TRUST Research Center

📊 **Correlation vs Regression — one of the most misunderstood concepts in research**

Many treat them as interchangeable… they’re not.

This infographic breaks it down clearly 👇

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🔗 **Correlation = Relationship (No direction)**
It answers: *Are two variables linked?*

✔ Measures **strength + direction** (r)
✔ **Symmetrical** → X with Y = Y with X
✔ No prediction, no causation

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📈 **Regression = Prediction (Directional model)**
It answers: *Can X predict Y?*

✔ Builds an equation:
Y = b₀ + b₁X

✔ **Directional** → X predicts Y
✔ Quantifies **how much Y changes when X changes**

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🏥 **Simple example:**

💰 Hospital expenses = fixed costs + (cost per patient × number of patients)

👉 **Intercept (b₀):** Running costs even with zero patients
👉 **Slope (b₁):** Added cost per patient

📊 If R² = 79% → most variation in cost is explained by patient numbers

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⚠️ **The BIG trap: Correlation ≠ Causation**

🍦 A real-life analogy:

A man noticed:
• When he ordered **vanilla ice cream** → his car didn’t work ❌
• When he ordered **strawberry** → his car worked ✔️

At first glance:
👉 Ice cream flavor seems “linked” to car failure!

But the real reason was:

⏱️ **Preparation time**
Vanilla was served faster → he returned to the car sooner → engine still overheated
Strawberry took longer → engine had time to cool → car worked fine

💡 Hidden factor = **waiting time**, not the flavor

👉 So yes, there is **correlation**
❌ But no **causation**

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📌 **What to report in research:**

✔ Correlation → r, p-value
✔ Regression → slope (B), CI, R²
✔ Always include descriptive statistics

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💡 Bottom line:
Correlation tells you **“they move together”**
Regression tells you **“how one predicts the other”**
Neither proves causation on its own.

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If you want to *actually understand statistics and apply it in clinical research*…

👉 Message us here to join **Statistics for Clinicians (S4C):**
https://wa.me/201119678899?text=I%20want%20to%20join%20the%20Statistics%20for%20Clinicians%20course

🔬📊 THE CLINICIAN'S GUIDE TO CHI-SQUARE TESTING 📊🔬
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Ever wondered how researchers test whether occupation influences disease — or whether a drug truly changes outcomes? The answer lies in one powerful tool: the Chi-Square Test (χ²) ✅

🧩 WHAT DOES IT DO?
✔️ Goodness of Fit → Does your observed data match a theoretical model?
✔️ Test of Independence → Are two qualitative variables associated with each other?

🏥 REAL CLINICAL EXAMPLES:
👨‍⚕️ Are doctors more hypertensive than nurses?
💊 Does the type of anticoagulant affect thromboembolic complications?
👶 Is the gender ratio of newborns consistent with the expected 1:1 ratio?

🧮 THE FORMULA:
χ² = Σ [(O − E)² / E]
→ Sum the standardized squared differences between Observed (O) and Expected (E) frequencies

📏 KEY RULES TO REMEMBER:
📌 Reject H₀ when p < 0.05
📌 Always report Effect Size (Phi φ or Cramér's V) — not just p-value!
📌 Apply Cochran's Rule: 80% of cells must have expected count > 5
📌 If conditions are violated → use Yates' Correction or Fisher's Exact Test

🔍 WHEN YOU HAVE >2 GROUPS:
Don't stop at the overall chi-square!
➡️ Perform Post Hoc 2×2 comparisons
➡️ Apply Bonferroni correction to avoid inflated p-values

💡 PRO TIP:
A significant p-value tells you THAT a difference exists.
Effect Size (like Odds Ratio or Relative Risk) tells you HOW BIG that difference is.
Both matter! 🎯

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