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Pearson Correlation

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Pearson Correlation

  1. 1. The Pearson Product Moment Coefficient of Correlation (r)
  2. 2. Proponent
  3. 3. Karl Pearson (1857-1936)  “Pearson Product-Moment Correlation Coefficient”  has been credited with establishing the discipline of mathematical statistics  a proponent of eugenics, and a protégé and biographer of Sir Francis Galton.  In collaboration with Galton, founded the now prestigious journal Biometrika
  4. 4. What is PPMCC?  The most common measure of correlation  Is an index of relationship between two variables  Is represented by the symbol r  reflects the degree of linear relationship between two variables
  5. 5.  It is symmetric. The correlation between x and y is the same as the correlation between y and x.  It ranges from +1 to -1.
  6. 6. correlation of +1 there is a perfect positive linear relationship between variables X Y
  7. 7. A perfect linear relationship, r = 1.
  8. 8. correlation of -1 there is a perfect negative linear relationship between variables X Y
  9. 9. A perfect negative linear relationship, r = -1.
  10. 10. A correlation of 0 means there is no linear relationship between the two variables, r=0
  11. 11. • A correlation of .8 or .9 is regarded as a high correlation • there is a very close relationship between scores on one of the variables with the scores on the other
  12. 12. •A correlation of .2 or .3 is regarded as low correlation •there is some relationship between the two variables, but it’s a weak one
  13. 13. -1 -.8 -.3 0 .3 .8 1 STRONG MOD WEAK WEAK MOD STRONG
  14. 14. Significance of the Test  Correlation is a useful technique for investigating the relationship between two quantitative, continuous variables. Pearson's correlation coefficient (r) is a measure of the strength of the association between the two variables.
  15. 15. Formula Where: x : deviation in X y : deviation in Y r = Ʃxy (Ʃx2) (Ʃy2)
  16. 16. Solving Stepwise method I. PROBLEM: Is there a relationship between the midterm and the final examinations of 10 students in Mathematics? n = 10
  17. 17. II. Hypothesis  Ho: There is NO relationship between the midterm grades and the final examination grades of 10 students in mathematics  Ha: There is a relationship between the midterm grades and the final examination grades of 10 students in mathematics
  18. 18. III. Determining the critical values  Decide on the alpha a = 0.05  Determine the degrees of freedom (df)  Using the table, find the value of r at 0.05 alpha
  19. 19. Degrees of Freedom: df = N – 2 = 10 – 2 = 8 Testing for Statistical Significance: Based on df and level of significance, we can find the value of its statistical significance.
  20. 20. IV. Solve for the statistic X Y x y x2 y2 xy 75 80 2.5 1.5 6.25 2.25 3.75 70 75 7.5 6.5 56.25 42.25 48.75 65 65 12.5 16.5 156.25 272.25 206.25 90 95 -12.5 -13.5 156.25 182.25 168.75 85 90 -7.5 -8.5 56.25 72.25 63.75 85 85 -7.5 -3.5 56.25 12.25 26.25 80 90 -2.5 -8.5 6.25 72.25 21.25 70 75 7.5 6.5 56.25 42.25 48.75 65 70 12.5 11.5 156.25 132.25 143.75 90 90 -12.5 -8.5 156.25 72.25 106.25 X =775 Y =815 0 0 862.5 905.5 837.5 X = 77.5 Y = 81.5 Table 1: Calculation of the correlation coefficient from ungrouped data using deviation scores
  21. 21. Putting the Formula together: r = 837.5 (862.5) (905.5) r = Ʃxy (Ʃx2) (Ʃy2) r = 837.5 780993.75 Computed value of r = .948
  22. 22. V. Compare statistics  Decision rule: If the computed r value is greater than the r tabular value, reject Ho  In our example:  r.05 (critical value) = 0.632  Computed value of r = 0.948  0.948 > 0.632 ;therefore, REJECT Ho
  23. 23. VI. Conclusion / Implication There is a significant relationship between midterm grades of the students and their final examination.
  24. 24. LET’s PRACTICE! 
  25. 25. Correlates of Work Adjustment among Employed Adults with Auditory and Visual Impairments Blanca, Antonia Benlayo SPED 2009
