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.
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.
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.
correlation of +1
there is a perfect positive
linear relationship between
variables
X Y
8.
correlation of -1
there is a perfect negative
linear relationship between
variables
X Y
9.
A perfect negative linear relationship, r = -1.
10.
A correlation of 0 means there is no linear
relationship between the two variables, r=0
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.
•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.
-1 -.8 -.3 0 .3 .8
1
STRONG MOD WEAK WEAK MOD STRONG
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.
Formula
Where:
x : deviation in X
y : deviation in Y
r = Ʃxy
(Ʃx2) (Ʃy2)
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.
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.
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.
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.
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.
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.
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.
VI. Conclusion / Implication
There is a significant
relationship between midterm
grades of the students and
their final examination.
25.
Correlates of Work Adjustment among
Employed Adults with Auditory and
Visual Impairments
Blanca, Antonia Benlayo
SPED 2009
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.
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.
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.
PROBLEM
Is there a relationship
between gender and the
level of work adjustment
of the individual with
hearing impairment?
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.
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.
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.
DATA
FORMULA
r = Ʃxy
(Ʃx2) (Ʃy2)
x2 y2 xy
8.2432 30473.64 136.8176
34.
Putting the Formula together:
r = 136.8176
r = Ʃxy
(Ʃx2) (Ʃy2)
(8.2432) (30473.64)
r = 136.8176
501.198872
35.
r = 136.8176
15238.70925
Computed value of r = 0.272980
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.
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.
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.
DATA
FORMULA
X2 = 140.0612
Y2 = 36 388.9092
xy = 259.4548
r = Ʃxy
(Ʃx2) (Ʃy2)
42.
Contd.
V. Compare the statistics
VI. State a conclusion
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.
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.
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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