How do you establish causality between two variables in statistics?

1 Correlation First

Correlation is the initial stepping stone in establishing causality. You must first determine if two variables are related at all. This is done using correlation coefficients, such as Pearson's r, which measures the strength and direction of a linear relationship between two variables. A high absolute value of the coefficient indicates a strong relationship, but remember, correlation does not imply causation. It's simply the prerequisite for any further analysis aimed at establishing a causal link.

2 Establish Temporality

Once correlation is confirmed, you must establish temporality, meaning the cause precedes the effect in time. Without this temporal order, you cannot claim that one variable is causing changes in another. Analyzing longitudinal data, where measurements are taken over time, can help in determining whether changes in the supposed cause precede changes in the effect, laying the groundwork for a potential causal relationship.

4 Experimental Design

The gold standard for establishing causality is through experimental design, specifically randomized controlled trials (RCTs). By randomly assigning subjects to different conditions and manipulating the independent variable, you can observe the direct effects on the dependent variable. This method controls for confounders and ensures that any observed changes can be attributed to the manipulation of the independent variable.

5 Causal Inference

Causal inference involves using statistical methods to deduce the likelihood of a causal relationship when you cannot use controlled experiments. Methods like Granger causality tests or instrumental variables can provide evidence of causation by exploiting natural experiments or using variables that are related to the cause but not directly to the effect. These methods help infer causality from observational data where RCTs are not feasible.

6 Alternative Explanations

Finally, it's crucial to consider and rule out alternative explanations for the observed relationship between variables. This involves critical thinking and a thorough examination of the data and study design. Look for any potential biases or errors that could lead to incorrect conclusions. By eliminating other possible causes, you strengthen the case for a causal relationship between your variables of interest.

7 Here’s what else to consider

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