Chi Square Tools in SPSS - Word

8/12/2019 Chi Square Tools in SPSS - Word

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SPSS: Chi Squared Tests

So, lets say you count some (1851) plain M Ms, and heres !hatyou "ind# $lso, notice that the in"ormation "rom the M M%MarsCorp# is that &' o" plain M Ms are ro!n, *' each yello!and red, and 1' each o" lue, oran+e, and +reen#

n -.cel, it is not too hard to type in the "ormulas "or the Chi/Squared tests, ut you can also do it in SPSS#

0irst, !e need to enter our data into SPSS# otice that la eledthe columns, and ar itrarily assi+ned num ers to the colors (could2e used any num ers, ut +oin+ in order ma3es the mostsense)# also typed in the 2alue la els on the 2aria le 2ie! screen(so, 14 ro!n, *4yello!, etc# on any printouts)#

o!e2er, SPSS typically thin3s o" each ro! as an indi2idual#There"ore, i" !e ran our analysis no!, it !ould thin3 !e had 6M Ms, not 1851# To run our test the 7normal !ay, !e !ould

need to enter 1851 ro!s o" data9 To +et around this, !e use acommand called ei+ht Cases#

ei+ht CasesThis "eature is a !ay o" tellin+ SPSS to pretend that a sin+le ro! o" data is, in "act, a !hole unch o" ro!s# n our "irst ro!, !e !ant to tell SPSS that !e ha2e 51; ro!n M Ms# So, loo3 "or the menuitem:


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Chi/Squared Test o" @oodness o" 0itSo, our ull ypothesis !ill e that the pro a ilities +i2en to us y the corporation are correct:

' : Plain M Ms are &' ro!n, *' each yello! and red, and 1' each lue, oran+e, and +reen#1: Plain M Ms ha2e a di""erent distri ution than that#

This is not a 2ery speci"ic ypothesis# n particular, notice that i" you reAect the null hypothesis, youha2e no idea !hat distri ution you do ha2e (e.cept that it isnt the one listed in ' )#

o!, you clic3 on $nalyBe: on/Parametric: Chi/Square

o!, your test 2aria le is color# e sure to DT use Count (that !ould e sayin+ that you had 51;M MS o" type 51; E Dops)# Then, you need to enter in your e.pect 2alues# This is actually easier than -.cel, ecause you only need the pro a ilities, not the computed e.pected 2alues# So, clic3 onthe radio utton "or -.pected =alues: =alues# Then, enter in your si. relati2e pro a ilities "rom thenull hypothesis, clic3in+ on $dd a"ter you type each one# hen "inished it should loo3 li3e this:

Color is our Test =aria le

These correspond toour ' pro a ilities#?ou can lea2e out thedecimal, or include it#

Clic3 DF, and you +et the "ollo!in+ output:COLOR

Test Statistics

Chi-Square adf

Asy mp. Sig.

COLOR 8.063 5 .153

browny ellowredblueorangegreenTotal

a. 0 cells .0!" ha# e e$pec%ed f reque&cies less %ha& 5. 'he mi&imum e$pec%ed cell f reque&cy is 185.1.

Observ ed N 519 364 363 !! 1 193 1"51

#$%ected N 555&3 3'!& 3'!& 1"5&1 1"5&1 1"5&1

Residual (36&3 (6& ('& 14&9 6&9 '&9

Since the p/2alue is not less than #'5, !e "ail to reAect# Dur M Ms do "ollo! the distri ution !especi"ied# otice that it +i2es the sum, the de+rees o" "reedom, and it also has a little "ootnote a outthe assumptions you made#

Pa+e * o" >


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Crossta s and the Chi/Squared Test o" ndependenceThe other Chi/squared test deals !ith t!o cate+orical 2aria les# The hypotheses are:

' : ometo!n and @ender are independent#1: ometo!n and @ender are related#

otice these are also not 2ery speci"ic hypotheses

Gets say !e ha2e the "ollo!in+ data, detailin+ the +ender and hometo!n o" a +roup o" students: Dther StG FC Hr an Iural Sum M*5*&111>J& 0 >1*'186 85 Sum66>&*;*'158

To enter it into SPSS, you ha2e to really s!itch it around#t should loo3 li3e this# ?ou can see that, rather thanloo3in+ li3e a t!o/!ay ta le, it +i2es a 2aria le descriptiono" each cell# $+ain, you mi+ht !ant to +o into the 2aria le

2ie!, so you can la el the 2alues o" each 2aria le (0or +ender, ma3e 14 male and * 4 "emaleK "or hometo!n,14St# Gouis, * 4 Fansas City, &4Dther Hr an, and >4Iural)#

$+ain, youll !ant toei+ht Cases, this time,

y 7people#

The Command youll !ant"or this 3ind o" Chi/Squareis a little it hidden, so +o

to the menu "or:$nalyBe:


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Dnce you clic3 on Statistics, you can chec3 the o. "or Chi/Square# ts that easy#

)#N*#R + ,O-#TO.N Crosstabul ation

C(u&%

1.00)*+,*R

'(%al

1.00.00

5166

/O *'O +.003.00 311 018 3 2

.001 60

'(%al 3 85158

C/i(S0uare Tests

4alue 8.113 a 8. 13

3.636

158

df 33

1

Asy mp. Sig. -sided" .0 .0

.05

ears(& Chi-SquareLi elih((d Ra%i(Li&ear-7y -Li&ear

Ass(cia%i(&+ (f 4alid Cases

?ou +et output that loo3s li3e this:

This loo3s li3e your ori+inal data chart#

a. 0 cells .0!" ha# e e$pec%ed c(u&% less %ha& 5. 'he mi&imum e$pec%ed c(u&% is 2. .

ere is the p/2alue#

Since the p/2alue is less than #'5 ( arely), !e can reAect the null hypothesis, and say that +ender andhometo!n are related#

Pa+e > o" >

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Chi Square Tools in SPSS - Word