m.kanmani Appro Statistics

7/23/2019 m.kanmani Appro Statistics

1/50

Dr M.KanmaniDr M.Kanmani

Head-in ChargeHead-in Charge

Department of EducationDepartment of Education

Manonmaniam SundaranarManonmaniam SundaranarUniversity, irune!ve!i-"#.University, irune!ve!i-"#.

$an%mani%msc&yahoo.com$an%mani%msc&yahoo.com


2/50

'(()*()+'E S'+S+CS*) D'' ''/S+S


3/50

0'S+C C*CE(S0'S+C C*CE(S

(opu!ation(opu!ation

Co!!ection of a!! individua!s or o23ects or itemsCo!!ection of a!! individua!s or o23ects or items

under study and denoted 2y under study and denoted 2y

Samp!eSamp!e

' part of a popu!ation and denoted 2y n' part of a popu!ation and denoted 2y n 4aria2!e4aria2!e

Characteristic of an individua! or o23ect.Characteristic of an individua! or o23ect.

5ua!itative and 5uantitative varia2!es5ua!itative and 5uantitative varia2!es

(arameter(arameter

Characteristic of the popu!ationCharacteristic of the popu!ation

StatisticStatistic

Characteristic of the samp!eCharacteristic of the samp!e


4/50

NOTATIONS OF POPULATION AND SAMPLENOTATIONS OF POPULATION AND SAMPLE

n

xX =

_

n

2xxs

=

)_

(

1n

2xx

S

=

)_

(

n

xp =

yx

yxCOVr

=

),(

Characteristics Pp!"atin Sa#p"e

Si$e N n

Mean

SD

Prprtin P

Crre"atin

Ce%%icient


5/50

Chart on popu!ation, samp!e andChart on popu!ation, samp!e and

statistica! inferencestatistica! inference

(opu!ation too !arge(opu!ation too !arge

Co!!ect data fromCo!!ect data from

the samp!ethe samp!e

*rganise*rganise

datadata

'na!yse the'na!yse the

*rganised data*rganised data

Samp!e dra6n fromSamp!e dra6n from

the popu!ationthe popu!ation

Dra6 inference 6hich isDra6 inference 6hich is

app!ica2!e to the popu!ationapp!ica2!e to the popu!ation


6/50

*rganising a ra6 data set*rganising a ra6 data set

M a k e a f r e q u e n c y

t a b l e

C a t e g o r i c a l o r Q u a l i t a t i v e d a t a s e t

M a k e af r e q u e n c y t a b l e

O b t a i n t h e m o d i f i e d r a n g e

a n d t h e n d i v i d e i n t os e v e r a l c l a s s e s

Q u a n t i t a t i v ed a t a s e t

R a w d a t a s e t


7/50

Dec &' 2(1)

(ictoria! representation of(ictoria! representation of

a data seta data set

B a r D i a g r a mP i e D i a g r a m

C a t e g o r i c a l o r

Q u a l i t a t i v e d a t a s e t

i s t o g r a m! t e m l e a f d i s " l a y

P i e d i a g r a m

# i m e " l o t

Q u a n t i t a t i v e

d a t a s e t

$ r a " h i c a l r e " r e s e n t a t i o n

o f a d a t a s e t


8/50

Dec &' 2(1)

Summarising a ra6 data setSummarising a ra6 data set

on a 7uantitative varia2!eon a 7uantitative varia2!e

L o c a t i n g a c e n t r a l v a l u eo f t h e d a t a s e t b y t h e m e a s u r e s

M o d e

M e d i a n , M e a n

S t u d y t h e c e n t r a l

t e n d e n c y o f t h e d a t a s e t

Q u a n t i f y i n g t h e d i s p a r i t y a m o n g t h ed a t a e n t r i e s i s d o n e b y t h e m e a s u r e s

R a n g e , I n t e r - q u a r t i l e R a n g e

V a r i a n c e , S

S t u d y t h e v a r i a b l i t y

o r d i s p e r s i o n o f t h e d a t a s e t

S u m m a r i s i n g a r a ! d a t a s e t

o n a q u a n t i t a t i v e v a r i a b l e


9/50

Samp!ing echni7uesSamp!ing echni7ues

! i m " l e R a n d o m

! a m " l e

P r o " o r t i o n a t e D i s " r o " o r t i o n a t e

! t r a t i f i e d R a n d o m

! a m " l e

! y s t e m a t i c

R a n d o m

! a m " l e

O n e ! t a g e # w o ! t a g e M u l t i ! t a g e

C l u s t e r

! a m " l i n g

P r o b a b i l i t y

! a m " l i n g

C o n v e n i e n c e

s a m " l i n g

Q u o t a

! a m " l i n g

% u d g e m e n t

! a m " l i n g

! n o w b a l l

! a m " l i n g

& o n ' P r o b a b i l i t y

! a m " l i n g


10/50

Stages in Data 'na!ysisStages in Data 'na!ysis

EditingEditing

CodingCoding

Data Entry

(Keyboarding)

Data

Analysis

Error

Chec$ing

'nd

4erification

Descriptive

'na!ysis

Univeriate

'na!ysis

0ivariate

'na!ysis

Mu!tivate

'na!ysis

+nterpretation


11/50

Dec &' 2(1)

Statistica! +nferenceStatistica! +nference

" o i n t

# s t i m a t i o n

I n t e r v a l

# s t i m a t i o n

$ h e o r y o f

# s t i m a t i o n

" a r a m e t r i c

$ e s t

% o n " a r a m e t r i c

$ e s t

$ e s t i n g o f

& y p o t h e s i s

S t a t i s t i c a l

I n f e r e n c e


12/50

Dec &' 2(1)

he Concept of ( 4a!uehe Concept of ( 4a!ue

8iven the o2served data set, the ( va!ue is the8iven the o2served data set, the ( va!ue is thesma!!est !eve! for 6hich the nu!! hypothesis issma!!est !eve! for 6hich the nu!! hypothesis isre3ected 9and the a!ternative is accepted:re3ected 9and the a!ternative is accepted:

