Applying Data
High-Yield Summary
- Correlation (quantified by r, from -1 to +1) describes how two variables move together — it never establishes causation.
- A confounding variable can drive two unrelated variables to appear correlated (e.g., hot weather → ice cream sales AND drownings).
- Hill's criteria (temporality, strength, consistency, elimination of alternatives) help judge whether a relationship is likely causal.
- Statistical significance (unlikely due to chance) and practical significance (large enough to matter) are different — meaningful conclusions need both.
Key Terms
- Correlation coefficient (r)
- Value from -1 to +1 describing strength/direction of a relationship; +1 perfect positive, -1 perfect negative, ~0 no meaningful correlation.
- Confounding variable
- A third factor that influences two variables, creating the appearance of a direct relationship between them.
- Hill's criteria
- Bradford Hill's (1965) framework for judging causality: temporality, strength of association, consistency across studies, elimination of alternative explanations.
- Statistical significance
- Result is unlikely to be due to chance, per a threshold like p < 0.05.
- Practical significance
- The effect is large enough to matter in the real world — separate from whether it's statistically significant.
Statistical vs. Practical Significance
| Type | What it answers / limitation alone |
|---|---|
| Statistical significance | Is this unlikely due to chance? / Doesn't guarantee the effect is large enough to matter |
| Practical significance | Is the effect large enough to matter? / Can be overlooked if a study only reports a p-value |
Common MCAT Trap
- "Statistically significant" (p < 0.05) does not mean the effect is meaningful — a drug reducing blood pressure by 0.5 mmHg can be statistically significant yet practically irrelevant.
- A strong correlation (even r close to ±1) never by itself proves causation — always check for a plausible confounding variable before concluding one variable causes the other.
Quick Recall
Ice cream sales and drowning incidents rise together. What explains this without causation?
A study reports p < 0.05 for a tiny, clinically meaningless effect. What distinction is this testing?