SPS
SS: 2x2 Pe
earson’s Chi-Square Test of Ind
dependenc
ce
Appllication: To te
est if two or more
m
populatio
ons or subpopulations havve different pa
atterns of resp
ponse to a
qualitative/categorical DV. This
s can also be characterized
d as a test of a pattern of rrelationship between two
qualitative/categorical variables
s.
Rese
earch Hypoth
hesis: The re
esearcher hyp
pothesized tha
at those store
es that did nott have a sepa
arate reptile d
department
would
d tend to disp
play only fresh
hwater fish, whereas
w
those
e stores that d
did have a se
eparate reptile
e department would tend to
o
displa
ay both freshwater and saltwater fish.
departments and whether
H0: T
There is no pa
attern of relattionship betwe
een whether or
o not pet sto
ores have sep
parate reptile d
they display only freshwater
f
fis
sh or both salttwater and fre
eshwater fish in the popula
ation represen
nted by these
e pet stores.
Analyze Descriptive Sta
atistics 
Crosstabs
 h
highlight the variable
v
you want
w
to define
e the rows (be
e sure it is qua
alitative/categ
gorical) and click arrow
 h
highlight the variable
v
you want
w
to define
e the columns (be sure it iss qualitative/ca
ategorical) an
nd click arrow
w
 “Statistics” — check that yo
ou want a “Ch
hi-square ana
alysis”
SPSS
S Syntax
CRO
OSSTABS
/TA
ABLES=reptde
ept BY fishdep
pt
/STA
ATISTICS=C
CHISQ
/CE
ELLS=COUNT
T ROW COLU
UMN TOTAL.
 “row
w variable” BY
Y “column variiable”
 get Chi-square
C
sig
gnificance tesst
 get various
v
row, ccolumn and/o
or total cell percentages (op
ptional)
1
The p-value of .021
1 means that there is
nce that this re
esult is a
about a 2.1% chan
Type I error.
Reme
ember, even iff the printout shows it,
never report p = .00
00, because tthat would
sugge
est there is no
o possibility off a Type 1
error. Instead, repo
ort “p < .001”
Chi-sq
quare results are “suspicio
ous” if more
than 1
15% of the ce
ells have expe
ected
freque
encies less th
han 5.
The “ccorrection for continuity” is computed fo
or
2x2 de
esigns, to givve a better esttimate of
Type I error for thiss small design
n, especially
when N is small.
Repo
orting the Re
esults:
nt to show the
e cell and ma
arginal
It is importan
frequencies in an conting
gency table be
efore
presenting the Chi-squarre results.
As in the exa
ample, be sure to commun
nicate:
 The
e research hyp
pothesis (if th
here is one)
 The
e statistical ressults
 Whe
ether or not th
hose results ssupport the
rese
earch hypothe
esis
Ta
able 1 shows the contingency table forr these variab
bles. The
samp
ple of stores was
w evenly divided betwee
en the two typ
pes of
reptile departmentts and also ev
venly divided between the two types
of fish departmentts. Inspection
n of the table suggests tha
at, as
hypo
othesized, those stores with
h separate reptile departments
tende
ed to have bo
oth fresh- and saltwater fish
h, whereas, th
hose
store
es without sep
parate reptile departments tended to have only
fresh
hwater fish. Ho
owever, contrrary to the hypothesis, there was not
a sta
atistically significant relation
nship between the variable
es, X²(1) =
3.00,, p = .083, wh
hen the correc
ction for continuity was app
plied to this
2x2 d
design .
2