+f the ( va!ue+f the ( va!ue then re3ect Hthen re3ect H;;< *ther6ise accept< *ther6ise acceptHH;; +f the ( va!ue+f the ( va!ue ;.;";.;" then re3ect Hthen re3ect H;; at "= !eve! ofat "= !eve! of

significancesignificance

+f the ( va!ue !ies 2et6een ;.;" to ;.;> 9ie. ;.;"?+f the ( va!ue !ies 2et6een ;.;" to ;.;> 9ie. ;.;"? ((va!ueva!ue ;.;>:;.;>: then re3ect Hthen re3ect H;; at >= !eve! ofat >= !eve! ofsignificancesignificance

+f the ( va!ue+f the ( va!ue >>;.;>;.;>then accept Hthen accept H;; at >= !eve! ofat >= !eve! ofsignificancesignificance


13/50

Measurement Sca!esMeasurement Sca!es

* Types of measurement scales areTypes of measurement scales are

* Nominal ScaleNominal Scale

* rdinal Scalerdinal Scale

* !nter"al scale!nter"al scale

* #atio Scale#atio Scale


14/50

Sca"es % Meas!re#entSca"es % Meas!re#ent

Scale Level Scale ofMeasurement

ScaleQualities

#'ample(s)

( RatioMagnitude)qual *ntervals

+bsolute ,ero

+ge- eight-.eight-Percentage

/ IntervalMagnitude)qual *ntervals

#em"erature

0 *rdinal Magnitude1ikert !cale-

+nything rank

ordered

2 %ominal &one&ames- 1istsof words


15/50

'ppropriate Statistics'ppropriate Statistics

Nominal rdinal !nter"al #atio

$ Cross tabs %

C&i s'uare,&iCramersContingency

$ Nonparametric %

C&i*s'uare,#uns+inomialcNemar

Coc&ran

$ -re'uencies %

edian,!nter'uartile range

$ Nonparametric %

Kolmogoro"*Smirno"Sign.ilco/enKendall coefficient of

concordance-riedman t0o*0ay ano"aann*.&itney U.ald*.olfo0it1Krus2al*.allis

eanStandard De"iationearsons product*

moment correlationttestAnalysis of "ariance,ulti"ariate analysis of

"ariance, AN3A-actor analysis#egressionultiple correlation, R

Coefficient of3ariation,

(CV4 SD5 M)

f S C


16/50

ype of Statistica! ests and its Characteristicsype of Statistica! ests and its Characteristics

HypothesisHypothesis

estingesting

um2er ofum2er of

Samp!esSamp!es

MeasurementMeasurement

Sca!eSca!e

estest

HypothesesHypotheses

'2out fre7uency'2out fre7uency

Distri2utionDistri2ution

*ne*ne omina!omina! Chi-s7uareChi-s7uare

6o or more6o or more omina!omina! Chi-s7uareChi-s7uare


'2out'2outmeansmeans

*ne 9arge samp!e*ne 9arge samp!e +nterva!+nterva!

*r )atio*r )atio

@ est@ est

*ne 9sma!!*ne 9sma!!

samp!esamp!e

+nterva!+nterva!

*r )atio*r )atio

t estt est

6o 9arge samp!e6o 9arge samp!e +nterva!+nterva!

*r )atio*r )atio

@ est@ est

6o 9Sma!! samp!e6o 9Sma!! samp!e +nterva!+nterva!

*r )atio*r )atio

t estt est

hree or more9Sma!!hree or more9Sma!!

samp!esamp!e

+nterva!+nterva!

*r )atio*r )atio

'*4''*4'


'2out'2out

(roportions(roportions

*ne 9arge samp!e*ne 9arge samp!e +nterva!+nterva!

*r )atio*r )atio

@ est@ est

*ne 9sma!!*ne 9sma!!

samp!esamp!e

+nterva!+nterva!

*r )atio*r )atio

t estt est

6o 9arge samp!e6o 9arge samp!e +nterva!+nterva!

*r )atio*r )atio

@ est@ est

6o 9Sma!! samp!e6o 9Sma!! samp!e +nterva!+nterva!

*r )atio*r )atio

t estt est

4ariance4ariance 6o or more6o or moresamp!esamp!e

+nterva!+nterva!*r )atio*r )atio

'*4''*4'


17/50

Exa#p"e %r Tests % +yptheses cncernin, T- pp!"atin #eansExa#p"e %r Tests % +yptheses cncernin, T- pp!"atin #eans

Sa#p"e I. 11(' 12(' 12/' 112' 12)Sa#p"e I. 11(' 12(' 12/' 112' 12)

Sa#p"e II. 12(' 120' 1//' 1/0' 12Sa#p"e II. 12(' 120' 1//' 1/0' 12

+roup Statistics

3 224566 75782 0594/

3 209576 75737 05988

Class

Class +

Class B

Mark

& Mean !td5 Deviation

!td5 )rror

Mean

Independent Samples $est

5284 574( '0583/ 4 5603 '22576 (502( '025/24 '25440

'0583/ 45666 5603 '22576 (502( '025/24 '25440

)qual variances

assumed

)qual variances

not assumed

Mark

: !ig5

1evene;s #est for

)quality of > ""A.;;""A.;; B.B"B.B"

