Siva correlation

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CORRELATION

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Siva correlation

  1. 1. Spearman’s Rank C.C. Measuring Correlation M.SIVASUBRAMANIAN
  2. 2. CORRELATION Correlation can be easily understood as co relation. Correlation is the average relationship between two or more variables. When the change in one variable makes or causes a change in other variable then there is a correlation between these two variables.
  3. 3. Types Of Correlation Positive correlation: r is close to +1.  An r value of exactly +1 Negative correlation : r is close to -1.  An r value of exactly -1   No correlation:   r is close to 0. A correlation greater than 0.8 is generally described as strong , whereas a correlation less than 0.5 is generally described as weak . 
  4. 4. Uses of Correlation <ul><li> correlations are used to construct indexes from data on several variables, such as: </li></ul><ul><ul><li>Intelligence Tests </li></ul></ul><ul><ul><li>Personality Tests </li></ul></ul><ul><ul><li>Marital happiness measures </li></ul></ul><ul><ul><li>Measures of financial strength </li></ul></ul><ul><ul><li>Stock Markets </li></ul></ul>
  5. 5. Spearman’s Rank C.C. Formula Perfect Negative Correlation No Correlation Perfect Positive Correlation This formula is on the formula sheet so you don’t need to learn it! This formula is on the formula sheet so you don’t need to learn it!
  6. 6. Interpretation of S.R.C.C. <ul><li>This applies to negative values too </li></ul><ul><li>There are no hard and fast rules about when “weak” becomes “strong” </li></ul><ul><li>If r > 1 then you went wrong !!!!!! </li></ul>
  7. 7. Outline of Procedure <ul><li>Let’s say you are exploring n heights and weights in an investigation </li></ul><ul><li>Rank the heights i.e. put them in order (1 = biggest, n = smallest) </li></ul><ul><li>Rank the weights (1 = biggest, n = smallest) </li></ul><ul><li>d = difference between the two ranks for each person </li></ul><ul><li>Square and add these differences </li></ul>
  8. 8. Problems With Equal Ranks <ul><li>What if two things are 3rd= ? </li></ul><ul><li>One has to be third, the other fourth. </li></ul><ul><li>To be fair, each takes the average: (3 + 4) ÷ 2 = 3.5 </li></ul><ul><li>What if three things are 5th= ? </li></ul><ul><li>Call them 5th, 6th and 7th </li></ul><ul><li>Give each one the average rank: (5 + 6 + 7) ÷ 3 = 6 </li></ul>
  9. 9. Fertiliser v. Plant Growth Crop A B C D E Fertiliser 12.8 17.1 8.3 6.7 10.2 Yield 103 108 89 75 105
  10. 10. First, Rank The Data: Crop A B C D E Fertiliser 12.8 17.1 8.3 6.7 10.2 Fertiliser RANK 2 1 4 5 3 Yield 103 108 89 75 105 Yield RANK 3 1 4 5 2
  11. 11. Second, Find The Rank Differences: Crop A B C D E Fertiliser 12.8 17.1 8.3 6.7 10.2 Fertiliser RANK 2 1 4 5 3 Yield 103 108 89 75 105 Yield RANK 3 1 4 5 2 Rank Difference -1 0 0 0 1
  12. 12. Third, Square The Rank Differences: Crop A B C D E Fertiliser 12.8 17.1 8.3 6.7 10.2 Fertiliser RANK 2 1 4 5 3 Yield 103 108 89 75 105 Yield RANK 3 1 4 5 2 Rank Difference -1 0 0 0 1 d^2 1 0 0 0 1
  13. 13. Now Find “Sigma D Squared” Crop A B C D E Fertiliser 12.8 17.1 8.3 6.7 10.2 Fertiliser RANK 2 1 4 5 3 Yield 103 108 89 75 105 Yield RANK 3 1 4 5 2 Rank Difference -1 0 0 0 1 d^2 1 0 0 0 1
  14. 14. Finally Use The Formula: n = 5 (there were 5 crops)
  15. 15. Conclusion There is very strong correlation between the amount of fertilizer and the crop yield r= 0.9
  16. 16. Reference <ul><li>Business Statistics – S.Manoharan </li></ul><ul><li>www.statsoft.com </li></ul><ul><li>www.socialresearchmethods.net </li></ul>

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