pearson correlation
DESCRIPTION
TRANSCRIPT
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IAN JULE MALONGKATRINA PARAISO
ANGELA CARLA ARANIEGONOREEN MORALES
The Pearson Product Moment Coefficient of Correlation (r)
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Proponent
Karl Pe
arson
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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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-1 -.8 -.3 0 .3 .8 1
STRONG MOD WEAK WEAK MOD STRONG
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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.
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Formula
Where:x : deviation in Xy : deviation in Y
r = Ʃxy
(Ʃx2) (Ʃy2)
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Solving Stepwise methodI. PROBLEM: Is there a relationship
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 = 837.5
(862.5) (905.5)
r = Ʃxy
(Ʃx2) (Ʃy2)
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) = 0.632Computed value of r = 0.9480.948 > 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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RESEARCH TITLE: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 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
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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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CONCEPTUAL FRAMEWORK
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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
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I. Problem
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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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II. Hypothesis
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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
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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
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IV. COMPUTING FOR THE STATISTIC
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DATA
FORMULAr = Ʃxy
(Ʃx2) (Ʃy2)
x2 y2 xy
8.2432 30473.64 136.8176
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Putting the Formula together:
r = 136.8176
r = Ʃxy
(Ʃx2) (Ʃy2)
(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 THE STATISTIC
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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
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VI. CONCLUSION
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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.
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THIS IS IT! SEATWORK.
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Is there a relationship between age and level of work adjustment of employees with hearing impairment?
PROBLEM:
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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
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DATA
FORMULA
X2 = 140.0612 Y2 = 36 388.9092 xy = 259.4548
r = Ʃxy
(Ʃx2) (Ʃy2)
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Contd.
V. Compare the statisticsVI. 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