On Jul 4, 2012, at 15:20 , syrvn wrote:

> 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.

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.

--

Peter Dalgaard, Professor

Center for Statistics, Copenhagen Business School

Solbjerg Plads 3, 2000 Frederiksberg, Denmark

Phone: (+45)38153501

Email:

[hidden email] Priv:

[hidden email]
______________________________________________

[hidden email] mailing list

https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide

http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.