BRM+Lecture+9+25-09-2014

7/21/2019 BRM+Lecture+9+25-09-2014

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BUSINESS RESEARCH METHODS

MBA – FALL 2014

7/21/2019 BRM+Lecture+9+25-09-2014


Agenda

Inferentia Ana!"i"

◦ Uni#ariate Inferentia Ana!"i"

◦ Bi#ariate Inferentia Ana!"i"

◦ H!$%t&e"i" te"ting◦ T!$e" %f Inferentia te"t"

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Inferentia Ana!"i"

Inferentia ana!"i" i" '"ed t%generai(e t&e re"'t" %)tainedfr%* a rand%* "a*$e )a+, t%

t&e $%$'ati%n fr%* -&i+& t&e"a*$e -a" dra-n.

T&i" ana!"i" i" re/'ired -&en A "a*$e i" dra-n )! rand%* $r%+ed're

T&e re"$%n"e rate i" #er! &ig&

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Inferentia Stati"ti+"

Inferentia "tati"ti+" are t&e *at&e*ati+ate+&ni/'e" f%r '"ing inf%r*ati%n fr%*"a*$e" t% *a,e +%n+'"i%n" a)%'t t&e$%$'ati%n $r%)a)ii"ti+ "tate*ent" a)%'t

$%$'ati%n.

Mea"'re*ent fr%* a "a*$e are +aed"tati"ti+".

Mea"'re*ent" fr%* a $%$'ati%n are +aed$ara*eter.

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Bi#ariate InferentiaAna!"i"Bi#ariate inferentia ana!"i" – i" +%n+erned -it& t&e

reati%n"&i$" )et-een t-% #aria)e" in t&e "a*$e3 t&at+%'d )e e$e+ted t% ei"t in t&e $%$'ati%n fr%* -&i+& it i"dra-n.

A "%+ia "+ien+e re"ear+&er intend" t% 5nd %'t t&ereati%n"&i$ )et-een t-% #aria)e" *%ti#ati%n and a+ade*i+$erf%r*an+e a*%ng A"ian "t'dent" at t&e grad'ate e#e.

T&e "tati"ti+a *et&%d '"ed "&%-ed t&at t&e reati%n"&i$)et-een *%ti#ati%n and a+ade*i+ $erf%r*an+e i" %f

*agnit'de 6 0.78

A inferentia "tati"ti+" gi#e '" *at&e*ati+a an"-er" )'tt&at ead" t% %ne )a"i+ /'e"ti%n and t&at i" 99..

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Inter$reting -it&C%n5den+e

What is the probability that the result isreal, versus the probability that it is just afuke?

S% -&at i" t&e $r%)a)iit! t&at t&e re"'t

%f t&e re"ear+& "t'd! reati%n"&i$ %f*%ti#ati%n and a+ade*i+ $erf%r*an+e-a" d'e t% rand%* +&an+e3 n%t d'e t%an! "!"te*ati+ re"ear+& e:e+t;

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Inter$reting -it&C%n5den+e T&e inferentia "tati"ti+" $r%#ide '" -it&

$r%)a)iit! %f getting re"'t" i,e t&e"e ift&e %n! fa+t%r at $a! i" rand%* +&an+e.

T&i" $r%)a)iit! $r%#ided )! inferentia"tati"ti+" i" ,n%-n a" Stati"ti+aSigni5+an+e %r Stati"ti+a Reia)iit!

den%ted )! etter p.

How the p-value is interpreted?

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Inter$reting -it&C%n5den+e<&en t&e p=#a'e i" "*a en%'g&3 t&e re"'t

i" +%n"idered t% )e "igni5+ant %r reia)e. Ift&i" #a'e i" t%% arge t&en t&e re"ear+&er -ide+ide t&at t&e re"'t i" >'"t a ?',e.

In t&e $re#i%'" ea*$e t&e reati%n"&i$)et-een *%ti#ati%n and a+ade*i+$erf%r*an+e &a" a *agnit'de %f 0.78 and

t&e $r%)a)iit! t&at t&e %)"er#ed reati%n"&i$i" d'e t% rand%* +&an+e i" 0.02@.

How these statistics will be interpreted?

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Inter$reting -it&C%n5den+e

T&e re"ear+&er need" t% de+ide &%-"*a i" en%'g&;

◦ <&at i" t&e e#e %f $r%)a)iit! t&at t&ere"'t i" a ?',e – re"ear+&er i" -iing t%t%erate;

◦ T&i" +'t%: i" +aed Signicance level.

◦ In )e&a#i%ra "+ien+e" t&e "igni5+an+e e#ei" genera! "et at 0.0.

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Inter$reting -it&C%n5den+eIf t&e $r%)a)iit! %f +%in+iden+e

p-#a'e i" e"" t&an 0.0 t&ere"'t i" reia)e and if it i" e""

t&an 0.01 t&en t&e re"'t i" &ig&!reia)e.

