Biostatistics: Correlation | Zoology Optional Notes for UPSC PDF Download

Correlation in Biostatistics

Definition of Correlation
Correlation refers to the relationship between two variables that can help determine whether a change in one variable influences the other. This relationship can be quantified using a measure known as the Correlation Coefficient.

Types of Correlation

1. Positive Correlation:

   • When both variables change in the same direction, it is referred to as a positive correlation.
   • Positive correlations can be perfect or moderately positive.
     • Perfect Positive Correlation: When both variables increase and decrease in the same proportion.
     • Moderately Positive Correlation: In this case, the two variables are positively correlated, but the changes don't occur in the same proportion, and the coefficient value falls between +1 and 0.

2. Negative Correlation:

   • If one variable increases while the other decreases (or vice versa), it is termed negative correlation.
   • An example is the negative correlation between the size and number of fruits per plant.
   • Negative correlations can also be perfect or moderately negative.
     • Perfect Negative Correlation: A very rare relationship, where an increase in one variable leads to an equivalent decrease in the other (e.g., increasing temperature decreases cell lipid content).
     • Moderately Negative Correlation: In this relationship, the variables are negatively correlated, but not perfectly so. An example might be an increase in the post-harvesting period, leading to a decrease in seed viability. The coefficient value lies between 0 and -1.

3. Zero Correlation:

   • When there is no consistent relationship between two variables, and their values are uncorrelated, it is referred to as zero correlation.

Coefficient of Correlation

Steps to calculate 'r':

1. Create two series of data for the x and y variables.
2. Calculate the mean of both series, denoted as x̄ and ȳ.
3. Calculate the deviation of each observation as dx and dy.
4. Square the deviations.
5. Multiply the deviations of both variables.
6. Sum up the data as per the formula to calculate 'r.'

Properties of Correlation Coefficient

1. The correlation coefficient always falls within the range of -1 to +1, i.e., -1 ≤ r ≤ +1.
2. A correlation of r = +1 indicates a perfect positive correlation, while a value less than +1 signifies a moderately positive correlation.
3. A correlation of r = -1 represents a perfect negative correlation, and a value higher than -1 indicates a moderately negative correlation.

If r = 0, there is no correlation between the variables.
The coefficient of correlation is not affected by change and scale of origin.