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