Research methodology, statistical literacy and communication When talking to clients or offering advice, I often find myself having to question the choice of plotting variables over time.  For example, if a client is interested in understanding the relationship between a response variable Y and variable X, the first thing they do is to plot them over time: 
The idea, I think, is to visually assess if changes in one variable over time are associated with changes in the other.
As a statistical consultant, I find this approach unsatisfactory for obvious reasons and suggest to do a scatterplot instead.  
The difficulty lies in explaining that for the type of problems faced, time is seldom causal, will distract the reader and is superfluous (again, we are not interested in changes over time).  
I am looking for suggestion on how to best explain to the non-statistician that there are far more effective ways to understand the relationship between two variables. Has any consultant dealt with it before and what have they done to address this?
 A: The position of a consultant is awkward because it's of the consultant's interest to not work as much as the client requests, so any push back of "let's not" is going to cause sour feelings.
Let them fall, then pick them up: From my experience, I would suggest granting their wish first by doing what they asked. And then present the alternative method and explain to them the pros and cons of the presented methods. Yes, some time is wasted at the beginning but can often cut down a lot of dreadful tug-a-wars.
This approach has not caused any problem so far. Most of the times I won, yet occasionally some stubborn ones insisted they'd keep the old one, but at least I felt I had presented a chance for the client to make an informed choice. If things get too ridiculous, I would request my name to be removed from all the works related to the project.
Slowly build up their statistical "taste": For example, in your case I'd suggest using a scatter plot to break them in, and then perhaps inspire them to appreciate a cross-correlation function plot, which probably can tell even more than a scatter plot.
Show evidence in literature: Arguments related to types of analysis, terminology, and data presentation can also be solved by presenting a few current publications that support your suggestions.
A: I'm not a consultant, but here is how I would try to convey your point to a non-statistician:
1) present one example with a plot where relationship is in fact causal.
2) follow up with several counterexamples where the relationship is spurious. Here are some humorous examples that you might mention:
http://www.tylervigen.com
The purpose of (1) would be to communicate to a non-expert that you've considered their concern and that you're also not being totally dismissive of them. The purpose of (2) is to obviously to doubt their assumptions about causal relationships, but also to illustrate the point in a simple way hopefully without being condescending. After than, you can offer what you think is a better approach. 