#.>#.> ;.;#>;.;#>C!ass 0C!ass 0 >> "#.B;"#.B; B.B>BB.B>B


18/50

C#parin, #!"tip"e pp!"atin #eansC#parin, #!"tip"e pp!"atin #eans

* Fr #re than t- pp!"atins' it is ass!#e that the pr3a3i"ityFr #re than t- pp!"atins' it is ass!#e that the pr3a3i"ity

istri3!tin 4 i5e5 +ist,ra# 6 % each pp!"atin is apprxi#ate"yistri3!tin 4 i5e5 +ist,ra# 6 % each pp!"atin is apprxi#ate"y

nr#a"5nr#a"5

*++

((. A"" the pp!"atin #eans are e7!a"s. A"" the pp!"atin #eans are e7!a"s

* ++11. At "east t-. At "east t-pp!"atin #eans are i%%erpp!"atin #eans are i%%er

* This test is ca""eThis test is ca""e Analysis f 3ariance (AN3A)Analysis f 3ariance (AN3A)

* Data %r# Unrestricte 4inepenent6 sa#p"es 4 One8-ay ANOVA6Data %r# Unrestricte 4inepenent6 sa#p"es 4 One8-ay ANOVA6

* Data %r# 9"c: ;estricte Sa#p"es 4T-8-ay ANOVA6Data %r# 9"c: ;estricte Sa#p"es 4T-8-ay ANOVA6

* O3


19/50

Exa#p"e %r One >ay ANOVAExa#p"e %r One >ay ANOVA

Sch" I . ?)' )?' /)' ?/' ?0Sch" I . ?)' )?' /)' ?/' ?0

Sch" II . )?' &)' &@' ))' )2Sch" II . )?' &)' &@' ))' )2

Sch" III . 0@' &)' @)' @' &@Sch" III . 0@' &)' @)' @' &@

,%*V,

Mark

02935066 0 26985766 2457(7 5666

8675(66 20 345478

09625766 2(

Between $rou"s

.ithin $rou"s

#otal

!um of

!quares df Mean !quare : !ig5

Mar-

Duncana

3 (3566

3 34576

3 8(576

!chool

!chool *

!chool **

!chool ***

& 2 0 /

!ubset for al"ha A 563

Means for grou"s in homogeneous subsets are dis"layed5

?ses armonic Mean !am"le !iBe A 356665a5


20/50

Nn8Para#etric TestsNn8Para#etric Tests

* In s#e sit!atins' the practica" ata #ay 3e nn8nr#a"In s#e sit!atins' the practica" ata #ay 3e nn8nr#a"anr it #ay nt 3e pssi3"e t esti#ate the para#eter4s6anr it #ay nt 3e pssi3"e t esti#ate the para#eter4s6% the ata% the ata

* The test -hich are !se %r s!ch sit!atins are ca""e nn8The test -hich are !se %r s!ch sit!atins are ca""e nn8

para#etric testspara#etric tests* Since these tests are 3ase n the ata -hich are %reeSince these tests are 3ase n the ata -hich are %ree

%r# istri3!tin an para#eter' these tests are :n-n as%r# istri3!tin an para#eter' these tests are :n-n asnn8para#etric4NP6 test r Distri3!tin Free testsnn8para#etric4NP6 test r Distri3!tin Free tests

* NP test can 3e !se e=en %r n#ina" ata 47!a"itati=eNP test can 3e !se e=en %r n#ina" ata 47!a"itati=e

ata "i:e ,reater r "ess' etc56 an rina" ata' "i:e ran:eata "i:e ,reater r "ess' etc56 an rina" ata' "i:e ran:eata5ata5

* NP test re7!ire "ess ca"c!"atin' 3eca!se there is n neeNP test re7!ire "ess ca"c!"atin' 3eca!se there is n neet c#p!te para#eters5t c#p!te para#eters5


21/50

List % Nn8Para#etric TestsList % Nn8Para#etric Tests

1515 One8sa#p"e testOne8sa#p"e test* One sa#p"e si,n testOne sa#p"e si,n test

* Chi8s7!are ne sa#p"e testChi8s7!are ne sa#p"e test

* B"#,r=8S#irn= testB"#,r=8S#irn= test

2525 T- re"ate sa#p"es testsT- re"ate sa#p"es tests* T- sa#p"es si,n testT- sa#p"es si,n test

* >i"cxn Matche8pairs si,ne ran: test>i"cxn Matche8pairs si,ne ran: test

/5/5 T- inepenent sa#p"es testT- inepenent sa#p"es test* Chi8S7!are test %r t- inepenent sa#p"esChi8S7!are test %r t- inepenent sa#p"es

* Mann8>hitney U testMann8>hitney U test

* B"#,r=8S#irn= t- sa#p"e testB"#,r=8S#irn= t- sa#p"e test


22/50

List % Nn8Para#etric TestsList % Nn8Para#etric Tests

?? B ;e"ate Sa#p"es testB ;e"ate Sa#p"es test* Frie#an T- -ay Ana"ysis % Variance 3y ;an:sFrie#an T- -ay Ana"ysis % Variance 3y ;an:s

* The Cehran testThe Cehran test

)5 B Inepenent sa#p"es)5 B Inepenent sa#p"es

* Chi8S7!are test %r : Inepenent sa#p"esChi8S7!are test %r : Inepenent sa#p"es

* The extensin % the Meian testThe extensin % the Meian test

* Br!s:a"8>a""is ne8-ay Ana"ysis % Variance 3y ;an:Br!s:a"8>a""is ne8-ay Ana"ysis % Variance 3y ;an:


23/50

Chi8s7!are test %r chec:in, inepenence % t-Chi8s7!are test %r chec:in, inepenence % t-

cate,ri$e atacate,ri$e ata

* Let !s cnsier t- %actrs -hich #ay r #ayLet !s cnsier t- %actrs -hich #ay r #aynt ha=e in%"!ence n the 3ser=e %re7!enciesnt ha=e in%"!ence n the 3ser=e %re7!encies%r#e -ith respect t c#3inatins % i%%erent%r#e -ith respect t c#3inatins % i%%erent"e=e"s % the t- %actrs"e=e"s % the t- %actrs

