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I have an x variable and a y variables. I have done a simple scatter plot. I however don't really know how to interpret (if there is anything to interpret) the plot. I can't find any other similar examples

scatter plot

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    $\begingroup$ Please give more information on the data-generating process. $\endgroup$ Commented Apr 8, 2015 at 16:30

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I would think that this suggests that you have several different populations being analysed with a few outliers that may or may not be freak instances. Perhaps 9 or 10. Perhaps different atomic isotopes or similar species of organic molecules might show these sorts of results.

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I think the answer strongly depends on what are the variables. In general, one can perform correlation analysis (Pearson or Spearman, however I think the latter is more appropriate). However, there is strong evidence (I mean by visual inspection) that in fact there are different classes of something in the plot. If indeed the response is on the vertical axis, and if this is somewhat related to quantum mechanics, I'd suspect there are discrete realisations of an observable, possibly obscured with some kind of noise (thermal most likely, if it relies strongly on electronic devices; or cosmic radiation, or...). Or, if this is some kind of resonant behaviour, this may show position of resonances in some mixing system (bifurcations ring a bell, but that would be going too far with this amount of information). An so on. If you are asking for what to do statistically, I would say that nearly everything; it depends what are the data, what are you looking for, what's the aim of collecting these data, etc.

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You may find it more sensible if you interchange x and y axes:

enter image description here

The variables seem to be inversely correlated with each other.

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  • $\begingroup$ Since the standard correlation coefficients (Pearson, Spearman) do not change when the axes are interchanged, could you explain the reason why you did so? And then, having observed there is a little positive correlation, what is the interpretation of that? What does it mean for these data? $\endgroup$ Commented Apr 8, 2015 at 16:59
  • $\begingroup$ The correlation was always present, but this form of graph makes it more apparent and hence understandable. What will be exact interpretation will depend on what variables are being studied and in what context and what are the results of statistical tests. My experience is nowhere close to yours and I look forward to your expert opinion on this. $\endgroup$ Commented Apr 8, 2015 at 17:34
  • $\begingroup$ I appreciate your confidence in me, but I'm just as much in the dark as you concerning what the variables mean! About all we can do is to find descriptions of the patterns in the scatterplot. I get a strong visual impression of multimodality (or clustering) on the (original) vertical axis. That might be the thing to focus on. That would provide justification for your proposal to switch axes, because conventionally we view the vertical axis is representing a response to values on the horizontal axis. $\endgroup$ Commented Apr 8, 2015 at 18:48

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