meeting 15 Associative Hypothesis Test

5/17/2011

1

Associative Hypothesis Test:

Correlation And Regression

Presented by:

Mahendra AN

Basic Principles

Population parameter

ρ

Reduction

Statistic

r

Generalization = correlation from between two or more variables

Basic Concepts

Positive correlation Negative correlation

Basic Concepts

r=0 _{r=0.5 r=1}

Statistics Techniques

Data Types Correlation techniques

Nominal 1. Contingency coefficient

Ordinal 1. Rank Spearman

2. Tau Kendal

Interval or ratio 1. Product moment Pearson 2 Multiple correlation 2. Multiple correlation 3. Partial correlation

Parametric Statistics for Correlations

1. Product moment z For searching of correlation

between two variables for interval or ratio data from the same source and normal distributed

2. Multiple correlation

Vs partial correlation

distributed

z Alternative significance test

∑

∑

=

y

x

r

xy xy2 2

r

n r

t ₂

1 2 −

− =

5/17/2011

2

Parametric Statistics for Correlations

Multiple correlation Partial correlation

r r r r r r R x x x x yx yx yx yx x x y − − + = 1 2 2 1 2 1 2 1 1 1 2 1 2 2 2 . r r r r r R x y x x x x yx yx x x y 2 2 . 1 1 12 2

2 1 2 1 2 1 . − − − − = zAlternative significance test zAlternative significance test

( )

1 2/

(

1

)

/ 2 − − − = k n R k Fh

R

r

r

p n t p 2 1 3 − − =

Correlation Coefficient Interpretation

Coefficient Interval Correlation

0.00 – 0.199 Very low

0.02 – 0.399 Low

0.40 – 0.599 Medium

0.60 – 0.799 Strong

0.80 – 1.000 Very strong

Non parametric statistics for correlations

1. Contingency coefficient

zFor nominal data

zStrong connection with chi square

2. Rank Spearman

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

χ

χ

+

=

N

C ₂ 2 distributed

• Alternative significance test

(

)

∑∑ + = = =r i k j EPij

E

OPij ij

1 1

2 2

χ

(

1

)

6 1 ₂ 2 − ∑ − = n n bi ρ 1 1 − = n

z

h ρ r n r t ₂ 1 2 − − =

Non parametric statistics for correlations

3. Tau Kendal

zFor ordinal or rank data

zFor more than 10 data

zCan be used for searching partial correlation

zSignificance test

(

)

2 1 − − =

∑ ∑

N N B A τ ( ) ( 1)) 9 5 2 2 − + = N N N z τ

Regression

z

Correlation search direction and strength

of symmetric , causal or reciprocal

relationships between two variables while

regression predict changes of dependent

regression predict changes of dependent

variables when independent variables are

change

Linear Regression Lines

5/17/2011

3

Linear Regression

1. Simple Linear Regression

2. Multiple linear Regression

ε

+

+

=

a

bX

Y

s

ε

+

+

+

+

+

=

a

b

X

b

X

b

n

X

n

Y

1 1 2 2

...

s

s

x y

r

b=

a

=

Y

−

bX

( ) ( )( )

( )

∑ ∑ ∑ ∑ ∑

∑ − − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ =

X X

Y X X X Y

i i n

i a i 2 i2 i i

2

( ) ( )

(

)

∑ ∑ ∑

∑

∑ −

− − =

X X

Y X Y X

i i n n

b i i i i

2 2

Simple Linear Regression Line

Simple Linear Regression Test Steps

z

Linearity test

z

Count a and b

z

Build regression equation and draw

i

li

s s

G TC F 2 2

=

regression line

z

Significance test

z

Correlation hypothesis test

s

s

sis reg F 2 2

=

(

)(

)

(

)

(

∑ ∑

)

(

∑

( )

∑

)

−

=

−

−

∑

∑

∑

Y

Y

n

X

X

n

Y

X

Y

X

i i i i n

r i i i i

2 2 2 2

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.

== MAHENDRAADHINUGROHO, 2008 ==