* ++((. Factr A an %actr 9 are inepenent. Factr A an %actr 9 are inepenent

* ++11.. Factr A an %actr 9 are nt inepenentFactr A an %actr 9 are nt inepenent

* O3


24/50

Chi8s7!are test %r ,ness % %itChi8s7!are test %r ,ness % %it

* T %it the ata t the nearest istri3!tin -hichT %it the ata t the nearest istri3!tin -hich

represents the ata #re #eanin,%!""y %r %!t!re ana"ysis5represents the ata #re #eanin,%!""y %r %!t!re ana"ysis5

S!ch %ittin, % ata t the nearest istri3!tin is neS!ch %ittin, % ata t the nearest istri3!tin is ne

!sin, the ,ness % %it test!sin, the ,ness % %it test

* ++((. The ,i=en ata %""- an ass!#e istri3!tin. The ,i=en ata %""- an ass!#e istri3!tin

* ++11.. The ,i=en ata nt %""- an ass!#e istri3!tinThe ,i=en ata nt %""- an ass!#e istri3!tin

*O3


25/50

B"#,r=8s#irn= testB"#,r=8s#irn= test* It is si#i"ar t the chi8s7!are test t ,ness % %it % aIt is si#i"ar t the chi8s7!are test t ,ness % %it % a

,i=en set % ata t an ass!#e istri3!tin,i=en set % ata t an ass!#e istri3!tin* This test is #re p-er%!" %r s#a"" sa#p"es -hereas the chi8This test is #re p-er%!" %r s#a"" sa#p"es -hereas the chi8

s7!are test is s!ite %r "ar,e sa#p"es7!are test is s!ite %r "ar,e sa#p"e

* ++((. The ,i=en ata %""- an ass!#e istri3!tin. The ,i=en ata %""- an ass!#e istri3!tin

++11.. The ,i=en ata nt %""- an ass!#e istri3!tinThe ,i=en ata nt %""- an ass!#e istri3!tin

* B8S test is an ne8tai"e test5 +ence i% the ca"c!"ate =a"!e %B8S test is an ne8tai"e test5 +ence i% the ca"c!"ate =a"!e %

D is #re than the theretica" =a"!e % D %r a ,i=enD is #re than the theretica" =a"!e % D %r a ,i=en

si,ni%icance "e=e"' then re


26/50

T- sa#p"es si,n testT- sa#p"es si,n test* T- sa#p"es si,n test is app"ie t a sit!atin' -here t-T- sa#p"es si,n test is app"ie t a sit!atin' -here t-

sa#p"es are ta:en %r# t- pp!"atins -hich ha=esa#p"es are ta:en %r# t- pp!"atins -hich ha=ecntin!!s sy##etrica" istri3!tins an :n-n t 3e nn8cntin!!s sy##etrica" istri3!tins an :n-n t 3e nn8

nr#a"nr#a"

* Mi%ie sa#p"e =a"!e' Mi%ie sa#p"e =a"!e' ii G H i% XG H i% Xii J Jii

G 8 i% XG 8 i% Xii K JK Jii

G ( i% XG ( i% Xii G JG Jii

* C"assi%ie int %!r cate,riesC"assi%ie int %!r cate,ries

11 One8tai"e t-8sa#p"e si,n tests -ith 3in#ia" istri3!tinOne8tai"e t-8sa#p"e si,n tests -ith 3in#ia" istri3!tin

22 T-8tai"e t-8sa#p"e si,n tests -ith 3in#ia" istri3!tinT-8tai"e t-8sa#p"e si,n tests -ith 3in#ia" istri3!tin

// One8tai"e t-8sa#p"e si,n tests -ith nr#a" istri3!tinOne8tai"e t-8sa#p"e si,n tests -ith nr#a" istri3!tin

?? T-8tai"e t-8sa#p"e si,n tests -ith nr#a" istri3!tinT-8tai"e t-8sa#p"e si,n tests -ith nr#a" istri3!tin


27/50

The >i"cxn Matche8pairs si,ne8ran:s testThe >i"cxn Matche8pairs si,ne8ran:s test

* The >i"cxn test is a #st !se%!" test %r 3eha=ira"The >i"cxn test is a #st !se%!" test %r 3eha=ira"

scientistscientist

* Let Let ii G the i%%erence scre %r any #atche pairG the i%%erence scre %r any #atche pair

* ;an: a"" the ;an: a"" the ii -ith!t re,ar t si,n-ith!t re,ar t si,n

* T G S!# % ran: -ith "ess %re7!ent si,nT G S!# % ran: -ith "ess %re7!ent si,n

* C#p!te C#p!te G T E4T6SD4T6G T E4T6SD4T6


28/50

Mann8>hitney U TestMann8>hitney U Test

* Mann8>hitney U test is an a"ternate t the t- sa#p"e t8testMann8>hitney U test is an a"ternate t the t- sa#p"e t8test

* This test is 3ase n the ran:s % the 3ser=atins % t-This test is 3ase n the ran:s % the 3ser=atins % t-sa#p"es p!t t,ethersa#p"es p!t t,ether

* A"ternate na#e %r this test isA"ternate na#e %r this test is #an2*Sum Test#an2*Sum Test

* Let ;Let ;11 G The s!# % the ran:s % the 3ser=atins % the %irstG The s!# % the ran:s % the 3ser=atins % the %irst

sa#p"esa#p"e* Let ;Let ;22 G The s!# % the ran:s % the 3ser=atins % the secnG The s!# % the ran:s % the 3ser=atins % the secn

sa#p"esa#p"e

* O3


29/50

Crre"atin an ;e,ressin Ana"ysisCrre"atin an ;e,ressin Ana"ysis

* The Chi8s7!are test #eas!res the assciatin 3et-een t- rThe Chi8s7!are test #eas!res the assciatin 3et-een t- r#re =aria3"es5This test is app"ica3"e n"y -hen ata is n#re =aria3"es5This test is app"ica3"e n"y -hen ata is n

n#ina" sca"e5n#ina" sca"e5

* Crre"atin an ;e,ressin ana"ysis is !se %r #eas!rin, theCrre"atin an ;e,ressin ana"ysis is !se %r #eas!rin, the

re"atinship 3et-een t- =aria3"es #eas!re n inter=a" rre"atinship 3et-een t- =aria3"es #eas!re n inter=a" rrati sca"e5rati sca"e5


