G5-Statistical-Relationship-Among-Variables.pptx

Statistical
Relationships
among Variables

Statistical Relationships Among Variables
Statistical
Relationships
Among
Variables
Objectives
Flow
To describe the ways in which variables
relate to one another
To appreciate correlation as a means to
explain the relationships of the variables
To be able to present on how to evaluate
Correlation
To explain the concept of Pearson R
Correlation and compute correlation using
the Pearson r formula.

Correlation
• Correlation Tests are used to determine how strongly
the scores of two variables are associated or
correlated with each other.
• Correlation is measured using values between +1.0
and -1.0. Correlations close to zero indicate little or no
relationship between two variables, while correlations
close to +1.0 or -1.0 indicate strong positive or
negative relationships.

Correlation
• Correlation denotes positive or negative association
between variables in a study.
• It is positively associated when larger values tend to be
accompanied by another larger values (when two variables
are of the same direction).
• It is negatively associated when larger values tend to be
accompanied by smaller values of the other (when two
variables are of different direction).
NOTE: When the result of the study is of scattered direction, it
means it is negligible or no relationship between two variables
at all.

HOW TO EVALUATE
CORRELATION
Marichu Y. Hechanova

Correlation
 is calculated as the level and direction of a relationship
between two variables X and Y. The range of values of a
correlation coefficient is from “-1” to ”+1”. The closer the value
is to +1, the stronger the positive correlation, the closer the value is
to -1, the stronger the negative correlation.
 Associations between two variables, a relationship, a relationship
that we want to know two things about what direction of between
two variables x and y? and what is the strength of the relationship.
 Some correlation have what we call the direct relationship, if
variable x happen to be high the other variable Y happen to be
high, or if the variable X happen to be low the other variable Y
happen to be low ,in other word two variables move in the same
direction, we can to predict the level of the other , we call this a
correlation a direct correlation or positive correlation ,the variables
that in the same direction.

STRENGTH OF CORRELATION
If one variables is high, the other is low and vice versa , in other words they moving
in opposite direction, we used the negative to describe an inverse relationship,
negative does not imply anything bad, it simply means the two variables are
moving in opposite direction.
The strength of the relationship or how many exception are there to the trend , it is
true in every case when variables is high so was the other and when variables is low
so was the other, we would have a perfect positive correlation or +1.and if the
correlation were in the other direction or if in inverse , that when one variables was
high the other was low, then we would have a perfect inverse relationship which
symbolized by a negative -1.

A zero correlation, means no relationship between the two variables,
such that there is no way to predict a level of one variables from a
knowledge of the other, in the real world correlation are not perfect
positive, perfect negative or zero , correlation that closed being perfect
are called high or strong or there are few exceptions to the direct or
inverse trend, correlation that closed to zero with only a very weak or
low trend will be those that have many exceptions to the trend, many
correlation are also are in moderate range. We used number between
zero and one to represent the strength of these correlation coefficients
, whether negative or positive , so when we are close to zero say
between zero and .2,we speak of this are low or weak correlation , and
when we are above.6 (between .6 and 1.00) positive or negative we
speak to this as high or strong correlation.

HOW TO EVALUATE A CORRELATION
STRENGTH OF CORRELATION POSITIVE NEGATIVE
Negligible Correlation 0 to +0.20 0 to to -0.20
Low Correlation +0.21 to +0.40 -0.21 to -0.40
Moderate Correlation +0.41 to +0.70 -0.41 to -0.70
High Correlation +0.71 to +0.90 -0.71 to -0.90
Very High Correlarion +0.91 to +0.99 -0.91 to -0.99
Perfect Correlarion +1.00 -1.00

Statistical Significance of
Correlation

What is
Statistical
Significance
of
Correlation?
• It is a Hypothesis Test that
decide whether the linear
relationship of sample data is
strong by finding the Critical
Value Boundary of “r”
(correlation coefficient)

Testing of
Significance
of
Correlation
• To conduct this Test we need to know two
things;
df = Degree of Freedom
n = Number of Pairs or
observation in the data
Formula for ; df = n- 2

Statistical
Significance
Correlation
Testing
• Lets assume the following data :
r = 0.90
n = 6
p = 0.05
df = 6 – 2 = 4
Using the Critical Value Table

Critical Value Table (Correlation r)
Df P=0.10 P=0.05
1 0.9877 0.9969
2 0.9000 0.950
3 0.805 0.878
4 0.729 0.811
5 0.669 0.754
6 0.621 0.708
Therefore, the
Critical Value
based on the
Table is 0.811

Assessing the
Results
• Since our correlation of r = 0.90 fell in the
Critical region in the Tail beyond 0.811, we can
conclude that test is statistically significant.
• Therefore, we reject the hypothesis and
conclude that our correlation is significantly
different from 0

Pearson Product-Moment Correlation
Coefficient
Statistical Relationship Among Variables

Is there a relationship between the number
of hours the students studied and their
exam results?
Pearson Product-Moment Correlation Coefficient | Statistics
Is there a relationship between the number
of student absences and their quiz
scores?
Is there a relationship between the
students’ allowance to their quiz scores?

DATA A DATA B DATA C

Magnitude
and strength
of the
Correlation
Continuous and
random variables

PEARSON
PRODUCT-
MOMENT
CORRELATION
Concept and Definition
Pearson r , linear or product moment,
Pearson correlation coefficient
Measures the strength of a linear relationship
between two variables
It does not depend on specific measurement
used.
It can take a range of values from +1 to -1. A
value of 0 means no association between
variables.
Regression line of least square lines.

PEARSON
PRODUCT-
MOMENT
CORRELATION
Assumptions
Assumption #1: The two variables should be
measured on a continuous scale
Assumption #2: Your two continuous variables
should be paired,
Assumption #3: There should be independence
of cases
Assumption #4: There should be a linear
relationship between your two continuous
variables.
Assumption #6: There should
be homoscedasticity
Assumption #5: Continuous variables should
follow a bivariate normal distribution
Assumption #7: There should be no
univariate or multivariate outliers.

PEARSON
PRODUCT-
MOMENT
CORRELATION
Computational
Formula

DATA A DATA B DATA C
Positive Correlation
between the No. of Hours of
Study and the Exam results.
r = 0.86
Negative Correlation
between the No. of Hours of
Study and the Exam results.
r = -0.98
No Correlation between the
No. of Hours of Study and
the Exam results.
r = 0.017
CONCLUSION

PEARSON
PRODUCT-
MOMENT
CORRELATION
References
https://journals.lww.com/anesthesia-
analgesia/fulltext/2018/05000/correlation_coefficients__
appropriate_use_and.50.aspx
https://statistics.laerd.com/statistical-guides/pearson-
correlation-coefficient-statistical-guide.php
https://www.statisticssolutions.com/pearsons-
correlation-coefficient/
https://www.statisticshowto.com/practically-cheating-
statistics-handbook/help-with-statistics-equations/

Statistical
Relationships
among
Variables
Questions

G5-Statistical-Relationship-Among-Variables.pptx

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