Correlation in Statistical Analysis .pdf
- 1. CORRELATION Dr. Balamurugan M Associate Professor Acharya Institute of Graduate Studies Bangalore
- 2. Correlation • Correlation is a statistical technique used for analyzing the behavior of two or more variables. Correlation is also described as co-variation in two or more variables. • Correlation does not necessarily indicate a cause and effect relationship, it only provides a quantitative measure.
- 3. Degree & Nature of Relationship Correlation is a measure of degree of relationship between X & Y. With the help of correlation analysis we can measure the degree of relationship existing between the variables. For example, there is the relationship between price and supply.
- 4. Correlation does not help in making predictions. Correlation coefficients are symmetrical. Types of Correlations Positive Correlation Negative Correlation No Correlation
- 5. Positive Correlation A positive correlation means that this linear relationship is positive, and the two variables increase or decrease in the same direction. Negative Correlation (Inverse Correlation) A negative correlation is just the opposite. The relationship line has a negative slope, and the variables change in opposite directions. No Correlation The variables behave very differently and thus, have no linear relationship.
- 7. Correlation Coefficient • Correlation coefficients give you the measure of the strength of the linear relationship between two variables. • The letter r denotes the value, and it ranges between -1 and +1 • If r < 0, it implies negative correlation • If r > 0, it implies positive correlation • If r = 0, it implies no correlation
- 8. Types of Correlationcoefficient There are mainly two types of correlation coefficients. 1. Karl Pearson Correlation Coefficient • Formula • r = Coefficient of correlation • x bar = Mean of x-variable • y bar = Mean of y-variable. • xi & yi = Samples of variable x, y
- 9. 2. Spearman’s Rank Correlation Coefficient • Formula • ρ= Spearman rank correlation • di= Difference between the ranks of corresponding variables • n= Number of Observations
- 10. Limitationsof Correlation • Correlation does not indicate causality and cannot be used to do so. • We cannot infer that one variable is the cause of another even though there is a very high relationship between them.
- 11. • We are limited by correlation to the information that is provided. For instance, suppose research revealed a link between the amount of time students spend on their homework (from half an hour to three hours) and the number of G.C.S.E. passes (1 to 6). It would be incorrect to conclude from this that putting in 6 hours of homework would probably result in 12 G.C.S.E. passes.
- 12. Examples • Let’s see some real-life examples and see what does negative correlation mean and what does positive correlation mean. Body Fat and Running Time • An individual's body fat tends to be lower the more time they spend jogging. In other words, there is a negative correlation between the variable body fat and the variable running time. Body fat decreases as running time increases.
- 13. Examples Exam Results and TV Viewing Time • Exam results typically suffer when a student watches more television. In other words, there is a negative correlation between the variable amount of time spent watching TV and the variable exam grade. Exam results decline as TV viewing time increases.