Types of Analysis for Association

TYPES OF ANALYSES FORTYPES OF ANALYSES FOR
ASSOCIATIONASSOCIATION
MR. EDELSON P. BOHOL
RH 630 Research Seminar 1

Correlation AnalysisCorrelation Analysis
Is a statistical measure
used to determine the
strength or degree of
relationship between
two or more variables.

Perfect Positive Linear AssociationPerfect Positive Linear Association
r = +1
Y
X

Perfect Negative Linear AssociationPerfect Negative Linear Association
r = -1
Y
X

Positive Linear AssociationPositive Linear Association
0 < r < +1
Y
X
●●●●
●●●●
●●●●
●●●●
●●●●
●●●●
●●●●
●●●●

Negative Linear AssociationNegative Linear Association
-1 < r < 0
Y
X
●●●●
●●●●
●●●●
●●●● ●●●●
●●●●

No Linear AssociationNo Linear Association
r = 0
Y
X
●●●●
●●●●
●●●●
●●●● ●●●●
●●●●
●●●●
●●● ●●●● ●●●●
●●●● ●●●● ●●●●

Nonlinear AssociationNonlinear Association
r = 0
Y
X
●●●● ●●●●
●●●●
●●●●
●●●● ●●●●
●●●● ●●●●

Pearson Product MomentPearson Product Moment
Correlation CoefficientCorrelation Coefficient

The most commonly
used measure is the
Pearson Product
Moment Correlation
Coefficient denoted by
p and estimated by
r.

n∑xy-(∑x)(∑y)
√[n(∑x²) - (∑x)²] [n(∑y²) - (∑y)²]
R =

Pearson Product Moment Correlation CoefficientPearson Product Moment Correlation Coefficient
R =
X Y X² Y² XY
3 9 9 81 27
4 13 16 168 52
5 15 25 225 75
6 16 36 256 96
7 17 49 289 119
∑X = 25 ∑ Y = 70 ∑ X² =
135
∑Y²=
1020
∑XY=369
n∑xy - (∑x)(∑y)
√[n(∑x²) - (∑x)²][n(∑y²) – (∑y)²]
√[ 5(135) – (25)² ] [5(1020) – (70)² ]
5 ( 369 ) – 25 ( 70 )
=
1845 - 1750
=
√ ( 50 ) ( 200 )
=
95
100
= .95

Simple Linear RegressionSimple Linear Regression
AnalysisAnalysis

REGRESSION ANALYSIS- is a
statistical used to determine the
functional relationship between
two or more variables.

Simple Linear regression AnalysisSimple Linear regression Analysis
 To establish the posible causation of
changes in one variable by changes
in other variables
To predict or estimate the value of a
variable given the values of other
variables.
To explain some of the variation of
one variable by the other variables.
The Objectives of Finding a Statistical FunctionalThe Objectives of Finding a Statistical Functional
Relationship Between Variables are:Relationship Between Variables are:

Data and ScatterData and Scatter
DiagramDiagram

Scatter Diagram- a plotted
points of the basic data on the X-
Y plane.
–It gives us an idea on the
posible relationship between X
andY.

A. Possitive Linear RelationshipA. Possitive Linear Relationship
Y
X
●●●● ●●●
●● ●●●● ●●●●
●●●● ●●●●

B. Negative Linear RelationshipB. Negative Linear Relationship
Y
X
●●●● ●●●
●●●● ●●
●●●● ●●

C. No RelationshipC. No Relationship
Y
X
●●●●
●●●●●● ●●●● ●●●
●●●●●● ●●●●
●●●●●●●●
●●●● ●●●

C. No RelationshipC. No Relationship
Y
X
●●●
●●●
●●● ●●●
●●●
●●● ●●● ●●●

The Data and theThe Data and the
Regression EquationRegression Equation

When b> 0,Y increases as X
increases.
When b< 0.Y decreases as X
increases, and wa say thatY is inversely
or negatively related to X.
When b = 0,Y is a constant and is
equal to the y-intercept.
Characteristics of the Regration LineCharacteristics of the Regration Line

