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The Pearson Product Moment Coefficient of Correlation (r)

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Proponent

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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

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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

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  • 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.

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correlation of +1

  • there is a perfect positive linear relationship between variables

X Y

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A perfect linear relationship, r = 1.

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correlation of -1

  • there is a perfect negative linear relationship between variables

X Y

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A perfect negative linear relationship, r = -1.

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A correlation of 0 means there is no linear relationship between the two variables, r=0

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  • 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

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  • 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

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-.3 0 .3 .8

STRONG

-1 -.8

1

MOD

WEAK

WEAK

MOD

STRONG

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Significance of the Test

  • Correlation investigating

is a useful the relationship

technique for between two

quantitative, continuous variables. Pearson's correlation coefficient (r) is a measure of the strength of the association between the two variables.

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Formula

r = Ʃxy

(Ʃx2) (Ʃy2)

​

Where:

x : deviation in X y : deviation in Y

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Solving Stepwise method

I. PROBLEM:

relationship

Is there a between the midterm

and the

final examinations of 10 students in Mathematics?

​

n = 10

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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

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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

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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.

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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

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Putting the Formula together:

r = Ʃxy

(Ʃx2) (Ʃy2)

r = 837.5

(862.5) (905.5)

r = 837.5

780993.75

Computed value of r = .948

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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

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VI. Conclusion / Implication

  • There is a significant relationship between midterm grades of the students and their final examination.

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LET’s PRACTICE!

☺

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Correlates of Work Adjustment among Employed Adults with Auditory and

Visual Impairments

Blanca, Antonia Benlayo

SPED 2009

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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:
    1. Gender
    2. Age
    3. Civil status
    4. number of children
    5. employment status
    6. length of service
    7. job category
    8. educational background
    9. job level
    10. salary
    11. degree of hearing loss degree of visual activity

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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.

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Correlates of Work Adjustment among Employed Adults with Auditory and Visual Impairments

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

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PROBLEM

Is there a relationship between gender and the level of work adjustment

of the individual with hearing impairment?

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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

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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

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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

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DATA

FORMULA

r = Ʃxy

(Ʃx2) (Ʃy2)

x2

y2

xy

8.2432

30473.64

136.8176

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(Ʃx2) (Ʃy2)

Putting the Formula together:

r =

136.8176

r = Ʃxy

(8.2432) (30473.64)

​

r = 136.8176

501.198872

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r = 136.8176

15238.70925

​

Computed value of r = 0.272980

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V. Compare statistics

RECALL Decision rule :

If the computed r value is greater than the r tabular value, reject Ho

​

  • In this exercise:
    • r.05 (critical value) = 0.344
    • Computed value of r = 0.27 0.27 < 0.344

: ACCEPT Ho

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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.

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THIS IS IT!

SEATWORK. ☺

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PROBLEM:

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Please follow the stepwise method and show the following:

  1. Hypothesis
    • State the null hypothesis in words and in symbol
    • State the alternative hypothesis in words and in symbol
  2. Compute for the critical value
    • use n = 33,
  3. Compute the statistic

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DATA

  • X2 = 140.0612
  • Y2 = 36 388.9092
  • xy = 259.4548

FORMULA

r = Ʃxy

(Ʃx2) (Ʃy2)

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Contd.

  1. Compare the statistics
  2. State a conclusion

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SOLVE! ☺

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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

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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.

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References:

  • Critical Values for Pearson’s Correlation Coefficient

Retrieved from: http://capone.mtsu.edu/dkfuller/tables/correlationtable.pdf

February 20, 2013