Does Correlation "Sometimes" Imply Causality? I am an MBA student taking courses in statistics.
I am sure that at some point, we have all heard the famous expression - "Correlation Does Not Imply Causality".
When we are being introduced to this concept, we are often shown an absurd example of two variables that are highly unlikely to have a causal relationship, yet seemingly appear to be correlated with one another. For example - it is highly unlikely that there might be a causal relationship between the "letters in the words of spelling bees" and the "number of people killed every year by spiders":

However, there are other examples in which it might be reasonable to assume that correlation does in fact imply causality. For example, it is quite likely that there might be some relationship between "life expectancy" and "GDP" - countries with higher GDP likely have stronger economies, stronger economies likely have stronger health sectors, countries with stronger health sectors likely have more hospitals/doctors ... using this logic, although there might be outliers and exceptions, it does not seem completely unreasonable to expect that there might be some causal correlation between income and life expectancy:

This leads me to my question - when we are told that "Correlation Does Not Imply Causality", does this statement indirectly mean that there might be some instances in which "Correlation DOES Imply Causality"?
For instance, suppose I have some data (for different countries) which shows a clear linear relationship between  "the number of doctors per 1000 people" and the "life expectancy" of those countries (i.e. people who live in countries with more doctors tend to live longer on average) - although there some philosophical arguments that suggest we might never be able to "truly" attribute causality between two concepts (e.g. perhaps tomorrow we find out that countries with more doctors have some newly discovered vitamins in their water and this is why they live longer, not actually due to more available doctors, yet this is highly unlikely) - would be fundamentally wrong and morally unreasonable to prematurely suggest that "there theoretically might exist some level of causal relationship between the number of doctors and life expectancy"?

To add to the excellent answers already given: the statement helps to create awareness of logical errors regarding correlation.
We all easily and intuitively accept there must be a relationship between causality and correlation. We feel that causality implies correlation. This is correct. Most people, including myself, have subsequent intuition that is logically flawed.
Personally, I have not succeeded in changing my intuition, which means that I constantly need to remind myself that I cannot reverse the argument, so I keep telling others but also mostly myself that correlation does not imply causality. Also, I need to remind myself that causality does not imply that I will be able to observe the correlation that I expected - for many reasons already mentioned in previous answers.
If it hasn’t settled in yet - the real problem is that our observations usually will only tell us if there is a correlation.
I therefore need to remind myself not to turn the argument on its head. I need to remind myself that observing a correlation when evaluating a hypothesis is much stronger than developing a hypothesis from an observed correlation. That does not mean I cannot use open observational studies to develop hypotheses (in fact, these studies can be very powerful for inspiration). it means that I need to test these developed hypotheses in carefully designed experiments, and that these experiments shall not use any of the previous observations that inspired the hypothesis. Most of the time, that implies a lot of work and therefore not a very appealing prospect.
I also need to remind myself to design my experiments such that I maximize the response to the supposed causal factor; or at least ensure that the response I expect is large enough to be observable.
When that goes wrong, it is where it becomes easy for me but maybe not for others: I’m an engineer, so in my application, there is no practical difference between an unmeasurable response vs. no response at all. That means I can abandon the experiments at this point. Whereas more Fundamental scientific work may run into the need to measure even the small causal responses, and/or find some other way to figure out if the supposed causality is or isn’t there.
