2 Correlation

8/10/2019 2 Correlation

1/60

CORRELATION


2/60

Learning Outcomes

Upon completion of this chapter, you should be able to:

Construct a scatter diagram given two sets of data

Interpret a given scatter plot in terms of strength ofrelationship and direction of relationships

Decide whether the relationship between two sets ofdata is linear/non-linear given the scatter diagram

Calculate earson correlation given the data

Calculate !pearman correlation given the data Interpret given correlation coefficient

Decide on whether to use earson or !pearman

correlation given the data sets


3/60

Correlation

A correlation is showing the degree or strength of

relationship between two variables. "he population correlation, denoted by "he sample correlation, denoted byr Usually, the variables denoted by # and $% &r' can ta(e on any value from ) to )% Three method can be used for the describe the

relation and estimating association between

variablesa) Scatter plotb) Pearsons Correlation Coefficientc) Spearmans Rank Correlation Coefficient


4/60

Scatter Plot / Diagram !catter plots usually consist of a large body of data%

"he closer the data points come when plotted to ma(inga straight line, the higher the correlation between thetwo variables, or the stronger the relationship%

In a positive linear relationship indicates that as the #score increase, the $ also tend to increase%


5/60

Cont.. In a negative linear relationship indicates that as the #

score increases, the $ score tend to decreases%

In a nonlinear relationship denotes that as the # scoresincreases, the $ score do not increases nor decreases%


6/60

erfect positive !trong positive ositivecorrelation r * ) correlation r * +% correlation r * +%+

!trong negative .o correlation .on-linearcorrelation r * +%++correlation r * -+%


7/60

Strength of Relationship

r Relationship Between Two Variables

r * -)%++ indicates a perfect negative linear relationship

r * )%++ indicates a perfect positive linear relationship

-)%++ 0 r 0 -+%1+ indicates a strong negative linear relationship

+%1+ 0 r 0

)%++

indicates a strong positive linear relationship

-+%1+ 0 r 0 + indicates awea( negative linear relationship

+ 0 r 0 +%1+ indicates awea( positive linear relationship

r * + indicates no linear relationship


8/60

The important of a scatter plot

We need a scatter plot to find if the

relationship between # and $ is a linearrelationship%

It can be positive linear relationship ornegative linear relationship%


9/60

Perkara Penting Untuk Melakar

Scatter Diagram

2engenal pasti pembolehubah bersandar danpembolehubah tida( bersandar

2ela(ar scatter diagram "a3u( 4raf

5abel a(si #

5abel a(si $

lot !era(an


10/60

Pearsons correlation coefficient ( r)

Definition

Pearsons correlation coefficient measures the strength or thedegree of the linear relationship between two variables.

It is assumed that both variables (often called X and Y) are of

interval or ratio scale. Data set approximately normally distribute.

Synonyms:product moment correlation coefficient

simple linear correlation coefficient


11/60

Cont Pearsons Correlation Coefficient is usuall signified b r

!rho").

#ormula for computing Pearson correlation is given as:-

))((

!

!

YNYXNX

YXNXYr

YxSSSS

SPr

$here%

X &ean of '

Y &ean of (

number of sample

))(())((

))((

YYNXXN

YXXYNrp


12/60

Spearman ran"

#ormally

distributed

$ida"

Ya

Pearson%orrelation

Interval&ratiodata'

ula

$amat

$ida"

Ya

How to choose the Correlation ?


13/60

Cont

Example 1

A high school guidance is interested in a relationship between pro*imit

to school and participation in e*tracurricular activities. +e collects the

data on the distance from home to school !in miles) and number ofclubs ,oined for a sample of - ,uniors. /sing the following data

compute a Pearsons correlation is significant.

Distance to

school (in miles)

X

Numbers of clubs

Joined

Y

5ee 6 7

8honda 9 )

ess ; 1


14/60

Penelesaian

!tep )


15/60

!tep 9

84.)*.+8(,.+-

.-/

),.4)(,(4+)(+./)(,(4,(

),.4)(+./)(,(**

p

p

p

r

r

r

Interpretation

#ilai pe"ali "orelasi Pearson 0.841 menun2u""an terdapatnya satu hubungan

linear positif diantara 2ara" dari se"olah dengan bilangan penyertaan dalam"elab.

))((

!

!

YNYXNX

YXNXYr


16/60

Pearsons Coefficient Correlation Test

earson>s Coefficient correlation test can be determineby using critical value from earson?s "able or "-test%

"o test the significant of a a measure of correlation, we

usually set up that

3

3

a

o

H

H ull hpothesis

Alternative hpothesis

4

5

0egree of freedom" df 1 n23

,

3

p

pr

nrTujianstatistik


17/60

Contoh soalan 3

daripada contoh -" u,i keertian pekali korelasi Pearson

dengan aras keertian" 41.5.

5ang(ah ):Nyatakan HodanHailai korelasi adalah positif !6.78)" maka u,ian

hipotesis satu hu,ung digunakan.

