Correlation – Definition, Types and Correlation Coefficient with Example
This topic is a part of Biostatistics in the B Pharmacy syllabus. Correlation is a basic statistical tool used in pharmaceutical research, formulation studies, clinical trials, and quality control.
📌 What is Correlation?
Correlation is a statistical technique that is used to determine the relationship or association between two variables. In simple terms, it tells us whether two variables increase or decrease together, or if there's no relation at all.
Example from Pharmacy: A researcher might study the correlation between dosage of a drug (mg) and the decrease in blood pressure (mmHg). If both are strongly linked, the correlation will be high.
📚 Importance of Correlation in B Pharmacy
- Used in dose-response relationship studies
- Important in clinical trial data analysis
- Used in comparing drug efficacy
- Helps in quality control of pharmaceutical products
📌 Types of Correlation
There are mainly three types of correlation:
- Positive Correlation: Both variables increase or decrease together.
Example: More exercise → Better metabolism - Negative Correlation: One variable increases while the other decreases.
Example: More drug dosage → Less symptoms - No Correlation: No predictable relationship between the variables.
Example: Shoe size and drug solubility
📌 Methods to Study Correlation
- Scatter Diagram Method
- Karl Pearson’s Correlation Coefficient
- Spearman’s Rank Correlation
📌 Correlation Coefficient
The **correlation coefficient** (denoted by **r**) is a numerical value between -1 and +1 that indicates the strength and direction of correlation.
| Value of r | Interpretation |
|---|---|
| +1 | Perfect Positive Correlation |
| -1 | Perfect Negative Correlation |
| 0 | No Correlation |
| +0.7 to +0.9 | Strong Positive Correlation |
| -0.7 to -0.9 | Strong Negative Correlation |
📌 Formula of Karl Pearson’s Correlation Coefficient
r = Σ[(x - x̄)(y - ȳ)] / √[Σ(x - x̄)² × Î£(y - ȳ)²]
Where,
x̄ = Mean of X values
ȳ = Mean of Y values
r = Correlation Coefficient
📌 Solved Example
Given Data:
| X (Drug Dose in mg) | Y (BP Drop in mmHg) |
|---|---|
| 10 | 20 |
| 20 | 40 |
| 30 | 50 |
| 40 | 65 |
| 50 | 80 |
Step-by-Step Calculation
| X | Y | X - x̄ | Y - ȳ | (X - x̄)(Y - ȳ) | (X - x̄)² | (Y - ȳ)² |
|---|---|---|---|---|---|---|
| 10 | 20 | -20 | -28 | 560 | 400 | 784 |
| 20 | 40 | -10 | -8 | 80 | 100 | 64 |
| 30 | 50 | 0 | 2 | 0 | 0 | 4 |
| 40 | 65 | 10 | 17 | 170 | 100 | 289 |
| 50 | 80 | 20 | 32 | 640 | 400 | 1024 |
| Σ | 1450 | 1000 | 2165 |
Now applying the formula:
r = 1450 / √(1000 × 2165) = 1450 / √2165000 ≈ 1450 / 1471.4 ≈ 0.99
✅ Conclusion
The correlation coefficient (r) is 0.99 which indicates a very strong positive correlation. This means as the drug dose increases, the blood pressure drop also increases.
📌 Summary:
- Correlation helps analyze the relationship between two variables
- It is important in various pharmaceutical applications
- Karl Pearson's method gives a precise numerical result
- r = 0.99 means both variables are highly related
