Measuring Correlation - Spearman Rank C.C.

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Measuring Correlation - Spearman Rank C.C.

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Measuring Correlation - Spearman Rank C.C.

  1. 1. Spearman’s Rank C.C. Measuring Correlation
  2. 2. Beyond The Scattergraph <ul><li>For GCSE Mathematics you simply draw a line of best fit through the data and talk about “strong” or “weak” correlation in vague terms. </li></ul><ul><li>For GCSE Statistics you learn how to CALCULATE the amount of correlation so that you can compare one scattergraph with another. </li></ul><ul><li>You don’t even need to draw the scattergraph! </li></ul>
  3. 3. 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!
  4. 4. Interpretation of S.R.C.C. <ul><li>Values close to 0 suggest no correlation </li></ul><ul><li>0.4 to 0.6 (0.5) is “weak correlation” </li></ul><ul><li>0.7 and higher suggests “strong correlation” </li></ul><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>
  5. 5. 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>
  6. 6. 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>
  7. 7. 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
  8. 8. 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
  9. 9. 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
  10. 10. 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
  11. 11. 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
  12. 12. Finally Use The Formula: n = 5 (there were 5 crops) -> There is very strong correlation between the amount of fertiliser and the crop yield.
  13. 13. Here’s One For You To Try… These data show the distances in metres (A) of shops from the Museum in Barcelona and the prices in Euros (B) for a 50cl bottle of water. Hypothesis: Shops closer to the museum charge more for their water than those further away. Do the data support this hypothesis? A 50 175 270 375 425 580 710 790 890 980 B 1.80 1.20 2.00 1.00 1.00 1.20 0.80 0.60 1.00 0.85
  14. 14. Procedure A 50 175 270 375 425 580 710 790 890 980 RA 10 9 8 7 6 5 4 3 2 1 B 1.80 1.20 2.00 1.00 1.00 1.20 0.80 0.60 1.00 0.85 RB 2 3.5 1 6 6 3.5 9 10 6 8
  15. 15. Differences and Squares A 50 175 270 375 425 580 710 790 890 980 RA 10 9 8 7 6 5 4 3 2 1 B 1.80 1.20 2.00 1.00 1.00 1.20 0.80 0.60 1.00 0.85 RB 2 3.5 1 6 6 3.5 9 10 6 8 d^2 64 30.25 49 1 0 2.25 25 49 16 49
  16. 16. Conclusion Do the data support our hypothesis?

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