Post on 25-Dec-2014
description
transcript
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