Chi-Square Test (Chi-Square Test (22))

Used when dependent variable is counts within categories

Used when DV has two or more mutually exclusive categories

Compares the counts sample to those expected under the null hypothesis

Also called the Chi-Square “Goodness of Fit” test.

One-way Chi-Square Test (2)

Chi-Square Test (Chi-Square Test (22))

One-way Chi-Square Test (2)

Which power would you rather have: flight, invisibility, or x-ray vision?

Flight Invisibility X-ray vision18 people 14 people 10 people

Is this difference significant, or is just due to chance?

EXAMPLE

Chi-Square Test (Chi-Square Test (22))One-way Chi-Square Test (2)

EXAMPLE

Chi-Square Test (Chi-Square Test (22))One-way Chi-Square Test (2)

EXAMPLE

Chi-Square Test (Chi-Square Test (22))One-way Chi-Square Test (2)EXAMPLE

Chi-Square Test (Chi-Square Test (22))One-way Chi-Square Test (2)

EXAMPLE

Chi-Square Test (Chi-Square Test (22))

One-way Chi-Square Test (2)

Review:Steps:

1) State hypotheses2) Write observed and expected frequencies3) Get 2 by summing up relative squared deviations4) Use Table I to get critical 2

Chi-Square Test (Chi-Square Test (22))

Chi-Square Test (Chi-Square Test (22))

Two-factor Chi-Square Test (2)

Used to test whether two nominal variables are independent or related

E.g. Is gender related to socio-economic class?

Compares the observed frequencies to the frequencies expected if the variables were independent

Called a chi-squared test of independence

Fundamentally testing, “do these variables interact”?

Chi-Square Test (Chi-Square Test (22))

Two-factor Chi-Square Test (2)A 1999 poll sampled people’s opinions concerning the use of the death penalty for murder when given the option of life in prison instead. 800 people were polled, and the number of men and women supporting each penalty were tabulated.

Preferred PenaltyDeath

PenaltyLife in Prison

No Opinion

Female 151 179 80Male 201 117 72

Contingency table: shows contingency between two variablesAre these two variables (gender, penalty preference) independent??

Chi-Square Test (Chi-Square Test (22))

Two-factor Chi-Square Test (2)

Preferred Penalty

Death Penalty Life in Prison No Opinion

Female 151 179 80

Male 201 117 72

H0: distribution of female preferences matches distribution of male preferences

HA: female proportions do not match male proportions

EXAMPLE

Chi-Square Test (Chi-Square Test (22))

Two-factor Chi-Square Test (2)

We want to test whether the distribution of preferences for men and women is the same (e.g. no interaction effects) . We need to look at the marginal totals to get our expected frequencies

Preferred PenaltyDeath

PenaltyLife in Prison No Opinion frow

Femalef0= 151fe= ___

f0= 179fe= ___

f0= 80fe= __ 410

Malef0= 201fe= ___

f0= 117fe= ___

f0= 72fe= __ 390

fcol 352 296 152 n = 800

EXAMPLE

Chi-Square Test (Chi-Square Test (22))

Two-factor Chi-Square Test (2)Preferred Penalty

Death Penalty

Life in Prison No Opinion frow

Female f0= 151 f0= 179 f0= 80 410

Male f0= 201 f0= 117 f0= 72 390

fcol352

pdeath=.44296

plife=.37152

pnone=.19 n = 800

EXAMPLE

)( rowcol

e fnff

Chi-Square Test (Chi-Square Test (22))

Two-factor Chi-Square Test (2)Preferred Penalty

Death Penalty Life in Prison No Opinion frow

Femalef0= 151

fe=.44(410)f0= 179

fe=.37(410)f0= 80

fe=.19(410) 410

Malef0= 201

fe=.44(390)f0= 117

fe=.37(390)f0= 72

fe=.19(390) 390

fcol 352pdeath=.44

296plife=.37

152pnone=.19 n = 800

EXAMPLE

Chi-Square Test (Chi-Square Test (22))Two-factor Chi-Square Test (2)

Preferred PenaltyDeath

PenaltyLife in Prison No Opinion frow

Femalef0= 151

fe=180.4f0= 179fe=151.7

f0= 80fe=77.9 410

Malef0= 201

fe=171.6f0= 117fe=144.3

f0= 72fe=74.1 390

fcol 352pdeath=.44

296plife=.37

152pnone=.19 n = 800

e

eo

fff 2

2 02.2006.016.504.506.091.479.4

)1)(1( preferencegender kkdf 221 99.52 crit

EXAMPLE

Chi-Square Test (Chi-Square Test (22))

Two-factor Chi-Square Test (2)

Steps:1) State hypotheses2) Get expected frequencies

3) Get 2 by summing up relative squared deviations4) Use table to get critical 2

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e fnff

Chi-Square Test (Chi-Square Test (22))PRACTICE

radio paper TVHS 10 29 61college 24 44 32

Suppose we want to determine if there is any relationship between level of education and medium through which one follows current events. We ask a random sample of high school graduates and a random sample of college graduates whether they keep up with the news mostly by reading the paper or by listening to the radio or by watching television.

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e

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fff 2

2

Chi-Square Test (Chi-Square Test (22))PRACTICE

radio paper TV frow

HSfo=10

fe=17fo=29

fe=36.5fo=61

fe=46.5100

collegefo=24

fe=17fo=44

fe=36.5fo=32

fe=46.5100

fcol34

pradio= .1773

ppaper= .36593

pTV= .465 N=200

e

eo

fff 2

2 = 17.89 99.52 critdf = (2)*(1) = 2