  26. 26. I. Statement of the Problem This study was conducted to identify the correlates of work adjustment among employed adults, Specifically, the study aimed to answer the following questions: 1. What is the profile of the respondents in terms of the following demographic variables: a. Gender b. Age c. Civil status d. number of children e. employment status f. length of service g. job category h. educational background i. job level j. salary k. degree of hearing loss degree of visual activity
  27. 27. Contd. 2. What is the level of work adjustment of the employed adults with auditory and visual impairment? Note: There were too many questions stated in the Statement of Problem of the Dissertation; however, we only included those we deemed relevant to our report today.
  28. 28. Socio- demographic Variable * Age *Gender * Civil Status * Number of Children *Employment status *Length of Service *Job level *Job Category * Educational Background *Salary * Degree of hearing impairment / degree of visual acuity Work Adjustment Variable * Knowledge - Job's Technical Aspect *Skills - performance - social relationships * Attitudes - Attendance -values towards work *Interpersonal Relations * Support of Significant others - Family -Friends - Employer - Co - workers *Nature of work Work Adjustment of Employed Adults with Auditory and Visual Impairments Employed Adults with Auditory and Visual Impairments Fulfilled/Satisfied Employed Adults with Auditory and Visual Impairments Correlates of Work Adjustment among Employed Adults with Auditory and Visual Impairments
  29. 29. PROBLEM Is there a relationship between gender and the level of work adjustment of the individual with hearing impairment?
  30. 30. Null Hypothesis (Ho) There is no relationship between gender and level of work adjustment according to the family of the individual with hearing impairment. In symbol: Ho: r = 0
  31. 31. ALTERNATIVE HYPOTHESIS (Ha) There is a relationship between gender and level of work adjustment according to the family of the individual with hearing impairment. In symbols: Ha: r 0
  32. 32. III. Determining the critical values  Decide on the alpha  Determine the degrees of freedom (df)  n = 33  df = 33-2 = 31  Using the table, find value of r at 0.05 alpha with df of 31 r.05 = 0.344
  33. 33. DATA FORMULA r = Ʃxy (Ʃx2) (Ʃy2) x2 y2 xy 8.2432 30473.64 136.8176
  34. 34. Putting the Formula together: r = 136.8176 r = Ʃxy (Ʃx2) (Ʃy2) (8.2432) (30473.64) r = 136.8176 501.198872
  35. 35. r = 136.8176 15238.70925 Computed value of r = 0.272980
  36. 36. V. Compare statistics  In this exercise:  r.05 (critical value) = 0.344  Computed value of r = 0.27 0.27 < 0.344 : ACCEPT Ho RECALL Decision rule : If the computed r value is greater than the r tabular value, reject Ho
  37. 37. VI. Conclusion / Implication Since: r = +.27 critical value, r(31) = .344 r = .27, p < .05 We can say that: Since the Computed r value is less than the tabular r value, we can say therefore that there is no relationship between gender and level of work adjustment according to the family of the individual with hearing impairment.
  38. 38. THIS IS IT! SEATWORK. 
  39. 39. PROBLEM:
  40. 40. Please follow the stepwise method and show the following: II. Hypothesis - State the null hypothesis in words and in symbol - State the alternative hypothesis in words and in symbol III. Compute for the critical value - use n = 33, IV. Compute the statistic
  41. 41. DATA FORMULA  X2 = 140.0612  Y2 = 36 388.9092  xy = 259.4548 r = Ʃxy (Ʃx2) (Ʃy2)
  42. 42. Contd. V. Compare the statistics VI. State a conclusion
  43. 43. SOLVE! 
  44. 44. Answer key:  Ho: There is no relationship between age and level of work adjustment according to the individual with hearing or visual impairment. Ho: r = 0  Ha: There is a relationship between age and level of work adjustment according to the individual with hearing or visual impairment. Ha: r 0
  45. 45. Answer key:  Critical value: 0.337  Computed r: 0.11492 = 0.11  0.11 < 0.337, ACCEPT Ho  There is NO relationship between age and level of work adjustment of employees with hearing impairment.
  46. 46. References:  Critical Values for Pearson’s Correlation Coefficient Retrieved from: http://capone.mtsu.edu/dkfuller/tables/correlationtable.pdf February 20, 2013

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