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This question is an extension of awesome thread Does causation imply correlation?.

As an example, let's say that I am running an online experiment on Stackoverflow to see whether asking more questions leads to an increase in time spent on stackoverflow. For this case, I would have historical data on # of questions asked over, say, 1 week and average time spent on stackoverflow. I can plot a scatterchart for the last two years and see the the relationship.

I have three interrelated questions:

Question 1: Before running an experiment, is it a good practice to plot a scatterchart between # of questions asked in 1 week and average time spent on stackoverflow?

Question 2: If we do decide to plot the chart, one could argue that this scatterchart will show me association between the two variables. If correlation (or association) doesn't imply causation, what's the need for plotting such a chart? It will be great if someone can talk about the value of plotting scatterchart before running an experiment.

Question 3: I learned from the Stackoverflow thread above that Causation doesn't imply correlation, but it does imply association. Hence, I'd believe that association (and not correlation) is a necessary condition for causation. If this is true, the benefit of scatterplot would be to check the necessary condition for causality. For instance, what if, I found from scatterplot that an increase in # of questions asked over a period of time is associated with a decrease in time spent on SO. This would mean that there is no causality. Hence, I'd not have to run an experiment. Am I correct?

I am new to the field of experimentation and causal-checks. I don't have a Ph.D. in econometrics or statistics. I took advanced graduate courses in Statistics long time ago. So, please excuse my ignorance. I'd appreciate if someone can guide me. Many thanks.

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Before running an experiment, is it a good practice to plot a scatterchart between # of questions asked in 1 week and average time spent on stackoverflow?

It is a very good idea to plot your data because it will give you an idea of what the association looks like. Visualisation is a great general tool in an analyst's chest, and where you have only 2 variables, a scatterplot can be very useful.

If we do decide to plot the chart, one could argue that this scatterchart will show me association between the two variables. If correlation (or association) doesn't imply causation, what's the need for plotting such a chart? It will be great if someone can talk about the value of plotting scatterchart before running an experiment.

One of the points of uncovering an association prior to performing an experiment is that you might find that the association is nonlinear and this will inform the type of model you want to fit. As you can see from the figure in one of the answers to the question you linked to, that of Anscombe's Quartet, it is possible for correlation to be zero yet a profound association to exist. If you simply analysed those data with correlation or linear regression you would be making a big mistake.

I learned from the Stackoverflow thread above that Causation doesn't imply correlation, but it does imply association. Hence, I'd believe that association (and not correlation) is a necessary condition for causation. If this is true, the benefit of scatterplot would be to check the necessary condition for causality. For instance, what if, I found from scatterplot that an increase in # of questions asked over a period of time is associated with a decrease in time spent on SO. This would mean that there is no causality. Hence, I'd not have to run an experiment. Am I correct?

Association is not a necessary condition for causation because there may be suppression. For example, if A truly causes B, but M also causes B (with an effect in the opposite direction to that of A, and A also causes M, then we can easily observe no association between A and B. For example, in R:

> N <- 1000
> set.seed(15)
> A <- rnorm(N)
> M <- A + rnorm(N)
> B <- A - M + rnorm(N)

> cor(A, B)
[1] 0.02033604

> plot(A, B)

enter image description here

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  • $\begingroup$ Thank you for your response. I've a quick question. You've mentioned two things: 1. It is a very good idea to plot your data because it will give you an idea of what the association looks like. 2. Association is not a necessary condition for causation. I am trying to reconcile the two statements. If association is not necessary for causation, why do we need to plot and see it? I believe I am missing something. I'd appreciate your help. $\endgroup$ – watchtower Jan 7 '20 at 19:17
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    $\begingroup$ Because knowing there is an association may bebuseful information. If you do find an association it might mean there is causation, and at the very least it gives you something that might require explanation. For example, it might be the result of confounding, or be the result of an actual causal effect. Always visualise your data...it may not answer your question, but it might point you in the right direction. $\endgroup$ – Robert Long Jan 7 '20 at 19:28
  • $\begingroup$ I would also turn your question around. Why would you not want to visualise your data ? $\endgroup$ – Robert Long Jan 7 '20 at 19:29
  • $\begingroup$ Thank you for your help. I was thinking to just save time (and in turn money) and run the experiment directly because that's what matters. Also, as you have explained that association is not necessary for causation. So, we might just skip the scatterplot step. I am open to your thoughts. $\endgroup$ – watchtower Jan 7 '20 at 19:43
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    $\begingroup$ You could, but how do you propose to uncover the true causal effect if it turns out to be highly non linear? Linearity is often a very strong assumption and visualisation is one of the best ways to find other possibilities. Also, how much time and money does it really save by not doing it in your actual research? $\endgroup$ – Robert Long Jan 7 '20 at 20:22

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