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Correlation analysis
- 1. Correlation analysis GROUP A ‘EVEREST’ Anil Pokhrel Amit Budachhetri Ajit Pudasaini Rikriti Koirala Roji shrestha Puja Neupane 1
- 2. CONTENTS • Introduction to correlation • History of correlation • Importance of correlation • Types of correlation • Methods of studying correlation • Scatter diagram method • Karl pearson correlation coefficient • Spearman rank correlation coefficient • Advantages and disadvantages of correlation • Conclusion 2
- 3. History of correlation • Francis Galton created stastical concept of correlation • It firstly used to relate the relationship between two things. 3
- 4. Introduction of correlation 4 • If two variable are so related that change in one variable affects the other variables are said to be correlated • A mutual relationship or connection between two or more things • The process of establishing a relationship or connection between two or more things • Correlation analysis shows us how to determine both the nature and strength of relationship between two variables
- 5. Importance of correlation analysis It is used in deriving the degree and direction of relationship within the variable It is use to reduce the range of uncertainty in matter of prediction Useful in presenting the average relationship between two variables In science, technology and philosophy these are used to make progressive conclusion 5
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- 7. Positive and negative correlation • In positive correlation both variable moves in same direction • Increament in one variable also increase in another variable and vice versa • Example Age (year ) 5 8 10 14 16 Weig ht(kg ) 20 28 34 40 49 7
- 8. Negative correlation • In negative correlation both variable moves in opposite direction • If one variable increase then another decrease and vice versa • Example X 15 20 25 30 Y 25 20 10 8 8
- 9. Linear and non-linear correlation • A correlation between two variable is linear if corresponding to a unit change in unit variable over a entire range of value • Example • ple X 6 7 8 9 Y 5 7 9 11 9
- 10. Non linear correlation • In this correlation there is unit change in one variable and no constant change in other variable • Example X 1 2 3 4 Y 7 8 10 15 10
- 11. Partial correlation • Partial correlation is a relationship between two variables keeping the other variabes constant or fixed. 11
- 12. Multiple correlation • The relationship among three or more at the same time 12
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- 14. Scatter diagram methods • It is one of the simplest ways of diagrammatic representation of the bi variate • Here points are represented by dots by keeping the independent variable on the x- axis and dependent variables on the y-axis • It is the simplest methods of measuring correlation • It is least affected by size of extra value • However it cannot give the exact idea (it gives rough idea only about correlation) 14
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- 22. Karl Pearson’s correlation coefficient Introduction: The Karl Pearson’s correlation coefficient measure the degree of association between the two variables. It is also known Pearsonian correlation coefficient 22
- 23. Formula of Karl Pearson’s correlation coefficient Let X and Y be two variables then Karl Pearson’s correlation coefficient is denoted by rᵪᵧ or rᵧᵪ or simply r is define as 23
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- 25. Deviation method(change in origin): 25
- 27. Properties of correlation coefficient • Correlation coefficient lies between -1 to 1 • Correlation coefficient is symmetrical i.e. rᵪᵧ=rᵧᵪ • It is independent of change in origin • It is the geometric mean of two regression coefficient r²=bᵧᵪx bᵪᵧ • It has no unit because of relative measure 27
- 28. Interpretation of calculated value of r • If r=+1, there is Perfect Positive Correlation between two variables • If r=-1, there is Perfect Negative Correlation between two variables • If r=o, there is no correlation 28
- 29. Goodness of fit measure • Probable error- use to test the calculated correlation coefficient whether it is significant or not then We have • S.E.(r)=1-squr(r)/√n Where “r” is the calculated correlation coefficient in “n” pair of observation • P.E.(r)=0.6745x1-squr(r)/√n • If r<P.E.(r), then value of r is not significant • If r>6P.E.(r), then the value of r is significant 29
- 30. Spearman rank coefficient • A method to determine correlation when the data is not available in numerical form then, as an alternative method the method of rank correlation is used • When the value of two variables are converted into their ranks • Then the correlation is obtained called as rank correlation • Rank correlation coefficient is also known as spearemans’s rank correlation 30
- 31. • Where ∑d=0 is always zero • D=R1-R2 or R2-R1 31
- 32. It can be computed in three condition a. When ranks are given b. When ranks are not given and not repeated c. When rank are not given and repeated Properties: a. This is the only methods for finding the correlation while dealing with qualitative features like beauty , GK , honesty b. How ever it is not suitable in case of large observation c. There is always some loss of information due to the ranking is used 32
- 33. EXAMPLE of Rank correlation 33
- 34. Advantages and disadvantages of correlation Advantages: • Can show strength of relationship between two variables • Study behaviour that you cannot study • It can collect much information from many subjects at a time • Gain quantitative data which can be easily analysed Disadvantages: • cannot show cause and effect (what variables control what) • No control of third variable that might affect the correlation 34
- 35. conclusion • Correlation is the relationship between variables • Correlation coefficient is symmetric i.e.r(xy)=r(yx) • Correlation coefficient is a pure number independent of unit of measurement • It is measured of direction and degree of linear relationship between variables • It cannot be used in estimating values • It studies only relationship between variables • It’s values lies between +1 to -1 35
- 36. Reference • Google.com • Vikash Raj Satyal--Probability and statistics • Teacher’s notes –Mahesh lal sir 36
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