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H!$%t&e"i" Te"ting

Re"ear+& i" de"igned t% an"-er a "$e+i5+/'e"ti%n.

S+ien+e *a>%r" "+%re &ig&er %n te"t" %f

inteigen+e t&an "t'dent" in t&e genera$%$'ati%n.

T&e $r%+e"" %f deter*ining -&et&er t&i""tate*ent i" "'$$%rted )! t&e re"'t" %ft&e re"ear+& $r%>e+t i" referred t% a"

&!$%t&e"i" te"ting

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What is a hypothesis?

A "tate*ent3 +ai* %r a""erti%n a)%'t %ne %r*%re $%$'ati%n".

e.g.

T&e *ean -eig&t %f a +an %f )ean" i" 420g

0 %f $e%$e ta,e %'t &%ida! in"'ran+e

T% te"t t&e"e &!$%t&e"e" -e "et '$ a est o!hypothesis

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T!$e" %f H!$%t&e"i"

"lternate Hypothesis Hypothesis is a state#ent that e$presses

relationship or di%erences a#ongvariables.

It i" a "tate*ent t&at +%'d )e a++e$ted%r re>e+ted.

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Aternate &!$%t&e"i" +an )e

Dire+ti%na &!$%t&e"i" %r

N%n=dire+ti%na &!$%t&e"i"

Dire+ti%na H!$%t&e"i" – $redi+t" t&edire+ti%n %f t&e di:eren+e %r reati%n"&i$)et-een t-% gr%'$" %r t-% #aria)e" %r

*%re.

N%n=dire+ti%na H!$%t&e"i" – d% n%t$redi+t t&e dire+ti%n %f t&e reati%n"&i$.

T!$e" %f H!$%t&e"i"

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Ste$ r%+ed're f%r H!$%t&e"i" Te"ting

Sate t&e n' HO and aternate &!$%t&e"i" H1

See+t t&e e#e %f "ignifi+an+e .

See+t t&e a$$r%$riate "tati"ti+a te"t.

C%*$'te t&e te"t "tati"ti+" %)tained#a'e".

Inter$ret t&e te"t '"ing "igni5+an+e e#eand "tati"ti+a "igni5+an+e

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H!$%t&e"i" Te"ting

Statehypotheses

Setsignificance

level α

Collect

data

Perform

Calculations

Draw a conclusion

Make

statistical

decision

Do ot

!e"ect #$

!e"ect #$

Conclude #$

may %e true

Conclude#a is true

&'

('

)'

*'

Set uptest

Perform test

+dentify ,estStatistic

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H%- t% "ee+t Inferentia Te"t"

T&ere are *an! Stati"ti+a Te"t" a#aia)et% &e$ a re"ear+&er de+ide if di:eren+e"-e 5nd are rea %r +&an+e.

T&e i*$%rtant fa+t%r" t&at deter*ine t&e+&%i+e %f a te"t are

◦ T&e t!$e %f data n%*ina3 %rdina3 inter#a %r

rati%.

◦ T&e "a*$e "i(e.

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H%- t% "ee+t Signi5+an+e Te"t"

◦ T&e n'*)er %f "a*$e" fr%* -&i+&inferen+e" are )eing *ade %ne3 t-%

%r , "a*$e" e.g. +&idren readinge#e" in Ne- Geaand3 A'"traia andEngand – @ "a*$e".

◦ T&e a*%'nt %f inf%r*ati%n -e &a#ea)%'t $%$'ati%n *ean and"tandard de#iati%n.

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H%- t% "ee+t Signi5+an+e Te"t"

◦ <&et&er -e &a#e inde$endent %r de$endent"a*$e". A de$endent "a*$e i" %ne -&ere*e*)er" %f t&e "a*$e are "%*e&%- reated t%

%t&er *e*)er".

E.g. -e -ant t% ,n%- t&e a*%'nt %f T a +&id-at+&e" i" in?'en+ed )! t&e a*%'nt %f T t&eir$arent" -at+&. <e *a! &a#e t-% "a*$e" a

gr%'$ %f +&idren and a gr%'$ %f $arent" – ea+&+&id i" +%nne+ted t% a $arent in t&e %t&ergr%'$3 "% )eing a *e*)er %f t&e "a*$ede$end" %n &a#ing a reati#e in t&e %t&er gr%'$.

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C%*$aring Mean" – SingeSa*$e

Re"ear+&er +%*$are" t&e $erf%r*an+e %ft&e gr%'$ "a*$e t% t&e $erf%r*an+e %ft&e $%$'ati%n a""'*ing $%$'ati%n dataare a#aia)e f%r a +ertain #aria)e.

