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The Pearson Product Moment
Coefficient of Correlation (r)
Proponent
Karl Pearson (1857-1936)
 “Pearson Product-Moment Correlation
Coefficient”
 has been credited with establishing the
disc...
What is PPMCC?
 The most common measure of
correlation
 Is an index of relationship between
two variables
 Is represent...
 It is symmetric. The correlation
between x and y is the same as the
correlation between y and x.
 It ranges from +1 to ...
correlation of +1
there is a perfect positive
linear relationship between
variables
X Y
A perfect linear relationship, r = 1.
correlation of -1
there is a perfect negative
linear relationship between
variables
X Y
A perfect negative linear relationship, r = -1.
A correlation of 0 means there is no linear
relationship between the two variables, r=0
• A correlation of .8 or .9 is regarded as
a high correlation
• there is a very close relationship
between scores on one o...
•A correlation of .2 or .3 is regarded
as low correlation
•there is some relationship
between the two variables, but it’s
...
-1 -.8 -.3 0 .3 .8
1
STRONG MOD WEAK WEAK MOD STRONG
Significance of the Test
 Correlation is a useful technique for
investigating the relationship between two
quantitative, ...
Formula
Where:
x : deviation in X
y : deviation in Y
r = Ʃxy
(Ʃx2) (Ʃy2)
Solving Stepwise method
I. PROBLEM:
Is there a relationship
between the midterm and the
final examinations of 10 students
...
II. Hypothesis
 Ho: There is NO relationship between the
midterm grades and the final examination
grades of 10 students i...
III. Determining the critical
values
 Decide on the alpha a = 0.05
 Determine the degrees of
freedom (df)
 Using the ta...
Degrees of Freedom:
df = N – 2
= 10 – 2
= 8
Testing for Statistical Significance:
Based on df and level of
significance, w...
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 ...
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
V. Compare statistics
 Decision rule: If the computed r value is
greater than the r tabular value, reject Ho
 In our exa...
VI. Conclusion / Implication
There is a significant
relationship between midterm
grades of the students and
their final e...
LET’s PRACTICE!

Correlates of Work Adjustment among
Employed Adults with Auditory and
Visual Impairments
Blanca, Antonia Benlayo
SPED 2009
I. Statement of the Problem
This study was conducted to identify the correlates of work
adjustment among employed adults, ...
Contd.
2. What is the level of work adjustment
of the employed adults with auditory
and visual impairment?
Note: There wer...
Socio-
demographic
Variable
* Age
*Gender
* Civil Status
* Number of
Children
*Employment
status
*Length of Service
*Job l...
PROBLEM
Is there a relationship
between gender and the
level of work adjustment
of the individual with
hearing impairment?
Null Hypothesis (Ho)
There is no relationship between gender
and level of work adjustment according
to the family of the i...
ALTERNATIVE HYPOTHESIS (Ha)
There is a relationship between gender
and level of work adjustment according
to the family of...
III. Determining the critical values
 Decide on the alpha
 Determine the degrees of freedom (df)
 n = 33
 df = 33-2 = ...
DATA
FORMULA
r = Ʃxy
(Ʃx2) (Ʃy2)
x2 y2 xy
8.2432 30473.64 136.8176
Putting the Formula together:
r = 136.8176
r = Ʃxy
(Ʃx2) (Ʃy2)
(8.2432) (30473.64)
r = 136.8176
501.198872
r = 136.8176
15238.70925
Computed value of r = 0.272980
V. Compare statistics
 In this exercise:
 r.05 (critical value) = 0.344
 Computed value of r = 0.27
0.27 < 0.344
: ACCE...
VI. Conclusion / Implication
Since:
r = +.27
critical value, r(31) = .344
r = .27, p < .05
We can say that:
Since the Comp...
THIS IS IT!
SEATWORK. 
PROBLEM:
Please follow the stepwise
method and show the following:
II. Hypothesis
- State the null hypothesis in words and
in symbo...
DATA
FORMULA
 X2 = 140.0612
 Y2 = 36 388.9092
 xy = 259.4548
r = Ʃxy
(Ʃx2) (Ʃy2)
Contd.
V. Compare the statistics
VI. State a conclusion
SOLVE! 
Answer key:
 Ho: There is no relationship between
age and level of work adjustment
according to the individual with heari...
Answer key:
 Critical value: 0.337
 Computed r: 0.11492 = 0.11
 0.11 < 0.337, ACCEPT Ho
 There is NO relationship betw...
References:
 Critical Values for Pearson’s Correlation Coefficient
Retrieved from: http://capone.mtsu.edu/dkfuller/tables...
Pearson Correlation
Pearson Correlation
Pearson Correlation
Pearson Correlation
Pearson Correlation
Pearson Correlation
Pearson Correlation
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  • Transcript of "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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