two-way ANOVA and (two-way) ANCOVA

3 messages · syrvn, Peter Dalgaard, Richard M. Heiberger

syrvn
# 
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!


--
View this message in context: http://r.789695.n4.nabble.com/Difference-between-two-way-ANOVA-and-two-way-ANCOVA-tp4635403.html
Sent from the R help mailing list archive at Nabble.com.
Peter Dalgaard
#
On Jul 4, 2012, at 15:20 , syrvn wrote:

            

      
      
      
    

        
Well, it's not really about R, is it?


Anyways, I'd call  y~A+x a ONE-way ANCOVA, because it deals with the covariation of two variables (y and x) in a one-way layout. In the traditional applications, x is often independent of A (pre-randomization measurement like soil quality, etc.) so that the group means of y can be estimated as the value of the regression at the grand mean of x ("adjusted means"), and the mean difference between two groups is the vertical difference between the parallel regression lines.