@o : "ida( terdapat per(aitan antara 3ara( dari se(olahdengan penglibatan dalam a(tiviti (elab

@o :s = +@a : "erdapat per(aitan antara 3ara( dari se(olah dengan

penglibatan dalam a(tiviti (elab%

@a :s > +

pr

pr


18/60

Aeputusan u3ian:0ar,ah kebebasan

d# 1 n23

1 -23

17

Compare the obtained Pearsons with the appropriate value of

Pearsons in Table #

Cari dengan menggunakan ,adual nilai kritikal

Pearsonscriticalr


19/60


20/60

0aripada ,adual didapati bahawa

maka" null hpotesis ditolak dan mempunai bukti ang

kukuh untuk membuat kesimpulan bahawa

9esimpulan" ini menun,ukkan bahawa wu,udna

hubungan ang signifikan pada aras signifikan .5 iaitu

,ika ,arak dari sekolah ,auh" penglibatan dalam aktivitikelab meningkat.

criticalp rr

pr


21/60

Contoh soalan : !menggunakan u,ian T)

,

3

p

pr

nrTujianstatistik

+8.4

84.,

884.

T

T

0aripada ,adual T" pada aras signifikan 41.5" T ; t.5" 7 1 -.7 +

Terdapat perhubungan positif

ang signifikan antara keputusan

u,ian aptitud dan hasilan ker,a

),8(8

)/.(-,

kiraansr

**4,.kiraansr

),(-,

nndrkiraans

P l i


50/60

Penyelesaian

#Menggunakan (adual Spearman' Daripada adual !pearman

rs kritikal = +0.643


51/60

Penyelesaian

#Menggunakan (adual Spearman'

5ang(ah 6: MembuatKeputusan

Jleh (erana rs kiraan * +%6 lebih besar daripada rskritikal * +%=67 dan berada di (awasan penola(an%

8e3ection region

+%=67

@o ditola( dan (esimpulannyaterdapat per(aitan antara(eputusan u3ian aptitud dan hasilan(er3a

.on re3ection region

P l i


52/60

Penyelesaian

#Menggunakan (adual Ta+uran,t'

5ang(ah ):NyatakanHodanHa

@o : "ida( terdapat per(aitan antara (eputusan

u3ian aptitud dan hasilan (er3a%@o :s = +

@a : "erdapat per(aitan antara (eputusan u3ianaptitud dan hasilan (er3a%

@a :s > +

P l i


53/60

Penyelesaian


5ang(ah 9: Menentukankawasanpenolakandankawasanpenerimaan

Degree of freedom, df * B 9 * =

!ignificant level , E * +%+1tkritikal * )%67 &ru3u( 3adual taburan-t'


8e3ection region

)%67


54/60

Penyelesaian


55/60

Penyelesaian


5ang(ah 7: Kirakannilaiujianstatistik,T

,

s

s

r

nrT

**4.,

8**4.

T

-.T

Penyelesaian


56/60

Penyelesaian


5ang(ah 6: MembuatKeputusan T> tkritikal

99%9= F )%67 @o ditola( dan terdapat per(aitan antara

(eputusan u3ian aptitud dan hasilan (er3a%


8e3ection region

)%67


57/60

Latihan 1 !yari(at insuran "a(aful telah men3alan(an

(ursus pen3ualan dan pemasaran yangdire(abentu( untu( mening(at(an prestasiwa(il-wa(il pen3ualan% Dalam usaha untu(

menilai program tersebut, pengurus latihanpemasaran dan pen3ualan ingin melihat samaada terdapat hubungan atau tida( antara

pencapaian program dan pen3anaan pen3ualantahunan selepas itu% adual beri(utmenun3u((an data yang di(umpul(an oleh

pengurus (e atas )) orang graduan program itu%

Latihan 1


58/60

Latihan 1 adual: 8ang(ing restasi encapaian Aursus dan 8ang(ing ualan

"ahunan Gagi )) orang e(er3a Di !yari(at Insuran "a(aful

Gerdasar(an 3adual, (ira(an (olerasi !pearman bagi data yang diberi(an%

Pe!er"a Ran!in' Prestasi

Pencapaian#ursus

Ran'!in' Jualan

Tahunan

!aifudin ) 6

.oraHlina 9 =

shraf 7 )

.or Hura 6 9

.orlaila 1 ;

.ura(ma = )+

4auri ; 7

8ahifa 1.orhidayu

innie )+

.urhaini )) ))


59/60

(aapan Latihan 1

rs kiraan * +%=7= lebih besar daripada rs kritikal *+%17= dan berada di (awasan penola(an%

@o ditola( dan (esimpulannya terdapatperhubungan antara pen(aitan antara prestasipencapaian (ursus dan pen3anaan 3ualan

tahunan%

8 b K


60/60

"he minimum values of rs needed for statisticalsignificance are shown in critical values table of

!pearman for values ofNfrom 1 to 7+%&.otethat when using this table, you need only refer toNB the number of pairs of ran(s B rather than

degrees of freedom%' WhenNis greater than 7+, the critical values for

testing a earson r for statistical significance will

give a very good approimation% "hat is, you canrefer the computed !pearman correlationcoefficient to critical values table of the earson

rwithNB 9 degrees of freedom%

8ememberK

2 Correlation

Documents

Transcript of 2 Correlation