30/50

Crre"atin Ana"ysisCrre"atin Ana"ysis* Crre"atin ana"ysis is a statistica" techni7!e !se t #eas!reCrre"atin ana"ysis is a statistica" techni7!e !se t #eas!re

the #a,nit!e % "inear re"atinship 3et-een t- =aria3"es5the #a,nit!e % "inear re"atinship 3et-een t- =aria3"es5* Crre"atin ana"ysis cannt 3e !se in is"atin t escri3e theCrre"atin ana"ysis cannt 3e !se in is"atin t escri3e the

re"atinship 3et-een =aria3"es5re"atinship 3et-een =aria3"es5

* It can 3e !se a"n, -ith re,ressin ana"ysis t eter#ine theIt can 3e !se a"n, -ith re,ressin ana"ysis t eter#ine thenat!re % the re"atinship 3et-een t- =aria3"es5nat!re % the re"atinship 3et-een t- =aria3"es5

* Th!s crre"atin ana"ysis can 3e !se %r %!rther ana"ysisTh!s crre"atin ana"ysis can 3e !se %r %!rther ana"ysis

* T- pr#inent types % crre"atin Ce%%icient areT- pr#inent types % crre"atin Ce%%icient are

* Pearsn Pr!ct M#ent crre"atin ce%%icientPearsn Pr!ct M#ent crre"atin ce%%icient

* Spear#ans ;an: crre"atin ce%%icientSpear#ans ;an: crre"atin ce%%icient

* Testin, the si,ni%icance % crre"atin ce%%icientTestin, the si,ni%icance % crre"atin ce%%icient

* Type IType I ++((.. G (G ( an +an +11.. ((

Type IIType II ++((.. G rG r an +an +11.. rr

Type III +Type III +((. r. r11G rG r22 an +an +11. r. r11rr22


31/50

Crre"atin Ana"ysisCrre"atin Ana"ysisExa#p"e.Exa#p"e.

Mar: in Mathe#atics. 01')0'@0'@1'0&')0Mar: in Mathe#atics. 01')0'@0'@1'0&')0

Mar:s in Statistics. @)'@1')1'@0'0?'&)Mar:s in Statistics. @)'@1')1'@0'0?'&)

.orrelations

2 5974

5 5660

7 75974 2

5660 5

7 7

Pearson Correlation

!ig5 =0'tailed>

&

Pearson Correlation

!ig5 =0'tailed>

&

M+#!

!#+#*!#*

C!

M+#!

!#+#*!#*

C!

Correlation is significant at the 6562 level =0'tailed>55


32/50

;e,ressin Ana"ysis;e,ressin Ana"ysis

* ;e,ressin ana"ysis is !se t preict the nat!re an;e,ressin ana"ysis is !se t preict the nat!re an

c"seness % re"atinships 3et-een t- r #re =aria3"esc"seness % re"atinships 3et-een t- r #re =aria3"es

* It e=a"!ate the ca!sa" e%%ect % ne =aria3"e n antherIt e=a"!ate the ca!sa" e%%ect % ne =aria3"e n anther

=aria3"e=aria3"e

* It !se t preict the =aria3i"ity in the epenent 4r criterin6It !se t preict the =aria3i"ity in the epenent 4r criterin6

=aria3"e 3ase n the in%r#atin a3!t ne r #re=aria3"e 3ase n the in%r#atin a3!t ne r #re

inepenent 4r preictr6 =aria3"es5inepenent 4r preictr6 =aria3"es5

* T- =aria3"es . Si#p"e r Linear ;e,ressin Ana"ysisT- =aria3"es . Si#p"e r Linear ;e,ressin Ana"ysis

* Mre than t- =aria3"es . M!"tip"e ;e,ressin Ana"ysisMre than t- =aria3"es . M!"tip"e ;e,ressin Ana"ysis


33/50

Linear ;e,ressin Ana"ysisLinear ;e,ressin Ana"ysis

* Linear re,ressin . J GLinear re,ressin . J G HH XX >here J . Depenent =aria3"e>here J . Depenent =aria3"e

X . Inepenent =aria3"eX . Inepenent =aria3"e

anan . T- cnstants are ca""e re,ressin ce%%icients . T- cnstants are ca""e re,ressin ce%%icients

. S"pe ce%%icient i5e5 the chan,e in the =a"!e % J -ith. S"pe ce%%icient i5e5 the chan,e in the =a"!e % J -ith the crrespnin, chan,e in ne !nit % Xthe crrespnin, chan,e in ne !nit % X

. J intercept -hen X G (. J intercept -hen X G (

* ;;22 .. The stren,th % assciatin i5e5 t -hat e,ree that theThe stren,th % assciatin i5e5 t -hat e,ree that the

=ariatin in J can 3e exp"aine 3y X5=ariatin in J can 3e exp"aine 3y X5

* ;;22G (51( then n"y 1( % the tta" =ariatin in J can 3eG (51( then n"y 1( % the tta" =ariatin in J can 3e

exp"aine 3y the =ariatin in X =aria3"esexp"aine 3y the =ariatin in X =aria3"es


34/50

Test % si,ni%icance % ;e,ressin E7!atiTest % si,ni%icance % ;e,ressin E7!atinn

* Linear re,ressin . J GLinear re,ressin . J G HH XX

* F test is !se t test the si,ni%icance % the "inear re"atinshipF test is !se t test the si,ni%icance % the "inear re"atinship