The Data and the Regression EquationThe Data and the Regression Equation
Given : Equation of the lineY = a + bX
Computing for a and b:
Calculation of Simple RegressionCalculation of Simple Regression
byx =
∑XY – [∑X∑Y/N]
[∑X²– [(∑X)²/N]
Ayx = Y – byxX

Correlation from RanksCorrelation from Ranks

Record the rank order of the first distribution
giving the highest score a rank of1.
Do the same with the second distribution.
Get the difference between these two ranks
for each individual and record in the D column.
Square each of these difference and sum this
column.
Apply the values in the formula:
Spearman Rank-Difference MethodSpearman Rank-Difference Method
R= 1-
n (n² - 1)
6 ∑ D²

Solution: Rx Ry D D²
1 6 5 1 1
2 2 8 -6 36
3 1 4 -3 9
4 4 6 -2 4
5 9 3 6 36
6 10 2 8 64
7 5 7 -2 4
8 3 10 -7 49
9 8 1 7 49
10 7 9 -2 4
∑D²= 265
R= 1-
6 ∑ D²
n (n² - 1)
6 ( 256 )= 1 -
10( 10² - 1)
1536
10( 99)
= 1 -
1536
= 1 -
990
= 1 - 1.55 = -0.55
Computer Product 1 2 3 4 5 6 7 8 9 10
Men (X) 6 2 1 4 9 10 5 3 8 7
Woman (Y) 5 8 4 6 3 2 7 10 1 9

Chi-Square (2)Chi-Square (2)²²

Chi-Square – The most commonly
used method of comparing proportions.
It is particularly useful in test evaluating
a relationship between nominal- or
ordinal data
Fo= Observed Number of Cases
Fe= Expected Number of Cases
X² = ∑ [ ( fo – fe )²
fe

Chi-Square (XChi-Square (X²)²)
Fo Fe Fo – Fe (Fo – Fe)² (Fo – Fe)² / Fe
A 98 105 -7 49 49/105 = 0.467
B 115 105 10 400 100/105 = 0.952
C 102 105 -3 49 9/105 = 0.056
1.505
X² = ∑ [ ( fo – fe )²
fe
X² = 1.505

Chi-Square as a Test of Independence:Chi-Square as a Test of Independence:
Two Variable ProblemsTwo Variable Problems
Chi-Square can also be used to test
the significance of the relationship
between two variables when data are
expressed in terms of frequencies of
joint occurence.
Fe = [ ]
(rowtotal) (columntotal)
N

Fe = [ ](rowtotal) (columntotal)
N
School Choice
Gender
Female Male Total
Public 42 65 107
Private 58 35 93
Total 100 100 200
C 1
C2
C 3
C4
Computational Procedure:
1. Compute the expected frequency of each cell.
C1 =
100x107 = 53.5
200
200
100x93 = 46.5C1 =
100x107 = 53.5
100x93 = 46.5
C4 = 200
C3 = 200

School Choice
Gender
Female Male Total
Public 42 65 107
Private 58 35 93
Total 100 100 200
C 1
C2
C 3
C4
2. Present in table form
fo fe fo-fe (fo-fe)² (fo-fe)²/fe
42 53.5 -11.5 132.25 2.48
58 46.5 11.5 132.25 2.85
65 53.5 11.5 132.25 2.48
35 46.5 -11.5 132.25 2.85
∑ =
10.66
(fo - fe)
fe

School Choice
Gender
Female Male Total
Public 42 65 107
Private 58 35 93
Total 100 100 200
C 1
C2
C 3
C4
3. Prepare the Hypothesis
4. Decision Rule

***********THE END********************THE END*********
THANKYOU!

Types of Analysis for Association

More Related Content

What's hot

Similar to Types of Analysis for Association

Recently uploaded

Types of Analysis for Association