How to use this tool

This interactive tool visualizes the core arguments from Isager (2023). It demonstrates why "Correlation does not equal a direct causal connection" by letting you explore competing causal models for the same data.

(Note: All data and correlations in this tool are simulated/made up for educational purposes)

1

The Causal Diagram
Look here first. This visualizes the theoretical model (e.g., A → B) being tested.

2

The Correlation Chart
This shows the observable data (Scatterplot).
Look for the Red Line (The observed correlation).

3

The Controls
Use these buttons to Intervene, Reveal Hidden Data, or Control for Variables.

"If you cannot imagine the truth, you cannot discover it."

Click "Next" to begin the investigation.

Built by Carsten Bergenholtz and Gemini 3.0 Pro

Model 1: Direct

vs

Model 2: Reverse

The Directionality Problem

Correlation r = 0.85

The scatterplot shows a clear pattern. But does this pattern truly represent the causal model we have in mind?

Does Exercise cause Mood? Or does Mood cause Exercise? Swap the axes to see if the pattern reveals the truth.

Result: The pattern is identical. You cannot infer causality from this chart alone; you would need a longitudinal design or preferably an experiment.

Model 4: Confounding (Common Cause)

What is Confounding?

Observed r = 0.82

To "confound" means to mix up. Isager (2023) describes this as a Lurking Third Variable.

The Illusion: It looks like Exercise causes Mood because they move together.
Other variables could be causal factors. For example, "Stress at work": High stress causes both low exercise and bad mood.

Why we "Control" for Variables:
Think of Statistical Control as "Comparing Like with Like."

Comparing a stressed person to a relaxed person is like comparing apples and oranges. We must compare a stressed person only to other stressed people.

When we do that (look within the colors), the correlation is zero (r=0.00). The "effect" was just the difference between the groups.

Model 5: Selection Bias (Collider)

Selection Bias

Sample r = 0.65

Did everyone answer the survey? Or did the "Unhappy Gym Rats" (High Exercise, Bad Mood) refuse to participate?

Insight: The correlation only exists because we are missing the grey dots. In the full population, there is no correlation (r=0.00).

(This is also called Conditioning on a Collider)

Feedback Loop

Model 3: Bidirectional

Isager mentions that "feedback relations often lead to complex relations".

Rather than a simple one-way street, the variables feed each other.

Exercise releases endorphins → Better Mood.
Better Mood increases motivation → More Exercise.

This creates a self-reinforcing cycle. In a scatterplot, this would look like a massive correlation, but calculating a single "causal effect" is mathematically difficult because cause and effect are intertwined.

The Real World is Messy

Confounding + Selection + Reverse Causality

Isager (2023) concludes that we must "consider all the causal relations."

In the real world, you don't just get one problem. You often get all of them at once.

As the diagram shows:

Red Dashed: Third variables causing both.
Grey Dashed: Selection bias distorting the sample.
Black Solid: Direct, Reverse, or Feedback effects.

Conclusion: A simple correlation (r=0.85) could be the result of this entire tangled web.

The Takeaway

Correlation ≠ Causation

Whenever you see a correlation like the one on the left—where Variable X and Variable Y seem to move together—you must pause.

Ask yourself Isager's Question:

"Consider all the causal relations."
Could it be confounding? Selection bias? Reverse causality? Or a feedback loop?

One needs an experiment, longitudinal data, or more complex statistical analysis to shed further light on the question.