3et-een t- =aria3"es J an X3et-een t- =aria3"es J an X

* ++((.. G (G ( 4There is n4There is n "inear re"atinship 3et-een J an X6"inear re"atinship 3et-een J an X6

* ++11.. ( 4( 4There isThere is "inear re"atinship 3et-een J an X6"inear re"atinship 3et-een J an X6

* O3


35/50

Exa#p"e %r ;e,ressin Ana"ysisExa#p"e %r ;e,ressin Ana"ysis

* Sc&ool Climate 6 78, 9:, 88, :8, 8;, :, ?8, =:, ?7, =

M e t r i c ' # h e s c a l e s a r e

r a t i o o r in t e r v a l

C o n E o i n t

+ n a l y s i s

& o n m e t r i c ' # h e

s c a l e s a r e n o m i n a l

o r o r d i n a l

! e v e r a l D e " e n d e n t

< a r i a b l e s

C a n o n i c a l

+ n a l y s i s

M u l t i " l e i n d e " e n d e n t

a n d d e " e n d e n t

v a r i a b l e s

o w m a n y v a r i a b l e s

a r e d e " e n d e n t G

D e " e n d e n c e

M e t h o d s


39/50

M!"ti=ariate Ana"ysis. C"assi%icatin % Inepenence MethsM!"ti=ariate Ana"ysis. C"assi%icatin % Inepenence Meths

: a c t o r

+ n a l y s i s

C l u s t e r

+ n a l y s i s

M e t r i c

M u l t i d i m e n s i o n a l

! c a l i n g

M e t r i c ' # h e

s c a l e s a r e r a t i o

o r * n t e r v a l

& o n m e t r i c

M u l t i d i m e n s i o n

! c a l i n g

& o n m e t r i c ' # h e

s c a l e s a r e n o m i n a l

o r o r d i n a l

+ r e i n " u t s

M a t r i c G

* n d e " e n d e n c e

M e t h o d s


40/50

Discri#inant Ana"ysisDiscri#inant Ana"ysis

* Discri#inant ana"ysis ai#s at st!yin, the e%%ect % t- rDiscri#inant ana"ysis ai#s at st!yin, the e%%ect % t- r

#re#re predictor "ariablespredictor "ariables 4inepenent =aria3"es6 n certain4inepenent =aria3"es6 n certaine=a"!atine=a"!atin criterioncriterion

* The e=a"!atin criterin #ay 3e t- r #re ,r!psThe e=a"!atin criterin #ay 3e t- r #re ,r!ps

* T0o groupsT0o groupss!ch as , r 3a' "i:e r is"i:e' s!ccess%!" rs!ch as , r 3a' "i:e r is"i:e' s!ccess%!" r

!ns!ccess%!"' a3=e expecte "e=e" r 3e"- expecte "e=e"!ns!ccess%!"' a3=e expecte "e=e" r 3e"- expecte "e=e"* T&ree groupsT&ree groupss!ch as ,' nr#a" r prs!ch as ,' nr#a" r pr

* Chec: -hether the preictr =aria3"e iscri#inate a#n, theChec: -hether the preictr =aria3"e iscri#inate a#n, the

,r!ps,r!ps

* T ienti%y theT ienti%y the predictor "ariablepredictor "ariable -hich is #re i#prtant-hich is #re i#prtant-hen c#pare t ther preictr =aria3"e4s65-hen c#pare t ther preictr =aria3"e4s65

* S!ch ana"ysis is ca""eS!ch ana"ysis is ca""e discriminant analysisdiscriminant analysis


41/50

Discri#inant Ana"ysisDiscri#inant Ana"ysis

* Desi,nin, a iscri#inant %!nctin. J G aXDesi,nin, a iscri#inant %!nctin. J G aX11H 3XH 3X22

-here J is a "inear c#psite representin, the iscri#inant %!nctin' X-here J is a "inear c#psite representin, the iscri#inant %!nctin' X 11an Xan X22 are theare the predictor "ariablespredictor "ariables 4inepenent =aria3"es6 -hich are4inepenent =aria3"es6 -hich are

ha=in, e%%ect n the e=a"!atinha=in, e%%ect n the e=a"!atin criterioncriterion% the pr3"e# % interest5% the pr3"e# % interest5

* Finin, theFinin, thediscriminant ratio (K)discriminant ratio (K) an eter#inin, the =aria3"es -hichan eter#inin, the =aria3"es -hich

acc!nt %r inter,r!p i%%erence in ter#s % ,r!p #eansacc!nt %r inter,r!p i%%erence in ter#s % ,r!p #eans

* This rati is the #axi#!# pssi3"e rati 3et-een the =aria3i"ity 3et-eenThis rati is the #axi#!# pssi3"e rati 3et-een the =aria3i"ity 3et-een,r!ps an the =aria3i"ity -ithin ,r!ps,r!ps an the =aria3i"ity -ithin ,r!ps

* Finin, the critica" =a"!e -hich can 3e !se t inc"!e a ne- ata set 4i5e5Finin, the critica" =a"!e -hich can 3e !se t inc"!e a ne- ata set 4i5e5

ne- c#3inatin % instances %r the preictr =aria3"es6 int itsne- c#3inatin % instances %r the preictr =aria3"es6 int its

apprpriate ,r!papprpriate ,r!p

* Testin, +Testin, +((. The ,r!p #eans are e7!a" in i#prtance. The ,r!p #eans are e7!a" in i#prtance

++11.. The ,r!p #eans are nt e7!a" in i#prtanceThe ,r!p #eans are nt e7!a" in i#prtance

!sin, F test at a ,i=en si,ni%icance "e=e"!sin, F test at a ,i=en si,ni%icance "e=e"

