pearson correlation

53
IAN JULE MALONG KATRINA PARAISO ANGELA CARLA ARANIEGO NOREEN MORALES The Pearson Product Moment Coefficient of Correlation (r)

Upload: noreen-morales

Post on 25-Dec-2014

4.069 views

Category:

Education


1 download

DESCRIPTION

 

TRANSCRIPT

Page 1: Pearson Correlation

IAN JULE MALONGKATRINA PARAISO

ANGELA CARLA ARANIEGONOREEN MORALES

The Pearson Product Moment Coefficient of Correlation (r)

Page 2: Pearson Correlation

Proponent

Karl Pe

arson

Page 3: Pearson Correlation

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

Page 4: Pearson Correlation

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

Page 5: Pearson Correlation

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.

Page 6: Pearson Correlation

correlation of +1

there is a perfect positive linear relationship between variables

X Y

Page 7: Pearson Correlation

A perfect linear relationship, r = 1.

Page 8: Pearson Correlation

correlation of -1

there is a perfect negative linear relationship between variables

X Y

Page 9: Pearson Correlation

A perfect negative linear relationship, r = -1.

Page 10: Pearson Correlation

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

Page 11: Pearson Correlation

• 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

Page 12: Pearson Correlation

•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

Page 13: Pearson Correlation

-1 -.8 -.3 0 .3 .8 1

STRONG MOD WEAK WEAK MOD STRONG

Page 14: Pearson Correlation

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.

Page 15: Pearson Correlation

Formula

Where:x : deviation in Xy : deviation in Y

r = Ʃxy

(Ʃx2) (Ʃy2)

Page 16: Pearson Correlation

Solving Stepwise methodI. PROBLEM: Is there a relationship

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

n = 10

Page 17: Pearson Correlation

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

Page 18: Pearson Correlation

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

Page 19: Pearson Correlation

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.

Page 20: Pearson Correlation

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

Page 21: Pearson Correlation

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

Page 22: Pearson Correlation

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

Page 23: Pearson Correlation

VI. Conclusion / Implication

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

Page 24: Pearson Correlation

LET’s PRACTICE!

Page 25: Pearson Correlation

RESEARCH TITLE:Correlates of Work Adjustment

among Employed Adults with Auditory and Visual

Impairments

Blanca, Antonia Benlayo SPED 2009

Page 26: Pearson Correlation

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

Page 27: Pearson Correlation

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.

Page 28: Pearson Correlation

CONCEPTUAL FRAMEWORK

Page 29: Pearson Correlation

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

Page 30: Pearson Correlation

I. Problem

Page 31: Pearson Correlation

PROBLEM

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

of the individual with hearing impairment?

Page 32: Pearson Correlation

II. Hypothesis

Page 33: Pearson Correlation

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

Page 34: Pearson Correlation

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

Page 35: Pearson Correlation

III. DETERMINING THE CRITICAL VALUES

Page 36: Pearson Correlation

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

Page 37: Pearson Correlation

IV. COMPUTING FOR THE STATISTIC

Page 38: Pearson Correlation

DATA

FORMULAr = Ʃxy

(Ʃx2) (Ʃy2)

x2 y2 xy

8.2432 30473.64 136.8176

Page 39: Pearson Correlation

Putting the Formula together:

r = 136.8176

r = Ʃxy

(Ʃx2) (Ʃy2)

(8.2432) (30473.64)

r = 136.8176 501.198872

Page 40: Pearson Correlation

r = 136.8176 15238.70925

Computed value of r = 0.272980

Page 41: Pearson Correlation

V. COMPARE THE STATISTIC

Page 42: Pearson Correlation

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

Page 43: Pearson Correlation

VI. CONCLUSION

Page 44: Pearson Correlation

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.

Page 45: Pearson Correlation

THIS IS IT! SEATWORK.

Page 46: Pearson Correlation

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

PROBLEM:

Page 47: Pearson Correlation

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

Page 48: Pearson Correlation

DATA

FORMULA

X2 = 140.0612 Y2 = 36 388.9092 xy = 259.4548

r = Ʃxy

(Ʃx2) (Ʃy2)

Page 49: Pearson Correlation

Contd.

V. Compare the statisticsVI. State a conclusion

Page 50: Pearson Correlation

SOLVE!

Page 51: Pearson Correlation

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

Page 52: Pearson Correlation

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.

Page 53: Pearson Correlation

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

February 20, 2013