Association is not causation

Association is not causation

An observational correlation describes how two variables vary together in the recorded cases. It does not by itself show that changing one variable would change the other

1. Describe the observed tendency A correlation describes how the recorded variables tend to vary together in the observed cases \(\displaystyle r=0.86\Rightarrow\text{higher }x\text{ tends to occur with higher }y\)
2. Do not infer a cause An association alone does not show that changing one variable would change the other \(\displaystyle r=0.86\;\text{does not imply}\;x\to y\)
3. Check the study design Deliberate manipulation, random allocation and control of other relevant conditions support a cause and effect conclusion \(\displaystyle \text{manipulation}+\text{random allocation}+\text{control}\Rightarrow\text{causal evidence}\)
4. Consider a third factor A third variable can influence both recorded variables and create an association without either one causing the other \(\displaystyle z\to x,\quad z\to y\)

Worked example

An observational study records weekly practice sessions x and an assessment score y for 40 students. State the conclusion supported by the data

1. \(\displaystyle 0.75\le0.84\le1\)The value is in the strong positive correlation band
2. \(\displaystyle x\text{ higher}\Rightarrow y\text{ tends to be higher}\)The positive sign gives the observed direction of the tendency
3. \(\displaystyle r=0.84\;\text{does not imply}\;x\to y\)Students with more weekly practice sessions tend to have higher assessment scores in the observed group. The study does not show that more practice sessions cause higher scores

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