How do you tell the difference between correlation and causation?

Correlation is a statistical metric that gauges the degree of association between two variables, signifying how they change in relation to each other. It ranges from -1 to 1: a score of -1 implies a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 denotes no correlation. For instance, in a dataset plotting height against weight, a positive correlation would imply that taller individuals tend to have higher weights. However, correlation doesn't elucidate the causative factors or mechanics of this connection; it solely quantifies the co-varying pattern between variables.

This method for measuring correlation is correlation coefficient (r). It is the covariance of the two variables divided by the product of their standard deviations. This standardizes the covariance (a measure of covariation between variables), which otherwise takes on any value, to stay between -1 and 1. It is important to note that this method of measuring correlation focuses on linear relationships. While r only tells you the strength of the relationship, If you want to know HOW the variables relate, the slope of the regression line is a good place to start. It is the covariance of the two variables divided by the variance of one of them. This tells you on average how the value of one variable changes when the other variable changes.

Causation, or causal inference, is a relationship with validated statistical significance that one variable causes a measurable change to another. Key to this definition is "validated" as a passing statistical test is not enough to prove causality. What makes causal inference so hard is the presence of observed and unobserved confounders, along with interaction effects. One of the best methods to show causality is through randomized controlled trials (RCT). Unlike observational studies that only account for observed covariates, randomization in RCTs also account for unobserved covariates. Even through an RCT, causality can still be questioned. Hence why meta-analyses of multiple RCTs is necessary for decisions like medical guidelines.

To establish causation one has to mind the analysis tools that are being used. The simplest statistical tools are only good to establish correlation, but to establish causation the tools in use need to be much more complex. Experimentation is a good way to establish this, either with physical experiments (lab and clinical experiments, controlled testing, etc) or with computer or virtual experiments provided that the virtual environment is fit for purpose.

Interestingly, correlation does not imply causality and the lack of correlation does not imply that there is no causal link between the variables you are looking at.

The best way to avoid confusing causation and correlation is considering how the relationship was determined. If an experiment was conducted, you're looking at causation. If data points were simply collected and compared, you're analyzing correlation.

Correlation often overlooks the underlying processes or mechanisms that produce data. When analyzing data, it's essential to delve into its origins and generation methods. By understanding how the data comes to be, we can more effectively discern between mere correlation and genuine causation.

Conducting an experiment is almost always a necessity to determine causation. Quality experiments should always include a treatment group and a control group where nothing changes (think placebo, sugar pill). Multiple groups can be used, but the goal is to minimize the impact of variables outside of the exterminator's control. Groups can be randomly assigned, created based on particular characteristics, or one participant could even receive multiple treatments. When determining causation, you should always consider what type of experiment will yield the most reliable results.

The process to identify causation is indeed a generally complex one, as it is heavily dependent on domain knowledge. This occurs especially due to the need to first identify possible confounding factors, and then to adjust for them and isolate the cause-effect pair. The complexity of this arises from the fact the often, datasets don't have all the factors the eventually affect an outcome, thus, greatly influencing the probability of a wrong assumption on causation. A previous approach with KOL on the subject helps to reduce this risk.

Having a wide range of tools at your disposal is a must when determining the relationship between two or more variables. I suggest using learning resources online to better understand each tool and which might be more appropriate for the task at hand. If you only need to create a line of best fit, using Excel is likely the simplest option. However, if you need to conduct a more thorough analysis R or Python are likely the more appropriate tool.

Increasingly it is common to show causation graphically using natural experiment strategies. Using "difference-in-difference" graphs is very popular for time series data and "regression discontinuity" graphs are very popular for data where there are cut-offs. In spatial data I often exploit administrative boundaries and use "boundary discontinuity" graphs. Still, it's important to remember that all causal inference rests on assumptions so being clear about those assumptions is critical.

One of my favorite examples to understand the difference between correlation and causation is examining the relationship between the number of TVs per capita and life expectancy. There is a strong, positive correlation between TVs per capita and life expectancy of a nation. Does that mean that if you want to live longer you should purchase more televisions? No! There is a confounding variable that is not being considered. That variable is nation wealth. When a nation has a higher amount of wealth, yes, they can purchase more televisions - but more importantly, they have access to better health care and a higher quality hospital system. Always remember that if you want to determine causation, you need to conduct an experiment!

A lot of times people assume causal studies are better, but it really all depends on the research or evaluation question. Correlation will answer many questions perfectly. Additionally, correlation may be the initial exploratory study before a more rigorous causality study can be done. Further, in real world policy analysis, correlation may be all that can technically be done. At the same time, causality can still practically be inferred even if no ability to statistically verify it can occur. For instance, in programs I evaluated, we would see dozens of percentage point differences in several outcomes between a newer and older program. While technically correlation, we can reasonably infer a causal relationship in many cases.

For future discussion Stereopathical perception relative to co- location in research and diagnosis. What does a co-localized signal really mean?