pearson correlation

IAN JULE MALONGKATRINA PARAISO

ANGELA CARLA ARANIEGONOREEN MORALES

The Pearson Product Moment Coefficient of Correlation (r)

Proponent

Karl Pe

arson

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

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

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.

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 of the variables with the scores on the other

•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

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

Formula

Where:x : deviation in Xy : deviation in Y

r = Ʃxy

(Ʃx2) (Ʃy2)

Solving Stepwise methodI. PROBLEM: Is there a relationship

between the midterm and the final examinations of 10 students in Mathematics?

n = 10

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

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

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.

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

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 example:r.05 (critical value) = 0.632Computed value of r = 0.9480.948 > 0.632 ;therefore, REJECT

Ho

VI. Conclusion / Implication

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

LET’s PRACTICE!

RESEARCH TITLE:Correlates of Work Adjustment

among Employed Adults with Auditory and Visual

Impairments

Blanca, Antonia Benlayo SPED 2009

I. Statement of the ProblemThis 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. Genderb. Agec. Civil statusd. number of childrene. employment statusf. length of serviceg. job categoryh. educational backgroundi. job levelj. salaryk. degree of hearing loss

degree of visual activity

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.

CONCEPTUAL FRAMEWORK

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

I. Problem

PROBLEM

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

of the individual with hearing impairment?

II. Hypothesis

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

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

III. DETERMINING THE CRITICAL VALUES

III. Determining the critical values

Decide on the alpha = 0.05a Determine the degrees of freedom

(df)n = 33df = 33-2 = 31

Using the table, find value of r at 0.05 alpha with df of 31

r.05 = 0.344

IV. COMPUTING FOR THE STATISTIC

DATA

FORMULAr = 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 THE STATISTIC

V. Compare statistics

In this exercise:r.05 (critical value) = 0.344Computed value of r = 0.270.27 < 0.344: ACCEPT Ho

RECALL Decision rule :If the computed r value is greater than the r tabular value, reject Ho

VI. CONCLUSION

VI. Conclusion / ImplicationSince:

r = +.27critical 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.

THIS IS IT! SEATWORK.

Is there a relationship between age and level of work adjustment of employees with hearing impairment?

PROBLEM:

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, = 0.05aIV. Compute the statistic

DATA

FORMULA

X2 = 140.0612 Y2 = 36 388.9092 xy = 259.4548

r = Ʃxy

(Ʃx2) (Ʃy2)

Contd.

V. Compare the statisticsVI. State a conclusion

SOLVE!

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

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.

References: Critical Values for Pearson’s Correlation Coefficient Retrieved from: http://capone.mtsu.edu/dkfuller/tables/correlationtable.pdf

February 20, 2013