ANOVA for increasing IV

Question

I wonder, how to analyze a dataset the right way.

My data are generated as follows:

• Take one graph $G$ with $G \in \{ \text{random}, \text{spanning-tree}, \text{empty}\}$
• Doing something with the graph, depending on parameter $n$ for $n=1$ to $100$:
  • Measuring parameter $a$, $b$ and $c$ (e.g. Cluster Coefficient C, Pathlength L and Powerlaw-Exponent Alpha)

I run this setup for each graph once and checked the correlation (what happens to a, b or c if I increase n).

My next task, is to check if there is a difference in the parameters between the different graph types for a series of $n=1$ to $100$.

I want to know if the graph-type has an influence on my parameters (depending on n). My best case would be, that I can take an empty graph.

My current approach is:

• For each graph type:
  • Calculate the parameters a, b and c for each n ($n=1$ to $100$) (averaged over 100 runs)

So far I get for each graph type a file with 100 rows (1 row per n) with 3 parameters.

Then I do a one-way-anova analysis for each parameter with the graph-type as my IV and the parameter as my DV.

Is this approach right? Or should I create 100 datasets (one for each n) for each graph type and perform a anova analysis on them?

Kind regards and thanks for any help,

Kai

Answer 1

It sounds to me like you have three DVs and two IVs. You have an IV of graph type, and an IV of n. But n is a bit tricky because it is a ratio-scaled variable, so would work better (in my opinion) as a covariate in an ANCOVA, provided you expect the effect of n to be something like linear. In any case a model something like

DV ~ GraphType + n + GraphType*n

would catch a) differences between graph types, independent of n, b) effects of n on the DV, and c) whether the effect of n depends on the graph type.