meeting 15 Associative Hypothesis Test

5/17/2011

Basic Principles

Associative Hypothesis Test:
Correlation And Regression

Reduction

Population
parameter

ρ

Presented by:
Mahendra AN

Statistic

r

Generalization = correlation from
between two or more variables

Basic Concepts

Basic Concepts

r=0
Positive correlation

r=0.5

r=1

Negative correlation

Statistics Techniques

Parametric Statistics for Correlations

Data Types

Correlation techniques

1. Product moment

Nominal

1. Contingency coefficient

Ordinal

1. Rank Spearman
2. Tau Kendal

Interval or ratio

1. Product moment Pearson
2. Multiple correlation
2

3. Partial correlation

z For searching of correlation
between two variables for
interval or ratio data from the
same source and normal
distributed

r

xy

=

∑ xy
∑x y
2

2. Multiple correlation
Vs partial

correlation

2

z Alternative significance test

t=

r n−2
1− r

2

© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!

1

5/17/2011

Parametric Statistics for Correlations

Correlation Coefficient Interpretation

Multiple correlation

Coefficient Interval

Correlation

0.00 – 0.199

Very low

2

R

y.x1x2

=

Partial correlation

1

1

1

1−r x x
1

2

1 2

2

R

y.x1x2

1

2

1−r x x
2

1

)

−

1 2

1−r y x
2

2

2

z Alternative
significance test

2

R /k
1 − R 2 / (n − k − 1)

(

=

2

z Alternative

significance test
Fh =

r yx − r yx .rx x

2

r yx + r yx − 2r yx r yx rx x

t=

r

p

0.02 – 0.399

Low

0.40 – 0.599

Medium

0.60 – 0.799

Strong

0.80 – 1.000

Very strong

n−3

1− r p

2

Non parametric statistics for correlations

Non parametric statistics for correlations

1. Contingency coefficient

2. Rank Spearman

3. Tau Kendal

z For nominal data
z Strong connection with
chi square

• For ordinal data from
different data sources
and not normal
di t ib t d
distributed

z For ordinal or rank data
z For more than 10 data
z Can be used for
searching partial
correlation

χ

C=

2

2

N +χ

ρ = 1−

2

(OPij + Eij )

2

r

k

χ = ∑∑
2

i =1 j =1

EP

ij

6∑ b i
n(n2 − 1)

• Alternative significance
test
ρ
n−2
zh = 1
t=r
1− r2
n −1

Regression

τ=∑

A−∑B
N ( N − 1)
2

z Significance test
z=

τ

2(2 N + 5)
9 N ( N − 1) )

Linear Regression Lines

z Correlation search direction and strength
of symmetric , causal or reciprocal
relationships between two variables while
regression predict changes of dependent
variables when independent variables are
change

© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!

2

5/17/2011

Linear Regression
1. Simple Linear
Regression

2. Multiple linear
Regression

Y =a+b1X1+b2X2 +...+bnXn +ε

Y = a + bX + ε
b=r

Simple Linear Regression Line

s a = Y − bX
s
y

x

(∑Y )⎛⎜⎝ ∑ X i ⎞⎟⎠ − (∑ X )(∑ X Y )
n∑ X i − (∑ X i )
2

a=

b=

i

i

2

i

i

2

n∑ X i Y i − (∑ X i ) − (∑Y i )

(

n∑ X i − ∑
2

X i)

2

Simple Linear Regression Test Steps
2

z Linearity test F = s
s
z Count a and b
z Build regression equation and draw
regression
i liline
z Significance test F = s
s
z Correlation hypothesis test
TC
2
G

Kita membangun langit dengan segala daya yang ada
kemudian merasa langit kita sudah cukup tinggi
bahkan mengungguli langit lain.
Tetapi akan selau ada langit di atas kita.

2

reg
2

== MAHENDRA

ADHI NUGROHO,

2008 ==

sis

r=

n∑ X i Y i − (∑ X i )(∑ Y i )

(n∑ X i −(∑ X i) ) (n∑ Y i −(∑ Y i ) )
2

2

2

2

© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!

3