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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 vision
18 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 hypotheses
2) Write observed and expected frequencies
3) Get 2 by summing up relative squared deviations
4) 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 Penalty
Death Penalty
Life in Prison
No Opinion
Female 151 179 80
Male 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 Penalty
Death Penalty
Life in Prison
No Opinion frow
Femalef0= 151fe= ___
f0= 179fe= ___
f0= 80fe= __
410
Malef0= 201fe= ___
f0= 117fe= ___
f0= 72fe= __
390
fcol352 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 Opinionfrow
Female f0= 151 f0= 179 f0= 80 410
Male f0= 201 f0= 117 f0= 72 390
fcol
352pdeath=.44
296plife=.37
152pnone=.19 n = 800
EXAMPLE
)( rowcol
e fn
ff
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
fcol352
pdeath=.44296
plife=.37152
pnone=.19 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
Femalef0= 151
fe=180.4f0= 179
fe=151.7f0= 80
fe=77.9410
Malef0= 201
fe=171.6f0= 117
fe=144.3f0= 72
fe=74.1390
fcol352
pdeath=.44296
plife=.37152
pnone=.19 n = 800
e
eo
f
ff 22 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
)( rowcol
e fn
ff
Chi-Square Test (Chi-Square Test (22))
PRACTICE
radio paper TV
HS 10 29 61
college 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.
)( rowcol
e fn
ff
e
eo
f
ff 22
Chi-Square Test (Chi-Square Test (22))
PRACTICE
radio paper TV frow
HSfo=10
fe=17
fo=29
fe=36.5
fo=61
fe=46.5100
collegefo=24
fe=17
fo=44
fe=36.5
fo=32
fe=46.5100
fcol
34
pradio= .17
73
ppaper= .365
93
pTV= .465N=200
e
eo
f
ff 22 = 17.89 99.52 critdf = (2)*(1) = 2