Cluster analysis as a preliminary analysis I want to produce four groups (high/high, high/low, low/high and low/low) using two continues variables and compare these groups in terms of a few dependent variables. I know that cluster analysis (k-means and hierarchical) is a type of 'end' analysis which is the main goal of the paper to reach such clusters and then discuss the nature of the clusters. However, I am willing to use this technique (k-means by using k=4) as a kind of preliminary analysis to produce the groups. I know that scatter plot and means splits are other alternatives but they have their own disadvantages that cluster analysis may resolve. What do you think?
 A: If you have a predefined goal, such as your high/low splits, don't use cluster analysis at all. Instead, bin your data into your four predefined bins (maybe using quantiles such as the median to define the split)
You can also use more than two bins, e.g. low/normal/high this way easily.
The benefit is that the results will be easy to understand. With cluster analysis, you will likely need to perform another analysis to understand why it clustered the data the way it did.
Cluster-analysis should never be the "end" analysis. It's an interim step to understand your data, but it doesn't really return any further usable result except better knowledge of your data. If you run cluster analysis, you next need to analyze the clusters found, and most likely you will need to iterate through this a number of times.
A: It is fine to use cluster analysis as a preliminary analysis.  However, I don't see how using CA will resolve any of the disadvantages of using (say) median splits.  Unless the true data generating process is that there are four latent groups that are exactly identified by the clustering, and which differ on mean $Y$, but do not differ based on their $X_1$ and $X_2$ values, you will be better served by regressing $Y$ onto $X_1$ and $X_2$ (and possibly the interaction) directly.  