A " iF A " i


42/50

Factr Ana"ysisFactr Ana"ysis

* Factr ana"ysis can 3e e%ine as a set % #eths in -hich the 3ser=a3"e rFactr ana"ysis can 3e e%ine as a set % #eths in -hich the 3ser=a3"e r#ani%est respnses % ini=i!a"s n a set % =aria3"es are represente as %!nctins#ani%est respnses % ini=i!a"s n a set % =aria3"es are represente as %!nctins

% a s#a"" n!#3er % "atent =aria3"es ca""e% a s#a"" n!#3er % "atent =aria3"es ca""e %actrs%actrs55* Factr ana"ysis he"ps the researcher tFactr ana"ysis he"ps the researcher t re!cere!ce the n!#3er % =aria3"es t 3ethe n!#3er % =aria3"es t 3e

ana"y$e' there3y #a:in, the ana"ysis easier5ana"y$e' there3y #a:in, the ana"ysis easier5

* Fr exa#p"e' Cnsier a #ar:et researcher at a creit car c#pany -h -ants tFr exa#p"e' Cnsier a #ar:et researcher at a creit car c#pany -h -ants te=a"!ate the creit car !sa,e an 3eha=i!r % c!st#ers' !sin, =ari!s =aria3"es5e=a"!ate the creit car !sa,e an 3eha=i!r % c!st#ers' !sin, =ari!s =aria3"es5The =aria3"es inc"!e a,e' ,ener' #arita" stat!s' inc#e "e=e"' e!catin'The =aria3"es inc"!e a,e' ,ener' #arita" stat!s' inc#e "e=e"' e!catin'

e#p"y#ent stat!s' creit histry an %a#i"y 3ac:,r!n5e#p"y#ent stat!s' creit histry an %a#i"y 3ac:,r!n5* Ana"ysis 3ase n a -ie ran,e % =aria3"es can 3e tei!s an ti#e cns!#in,5Ana"ysis 3ase n a -ie ran,e % =aria3"es can 3e tei!s an ti#e cns!#in,5

* Usin, Factr Ana"ysis' the researcher can re!ce the "ar,e n!#3er % =aria3"es intUsin, Factr Ana"ysis' the researcher can re!ce the "ar,e n!#3er % =aria3"es inta %e- i#ensins ca""e %actrs that s!##ari$e the a=ai"a3"e ata5a %e- i#ensins ca""e %actrs that s!##ari$e the a=ai"a3"e ata5

* Its ai#s at ,r!pin, the ri,ina" inp!t =aria3"es int %actrs -hich !ner"yin, theIts ai#s at ,r!pin, the ri,ina" inp!t =aria3"es int %actrs -hich !ner"yin, theinp!t =aria3"es5inp!t =aria3"es5

* Fr exa#p"e' a,e' ,ener' #arita" stat!s can 3e c#3ine !ner a %actr ca""eFr exa#p"e' a,e' ,ener' #arita" stat!s can 3e c#3ine !ner a %actr ca""ee#,raphic characteristicse#,raphic characteristics5 The inc#e "e=e"' e!catin' e#p"y#ent stat!s can5 The inc#e "e=e"' e!catin' e#p"y#ent stat!s can3e c#3ine !ner a %actr ca""e3e c#3ine !ner a %actr ca""e sci8ecn#ic stat!ssci8ecn#ic stat!s5 The creit car an5 The creit car an%a#i"y 3ac:,r!n can 3e c#3ine !ner %actr ca""e%a#i"y 3ac:,r!n can 3e c#3ine !ner %actr ca""e3ac:,r!n stat!s3ac:,r!n stat!s55

9 %i % F A " i9 %i % F A " i


43/50

9ene%its % Factr Ana"ysis9ene%its % Factr Ana"ysis

* T ienti%y the hien i#ensins r cnstr!ct -hichT ienti%y the hien i#ensins r cnstr!ct -hich

#ay nt 3e apparent %r# irect ana"ysis#ay nt 3e apparent %r# irect ana"ysis

* T ienti%y re"atinships 3et-een =aria3"esT ienti%y re"atinships 3et-een =aria3"es

* It he"ps in ata re!ctinIt he"ps in ata re!ctin

* It he"ps the researcher t c"!ster the pr!ct anIt he"ps the researcher t c"!ster the pr!ct anpp!"atin 3ein, ana"y$e5pp!"atin 3ein, ana"y$e5

T i " i F t A " iTer#in",y in Factr Ana"ysis


44/50

Ter#in",y in Factr Ana"ysisTer#in",y in Factr Ana"ysis

* FactrFactr.. A %actr is an !ner"yin, cnstr!ct r i#ensin thatA %actr is an !ner"yin, cnstr!ct r i#ensin thatrepresent a set % 3ser=e =aria3"es5 In the creit car c#panyrepresent a set % 3ser=e =aria3"es5 In the creit car c#pany

exa#p"e' the e#,raphic characteristics' sci ecn#ic stat!sexa#p"e' the e#,raphic characteristics' sci ecn#ic stat!san 3ac:,r!n stat!s represent a set % =aria3"es5an 3ac:,r!n stat!s represent a set % =aria3"es5

* Factr Lain,sFactr Lain,s..Factr "ain, he"p in interpretin, an "a3e"in,Factr "ain, he"p in interpretin, an "a3e"in,the %actrs5 It #eas!re h- c"se"y the =aria3"es in the %actr arethe %actrs5 It #eas!re h- c"se"y the =aria3"es in the %actr areassciate5 It is a"s ca""e %actr8=aria3"e crre"atin5 Factrassciate5 It is a"s ca""e %actr8=aria3"e crre"atin5 Factr

"ain,s are crre"atin ce%%icients 3et-een the =aria3"es an the"ain,s are crre"atin ce%%icients 3et-een the =aria3"es an the%actrs5%actrs5