E.g. +%*$aring I "+%re" %f +&idren -&%attend after="+&%% $r%gra*" "a*$e t%t&e I "+%re" in t&e genera $%$'ati%n. S%

&!$%t&e"i" te"ted i" -&et&er +&idren inafter="+&%% $r%gra* $erf%r* di:erent!t&an t&e +&idren in genera $%$'ati%n.

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G = te"t

G te"t i" a te"t %f t&e n'&!$%t&e"i" f%r a "inge "a*$e-&en t&e $%$'ati%n "tandard

de#iati%n i" ,n%-n and "a*$e"i(e i" greater t&an @0.

n

X z

/ σ

µ −

=

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G = te"t

G= te"t i" '"ed -&en t&e f%%-inga""'*$ti%n" are &ed f%r t&e"a*$e data.

Sa*$e "i(e i" greater t&an @0 Sa*$e i" n%r*a! di"tri)'ted

Data i" inter#a %r rati%

%$'ati%n $ara*eter" are ,n%-n

N%t a$$r%$riate f%r "*a "a*$e"n J @0.

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-.ample

/ food manufacturer processes and cans %aked%eans' ,he net weight of a standard can of %eansis supposed to %e *($g %ut a random sample of0$ cans gave an average weight of *&0g with a

standard deviation of )$g' +s there any evidencethat the true mean weight is not *($g? 12se a03 significance level4

#ow will you interpret this statistic?

&'&56

*'(*)

*($*&0

7

−=

−

=

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T te"t

T te"t i" a"% a "tati"ti+a te"t %f t&en' &!$%t&e"i".

T te"t i" '"ed f%r "*a gr%'$"nJ@0 and -&en $%$'ati%n"tandard de#iati%n i" n%t ,n%-.

X s

X t

µ −

=

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T = te"t

n

s s

X =

X s I" t&e "tandard err%r %f t&e "a*$ing

di"tri)'ti%n

s i" t&e "tandard de#iati%n f%r $%$'ati%n)a"ed %n "a*$e data.

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Ea*$e

A t%*at% gr%-er &a" de#e%$ed a ne- #ariet! %ft%*at%. T&e #ariet! i" "'$$%"ed t% gi#e g%%d +r%$"-it&%'t t&e need f%r a green&%'"e. One %f t&e"'$$%"ed attri)'te" %f t&i" t%*at% i" t&at a#erage!ied $er $ant i" 4 ,g %f fr'it. A gardening *aga(ine

de+ide" t% te"t t&i" +ai* and gr%-" 8 $ant" in+%ntr%ed +%nditi%n". T&e !ied f%r ea+& $ant i"+aref'! re+%rded and i" a" f%%-"

Ca+'ate t #a'e.

Plant 1 2 3 4 5 6 7 8

Kied @. 4.2 @.@ 2. 4.8 2.7 4.2 4.

74.3= x

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#ypothesis tests involving two means

We can have8

• ,wo large independent samples 9 : test

• ,wo small independent samples 9 ,; test

• Paired samples 9 , ; test

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<&at te"t t% '"e;

Means ,wo

sam

ples

Single

sample

+ndependent

sample

s

Paired

sam

ples

<ar

gesa

mpl

e

Sm

allsa

mpl

e

<ar

gesa

mpl

e

Sm

allsamp

le

Pai

red;

,wosa

t;

test

:;

test

,wo

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C%*$aring M%re T&an 2 Mean"

Ana!"i" %f #arian+e ANOA te"tt&e "igni5+an+e %f t&edi:eren+e" )et-een *%re t&an

t-% *ean".

T&at i" t&e di:eren+e )et-een

t&e *ean" %f an %'t+%*e#aria)e f%r di:erent +ateg%rie"%f t&e $redi+t%r #aria)e.

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Ana!"i" %f #arian+e i" aninferentia "tati"ti+a te"t f%r+%*$aring t&e *ean" %f *%re

t&an t-% gr%'$" +%'d )e '"edf%r t-% gr%'$" a"%.

One=-a! ANOA +%*$are" t&e*ean" %f gr%'$" '"ing a "ingefa+t%r )rand" %f +%:ee3 t!$e" %f

internet +%nne+ti%n".

C%*$aring Mean" = ANOA

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Well-being

score

Women Well-being

score

Men

A

4 B 4 C

@ DE @ F

2 H 2 I

1 F%r Aindi#id'a"

1

Mean @.40 @.00 Mean 2.0

SS .20 12.00 SS .20

arian+e 1.@0 1.@@ arian+e 1.@0

SD 1.14 1.1 SD 1.14

Ea*$e = ANOA

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Sum of Squares df MeanSquare

<e=)eing

Bet-eenr%'$"

1.0n-=P2Qn*=P2

1

,=1

1.0SSdf

1.2@MSBMS-

<it&inr%'$"

10.40

SS- Q SS*

8

n=,

1.@0SSdf

T%ta 12.00 Sig .2

Ea*$e – ANOA S'**ar!ta)e

BRM+Lecture+9+25-09-2014

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