Chi-Square Presentation - Nikki

8/17/2019 Chi-Square Presentation - Nikki

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Tutorial: Chi-Square Tutorial: Chi-Square

DistributionDistributionPresented by: Nikki NatividadCourse: BIOL 5!" - Biostatisti#s


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Pur$osePur$ose

To %easure dis#ontinuous #ate&ori#al'binneddata in (hi#h a nu%ber o) sub*e#ts )all into#ate&ories

+e (ant to #o%$are our observed data to

(hat (e e,$e#t to see Due to #han#e. Dueto asso#iation.

+hen #an (e use the Chi-Square Test.

◦ Testin& out#o%e o) /endelian Crosses0 Testin&

Inde$enden#e 1 Is one )a#tor asso#iated (ithanother.0 Testin& a $o$ulation )or e,$e#ted$ro$ortions


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2ssu%$tions:2ssu%$tions:

" or %ore #ate&oriesInde$endent observations

2 sa%$le si3e o) at least "

4ando% sa%$lin&2ll observations %ust be used

or the test to be a##urate0 the

e,$e#ted )requen#y should be at least5


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Condu#tin& Chi-SquareCondu#tin& Chi-Square2nalysis2nalysis"6 /ake a hy$othesis based on your basi# biolo&i#al

question

76 Deter%ine the e,$e#ted )requen#ies

86 Create a table (ith observed )requen#ies0 e,$e#ted

)requen#ies0 and #hi-square values usin& the)or%ula:

9O-67

;6 ind the de&rees o) )reedo%: 9#-"69r-"6

56 ind the #hi-square statisti# in the Chi-SquareDistribution table


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,a%$le ": Testin& )or,a%$le ": Testin& )orPro$ortionsPro$ortions

LeafCutterAnts

CarpenterAnts

BlackAnts

Total

Observed 75 "! ">


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?7@5 @5AA"


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Chi-square statisti#: χ2 = 5.991 Our #al#ulatedvalue: χ2 = 1.90

I) #hi-square statisti# = your #al#ulated value0 then you donot reject your null hy$othesis There is a si&niE#ant diFeren#e

that is not due to #han#e

5AA" = "A ∴ +e do not reject our null hy$othesis

LeafCutterAnts

CarpenterAnts

BlackAnts

Total

Observed 75 "! ">


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S2S: ,a%$le "S2S: ,a%$le "

In#luded to )or%at the table

DeEne your data

Indi#ate (hatyour (ant in

your out$ut


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S2S: ,a%$le "S2S: ,a%$le "


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S2S: +hat does the $-valueS2S: +hat does the $-value%ean.%ean.

GThe e,a#t p-value )or a nondire#tional test isthe su% o) $robabilities )or the table havin& atest statisti# &reater than or equal to the value

o) the observed test statisti#

High p-value: i&h $robability that test statisti#= observed test statisti# Do not reect null

hy$othesis

Low p-value: Lo( $robability that test statisti#= observed test statisti# !eect null

hy$othesis


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S2S: ,a%$le "S2S: ,a%$le "

i&h $robability that

Chi-Square statisti#= our #al#ulated #hi-square statisti#

+e do not reject ournull hy$othesis


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S2S: ,a%$le "S2S: ,a%$le "


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,a%$le 7: Testin&,a%$le 7: Testin&

2sso#iation2sso#iation#

#ell#hi7 @ dis$lays ho( %u#h ea#h#ell #ontributes to the overall #hi-squared value

no #ol @ do not dis$lay totals o)#olu%n

no ro( @ do not dis$lay totals o)

ro(s

#hi sq @ dis$lay #hi square statisti#s

HO: Jender and eye #olourare not asso#iated (ith ea#hotherHA: Jender and eye #olour are

asso#iated (ith ea#h other


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,a%$le 7: /ore S2S,a%$le 7: /ore S2S

,a%$les,a%$les


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,a%$les,a%$les

97-"698-"6 @ "7@ 7

i&h $robability that

Chi-Square statisti# = our#al#ulated #hi-squarestatisti# 9>!75K6

+e do not reject our nullhy$othesis


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,a%$les,a%$les

I) there (as anasso#iation0 #an

#he#k (hi#hintera#tions

des#ribeasso#iation bylookin& at ho(%u#h ea#h #ell

#ontributes to theoverall Chi-square

value


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Li%itationsLi%itations

No #ate&ories should be less than "No %ore than "'5 o) the e,$e#ted #ate&ories

should be less than 5

◦ To #orre#t )or this0 #an #olle#t lar&er sa%$les or#o%bine your data )or the s%aller e,$e#ted#ate&ories until their #o%bined value is 5 or %ore

ates Corre#tion

◦ +hen there is only " de&ree o) )reedo%0 re&ular#hi-test should not be used

◦ 2$$ly the ates #orre#tion by subtra#tin& 5)ro% the absolute value o) ea#h #al#ulated O-ter%0 then #ontinue as usual (ith the ne(#orre#ted values


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+hat do these %ean.+hat do these %ean.