* Ei,en Va"!esEi,en Va"!es.. Ei,en =a"!es #eas!re the =ariance in a"" theEi,en =a"!es #eas!re the =ariance in a"" the=aria3"es crrespnin, t the %actr5 Ei,en =a"!es are ca"c!"ate=aria3"es crrespnin, t the %actr5 Ei,en =a"!es are ca"c!"ate3y ain, the s7!ares % %actr "ain, % a"" the =aria3"es in the3y ain, the s7!ares % %actr "ain, % a"" the =aria3"es in the%actr5 It ai in exp"ainin, the i#prtance % the %actr -ith respect%actr5 It ai in exp"ainin, the i#prtance % the %actr -ith respectt =aria3"es5 Qenera""y %actrs -ith ei,en =a"!es #re than 15( aret =aria3"es5 Qenera""y %actrs -ith ei,en =a"!es #re than 15( arecnsiere sta3"e5 The %actrs that ha=e "- ei,en =a"!es 4K15(6cnsiere sta3"e5 The %actrs that ha=e "- ei,en =a"!es 4K15(6#ay nt exp"ain the =ariance in the =aria3"es re"ate t that %actr5#ay nt exp"ain the =ariance in the =aria3"es re"ate t that %actr5



45/50


* C##!na"ities.C##!na"ities. C##!na"ities' ente 3y hC##!na"ities' ente 3y h22' #eas!re the' #eas!re the

percenta,e % =ariance in each =aria3"e exp"aine 3y thepercenta,e % =ariance in each =aria3"e exp"aine 3y the

%actrs extracte5 It ran,es %r# ( t 15 A hi,h c##!na"ity%actrs extracte5 It ran,es %r# ( t 15 A hi,h c##!na"ity=a"!e inicates that the #axi#!# a#!nt % the =ariance in=a"!e inicates that the #axi#!# a#!nt % the =ariance in

the =aria3"e is exp"aine 3y the %actrs extracte %r# thethe =aria3"e is exp"aine 3y the %actrs extracte %r# the

%actr ana"ysis5%actr ana"ysis5

* Tta" Variance exp"aineTta" Variance exp"aine..The tta" =ariance exp"aine is theThe tta" =ariance exp"aine is thepercenta,e % tta" =ariance % the =aria3"es exp"aine5 This ispercenta,e % tta" =ariance % the =aria3"es exp"aine5 This is

ca"c!"atin, 3y ain, a"" the c##!na"ity =a"!es % eachca"c!"atin, 3y ain, a"" the c##!na"ity =a"!es % each

=aria3"e an i=iin, it 3y the n!#3er % =aria3"es5=aria3"e an i=iin, it 3y the n!#3er % =aria3"es5

* Factr Variance exp"aine.Factr Variance exp"aine. The %actr =ariance exp"aine isThe %actr =ariance exp"aine isthe percenta,e % tta" =ariance % the =aria3"es exp"aine 3ythe percenta,e % tta" =ariance % the =aria3"es exp"aine 3y

the %actrs5 This is ca"c!"atin, 3y ain, the s7!are %actrthe %actrs5 This is ca"c!"atin, 3y ain, the s7!are %actr

"ain,s % a"" the =aria3"es an i=iin, it 3y the n!#3er %"ain,s % a"" the =aria3"es an i=iin, it 3y the n!#3er %

=aria3"es5=aria3"es5

P % "" % F t A " iP % "" % F t A " i


46/50

Prce!re %""-e %r Factr Ana"ysisPrce!re %""-e %r Factr Ana"ysis

*De%ine the pr3"e#De%ine the pr3"e#

* Cnstr!ct the crre"atin #atrix that #eas!res theCnstr!ct the crre"atin #atrix that #eas!res the

re"atinship 3et-een the %actrs an the =aria3"es5re"atinship 3et-een the %actrs an the =aria3"es5

* Se"ect an apprpriate %actr ana"ysis #ethSe"ect an apprpriate %actr ana"ysis #eth

* Deter#ine the n!#3er % %actrsDeter#ine the n!#3er % %actrs

* ;tatin % %actrs;tatin % %actrs

* Interpret the %actrsInterpret the %actrs

* Deter#ine the %actr scresDeter#ine the %actr scres

C" t A " iC" t A " i


47/50

C"!ster Ana"ysisC"!ster Ana"ysis

*C"!ster ana"ysis can 3e e%ine as a set %C"!ster ana"ysis can 3e e%ine as a set %techni7!es !se t c"assi%y the 3


48/50

Prce!re in C"!ster Ana"ysisPrce!re in C"!ster Ana"ysis

1515 De%inin, the pr3"e#De%inin, the pr3"e#.. First e%ine the pr3"e# an e !pn the =aria3"esFirst e%ine the pr3"e# an e !pn the =aria3"es

3ase n -hich the 3


49/50

Prce!re in C"!ster Ana"ysisPrce!re in C"!ster Ana"ysis

+ierarchica" c"!sterin, Apprach+ierarchica" c"!sterin, Apprach cnsists % either a tp8-ncnsists % either a tp8-n

apprach r a 3tt#8!p apprach5 Pr#inent hierarchica" c"!sterin,apprach r a 3tt#8!p apprach5 Pr#inent hierarchica" c"!sterin,

#eths are. Sin,"e "in:a,e' C#p"ete "in:a,e' A=era,e "in:a,e'#eths are. Sin,"e "in:a,e' C#p"ete "in:a,e' A=era,e "in:a,e'>ars #eth an Centri #eth5>ars #eth an Centri #eth5

Nn8+ierarchica" c"!sterin,Nn8+ierarchica" c"!sterin, Apprach. A c"!ster center is %irst eter#ineApprach. A c"!ster center is %irst eter#ine

an a"" the 3


50/50

m.kanmani Appro Statistics

Documents

Transcript of m.kanmani Appro Statistics