1 / 41

Correlation

Correlation. Assumptions: You can plot a scatter graph You know what positive, negative and no correlation look like on a scatter graph. Correlation describes the strength of the relationship between two variables. Paired data is often known as bivariate data.

Download Presentation

Correlation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Correlation Assumptions: You can plot a scatter graph You know what positive, negative and no correlation look like on a scatter graph

  2. Correlation describes the strength of the relationship between two variables. Paired data is often known as bivariate data. • In S1 we will look at ways of measuring the degree of linear association • First establish whether a linear correlation exists using a scatter diagram. x x x x x x x x x x x x x x x x x x x x x x x x x x x x

  3. Correlation describes the strength of the relationship between two variables. Paired data is often known as bivariate data. • In S1 we will look at ways of measuring the degree of linear association • First establish whether a linear correlation exists using a scatter diagram. We could plot a new point - the mean of the values and the values, i.e. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

  4. x x x x x x x x x x x x x x x x x x x x x x x x x x x x By redrawing axes through we can look at the scatter of points in quadrants ① ② Correlation Positive (most in 1st & 3rd) Negative (most in 2nd & 4th) None ③ ④ x x x Assuming you believe a linear relationship exists, we can calculate a measure of how strong it is.

  5. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  6. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  7. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  8. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  9. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  10. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x Complete the table… x x x x x x x x x x x x

  11. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  12. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  13. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  14. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  15. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  16. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  17. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  18. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  19. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  20. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  21. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  22. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  23. Product Moment Correlation Coefficient (PMCC) x x x x x x x x x x x x • If we sum the values… • For this example, since most points are in 1st & 3rd quadrants, the total will be positive (hence positive correlation) What would be the effect on the sum in the example above if we used a data set ten times bigger? x • A negative correlation would be overall negative • No correlation would give a sum close to zero

  24. Product Moment Correlation Coefficient (PMCC) x x x x x x x x x x x x • If we sum the values… • For this example, since most points are in 1st & 3rd quadrants, the total will be positive (hence positive correlation) What would be the effect on the sum if we changed the units, e.g. used cm instead of metres for a measurement? x • A negative correlation would be overall negative • No correlation would give a sum close to zero

  25. Product Moment Correlation Coefficient (PMCC) • If we sum the values… • For this example, since most points are in 1st & 3rd quadrants, the total will be positive (hence positive correlation) We for the PMCC • A negative correlation would be overall negative • No correlation would give a sum close to zero To eliminate these problems we use the following formula. This will always give a value between -1 and 1

  26. To eliminate these problems we use the following formula. This will always give a value between -1 and 1 : a perfect negative linear correlation : a perfect positive linearcorrelation : no linear correlation NB. Don’t use PMCC is a different type of correlation exists, For example if points follow a clear curve

  27. An easier version of the formula • The following are easier to use in calculations NB You are given all these formulas in the exam

  28. Example • Find PMCC

  29. Example • Find PMCC

  30. Example • Find PMCC

  31. Example Complete the table and calculate the totals • Find PMCC

  32. Example • Find PMCC

  33. Example • Find PMCC

  34. Example • Find PMCC Now calculate to 3 s.f.

  35. Example • Calculators – pro’s & cons • The Casio calculators can work out PMCC but the exam often asks you to find parts of the equation before finding (testing you are not simply using one) • Also there will be about 6 marks for PMCC – you will lose all 6 if you mistype one data value in the time pressure of the exam. • But, check your answer using a calculator. • Find PMCC to 3 s.f.

  36. Example • Find PMCC

  37. Example Enter data in the and columns

  38. Example Enter data in the and columns • Find PMCC

  39. Example Enter data in the and columns • Find PMCC to 3 s.f.

  40. Example of Q that can’t be done using the data function a) Find b) Find

  41. Example of Q that can’t be done using the data function a) Find 490.2 4 s.f. 0.906 3 s.f. b) Find

More Related