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Likelihood 4atio ChiLikelihood 4atio Chi

SquareSquare


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Continuity-2d*usted Chi-Continuity-2d*usted Chi-Square TestSquare Test


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/antel-aens3el Chi-/antel-aens3el Chi-

Square TestSquare TestM/ @ 9n-"6r7

r7 is the Pearson #orrelation #oe#ient 9(hi#h

also %easures the linear asso#iation bet(een ro(and #olu%n6

◦ htt$:''su$$ortsas#o%'do#u%entation'#dl'en'$ro#stat'


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Phi Coe#ientPhi Coe#ient


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Conti&en#y Coe#ientConti&en#y Coe#ient


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Cra%erQs RCra%erQs R


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ates 7 , 7 Contin&en#y ates 7 , 7 Contin&en#y

Tables TablesHO: eart Disease is not asso#iated (ith #holesterol levelsHA: eart Disease is %ore likely in $atients (ith a hi&h

#holesterol diet

Cal#ulate de&rees o) )reedo%: 9#-"69r-"6 @ "" @ 1

+e need to use the 2TS CO44CTION

H"#$C$olester

ol

Lo%C$olesterol

Total

eart Disease "5 > 22

,$e#ted "77 "75

TOTAL 2' 1( )0

C$"*+,uareTotal

2.2&


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#holesterol diet H"#$C$olester

ol

Lo%C$olesterol

Total

eart Disease "5 > 22,$e#ted "7


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?7@5 @8!;"


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#holesterol diet

8!;" = ";7 ∴ +e do not reject our null hy$othesis

H"#$C$olester

ol

Lo%C$olesterol

Total

eart Disease "5 > 22,$e#ted "7 8>


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isherQs ,a#t TestisherQs ,a#t Test

Le)t: Use (hen the alternative to inde$enden#e isne&ative asso#iation bet(een the variables Theseobservations tend to lie in lo(er le)t and u$$erri&ht #ells o) the table S%all $-value @ Likelyne&ative asso#iation

4i&ht: Use this one-sided test (hen the alternativeto inde$enden#e is $ositive asso#iation bet(eenthe variables These observations tend to lie inu$$er le)t and lo(er ri&ht #ells or the table S%all

$-value @ Likely $ositive asso#iation

T(o-Tail: Use this (hen there is no $rioralternative


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Tables Tables


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Tables Tables


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HO: eart Disease is not

asso#iated (ith#holesterol levels

HA: eart Disease is

%ore likely in $atients(ith a hi&h #holesterol

diet


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Con#lusionCon#lusion

The Chi-square test is i%$ortant in testin&the asso#iation bet(een variables and'or#he#kin& i) oneQs e,$e#ted $ro$ortions %eetthe reality o) oneQs e,$eri%ent

There are %ulti$le #hi-square tests0 ea#h#atered to a s$e#iE# sa%$le si3e0 de&rees o))reedo%0 and nu%ber o) #ate&ories

+e #an use S2S to #ondu#t Chi-square testson our data by utili3in& the #o%%and procfreq


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4e)eren#es4e)eren#es

Chi-Square Test Des#ri$tions:http://www.enviroliteracy.org/pdf/materials/121.pdf

http://12!.12".!2.22/#iol12/$tatistics/%ppendi& '2('2'2)he'2*hi-$quare'2)+st.pdf

O3de%ir T and yduran 75 Co%$arison o) #hi-square and likelihood ratio #hi-square tests: $o(er o)test Vournal o) 2$$lied S#ien#es 4esear#h "976:7;7-7;;

S2S Su$$ort (ebsite: http://www.sas.com/inde&.html

,+ procedure0

ouTube Chi-square S2S Tutorial 9user: m#ate16:http://www.youtu#e.com/watchv%*#34)q56

Chi-Square Presentation - Nikki

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