How do I show if two paired sets of quantitative values vary in relation to each other?

First I always — as in ALWAYS remind people — correlation is NOT causation. Consider the synonyms for the word correlation:

  • Association
  • Connection
  • Relationship
  • Link
  • Parallel
  • Correspondence

Nowhere on this list is the work “causation.” Now it doesn’t mean that there is never a causation factor between variables BUT the rigor, study (controlled) and statistical analysis that are required to show causation are EXTENSIVE (think tobacco). So, remember, as a general rule, correlation is NOT causation.

Okay, now that I have gotten that on the record one more time…

If you need to show how two paired sets of quantitative data values vary in relation to each other and in which direction, i.e., positively or negatively use of a scatter plot (this is not your only choice, but a most common and good choice).

This Post Has 2 Comments

  1. Nisrine Khazaal

    Thank you for the blog. I usually don’t bother to read blogs but when it comes to learning something I sure will.
    My question is on correlation not being causation. Let us say we know there is a strong correlation between two variables in healthcare setting and we really want administration to act on it, as a quality and process improvement specialist who has timelines to improve processes, how would I be able to statistically show a causation? This would be starting a research project. I usually look at the literature to see if the correlation has already been proved to be true. But if I don’t find anything out there, could monitoring the correlation over an acceptable period of time prove a causation if the variables are strongly correlated (ie go up and down together)? Thank you

    1. Kathy

      Thanks for you post. First I want to be on the record as saying I am not a statistician (I just play one on TV)…that said, I think I can provide some insight! What I believe you are truly driving at is how to get leaderships attention and resources for a quality improvement initiative which is a different issue than showing statistically significant correlation in data. While it is true that if you are recommending a change to a clinical course of treatment you need to do a literature search and find good studies with enough observations and statistical rigor to make the case — a QI initiative that changes an operational process of care doesn’t have to meet the same high standard.

      First and foremost, you most likely need to quantify how big the problem is that needs to be corrected. For example, wound infections extend lengths of stay and decrease net revenues (how much?), the time lost from cancelled cases cannot be re-found (how much?), readmissions to the hospital, poor HCAHPS scores will jeopardize the medical centers Medicare Annual Payment Updates (APU) (how much?). You have to identify what is important and urgent to the people you need to engage — more often than not people miss this step and you won’t get far without it. And yes, I KNOW, it is about the quality of care–but it is also about limited resources for projects and keeping the medical center financially viable so that they can continue to provide care.

      Next you most likely need to do a root cause analysis and some decision analysis around the process you are proposing to change. And then of course the Plan Do Study Act (PDSA) is the way in which you lay out a project and monitor results.

      A good resource is Alemi and Gustafson’s book “Decision Analysis for Healthcare Managers” you can read about it at the American College of Healthcare Executives website or on

      Bottom line — not everything requires or is amenable to a research study — rather — you often (very often) need to follow the money and make a compelling case for the resources you need to improve a process of care.

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