Chi square Test Using SPSS

A simple way to apply Chi Square test

1. Using SPSS for Chi Square
Dr Athar Khan
MBBS, MCPS, DPH, DCPS-HCSM, DCPS-HPE, MBA,
PGD-Statistics
Associate Professor
Liaquat College of Medicine & Dentistry

2. Outline
•Introduction
•Dataset
•Chi-square
•Exercise
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3. Introduction
•Thechi-squaretestforindependence,also
calledPearson'schi-squaretestorthechi-
squaretestofassociation,isusedto
discoverifthereisarelationshipbetween
twocategoricalvariables.
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4. BMI
•Bodymassindex(BMI)isameasureofbodyfat
basedonheightandweightthatappliestoboth
adultmenandwomen.
–Under&normalweight:BMI<25
–Overweight&obesity:BMI≥25
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5. Question 1
•Isthereanyassociationbetweenlivingin
asuburbanareaandbeingoverweight?
–Under&normalweight:BMI<25
–Overweight&obese:BMI≥25
Chi Square test
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6. Dataset
•30adultsaged18+(malesandfemales)wererecruitedto
studythedifferenceinBMIaccordingtotheirareaof
residence.
•Variables
–Sex(female=1,male=0)
–BMI
–Urbanorrural(urban=0,rural=1)
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7. Area of Residence
Total
Urban Rural
BMI Categories
Normal and
Underweight
7 11 18
Overweight and
Obesity
10 2 12
Total 17 13 30
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8. Assumptions
•Assumption#1:
•Twovariablesshouldbemeasuredat
an ordinal or nominal
level(i.e.,categoricaldata).
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9. Assumptions
•Assumption#2:
•Twovariableshouldconsistoftwoormore
categorical,independentgroups.Example
independentvariablesthatmeetthiscriterion
includegender(2groups:MalesandFemales),
ethnicity(e.g.,3groups:Caucasian,African
AmericanandHispanic),physicalactivitylevel
(e.g.,4groups:sedentary,low,moderateand
high),profession(e.g.,5groups:surgeon,doctor,
nurse,dentist,therapist),andsoforth.
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10. Hypothesis Testing–Step by Step
•Step1:Statingthenullhypothesis
–H
0:AreaofresidenceandBMIcategoriesare
independent
–H
a:AreaofresidenceandBMIcategoriesare
dependent
OR
–H
0:Thereisnoassociationbetweenlivinginan
urbanareaandbeingoverweight
–H
a:ThereisanassociationbetweenLivinginan
urbanareaandbeingoverweightaredependent
•Step2:Significancelevel
–Alpha=0.05
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11. Hypothesis Testing–Step by Step
•Step 3: Critical value
–Sampling distribution = χ
2
distribution
–Df = (r-1)(c-1) = 1 (a 2-by-2 table)
–χ
2
(critical) = 3.481
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12. Hypothesis Testing–Step by Step
•Step 4: Calculated Value
–1. Draw a contingency table.
–2. Enter the Observed frequencies or counts (O)
–3. Calculate totals (in the margins).
Area of Residence
Total
Urban Rural
BMI Categories
Normal and
Underweight
7 11 18
Overweight and
Obesity
10 2 12
Total 17 13 30
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13. Hypothesis Testing–Step by Step
•Step4:CalculatedValue
•4.CalculatetheExpectedfrequencies(E)a.Foreachcell:Columntotalx
Rowtotal/Nb.WritetheExpectedfrequencyintotheappropriatebox
inthetable.
•CHECK:Expectedfrequencies(E)marginaltotalsarethesameasfor
Observedfrequencies(O)Eyeballthecontingencytable,notingwhere
thedifferencesbetweenO(observed)andE(Expected)valuesoccur.If
theyareclosetoeachother,thelevelsoftheindependent(predictor)variableare
nothavinganeffect.
Area of Residence
Total
Urban Rural
BMI Categories
Normal and
Underweight
7 11 18
Overweight and
Obesity
10 2 12
Total 17 13 30
10.2 7.8
6.8 5.2
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14. Important Point:
Chi-squarecanbeusedifnomorethan20%of
theexpectedfrequenciesarelessthan5andnone
islessthan1(seenote'a.'atthebottomofSPSS
outputtoseeifthisisaproblem).
Itispossibleto'pool'or'collapse'categoriesinto
fewer,butthismustonlybedoneifitismeaningful
togroupthedatainthisway.
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15. Hypothesis Testing–Step by Step
Area of Residence
Total
Urban Rural
BMI Categories
Normal and
Underweight
7 11 18
Overweight and
Obesity
10 2 12
Total 17 13 30
10.2 7.8
6.8 5.2
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16. Hypothesis Testing–Step by Step
O E O-E (O-E)
2
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17. Hypothesis Testing–Step by Step
•Step 5: Decision
•Step 6: Conclusion
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18. Hypothesis Testing–Step by Step
Step 4: computing the test statisticin SPSS
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19. Hypothesis Testing–Step by Step
•Step 5: making a decision and interpreting the
results of the testoverweight_1 * urban Crosstabulation
329 468 797
385.7 411.3 797.0
155 48 203
98.3 104.7 203.0
484 516 1000
484.0 516.0 1000.0
Count
Expected Count
Count
Expected Count
Count
Expected Count
0
1
overweight_1
Total
0 1
urban
Total Chi-Square Tests
79.699
b
1 .000
78.301 1 .000
82.696 1 .000
.000 .000
79.619 1 .000
1000
Pearson Chi-Square
Continuity Correction
a
Likelihood Ratio
Fisher's Exact Test
Linear-by-Linear
Association
N of Valid Cases
Value df
Asymp. Sig.
(2-sided)
Exact Sig.
(2-sided)
Exact Sig.
(1-sided)
Computed only for a 2x2 tablea.
0 cells (.0%) have expected count less than 5. The minimum expected count is 98.
25.
b.
Result
(χ
2
obtained)12/7/2016 19DR ATHAR KHAN -LCMD

20. Exercise
•Does a significant relationship exist between
Gender and BMI categories ?
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21. BMI Categories * Gender Crosstabulation
Gender
TotalMale Female
BMI Categories
<25
Count 7 11 18
Expected Count 7.2 10.8 18.0
% within Gender58.3% 61.1% 60.0%
>25
Count 5 7 12
Expected Count 4.8 7.2 12.0
% within Gender41.7% 38.9% 40.0%
Total
Count 12 18 30
Expected Count12.0 18.0 30.0
% within Gender100.0%100.0%100.0%
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22. Chi-Square Tests
Value df
Asymp. Sig.
(2-sided)
Exact Sig. (2-
sided)
Exact Sig.
(1-sided)
Pearson Chi-Square
.023
a
1 .879
Continuity Correction
b
.000 1 1.000
Likelihood Ratio
.023 1 .879
Fisher's Exact Test
1.000 .588
Linear-by-Linear
Association
.022 1 .881
N of Valid Cases
30
a. 1 cells (25.0%) have expected count less than 5. The minimum expected count is
4.80.
b. Computed only for a 2x2 table
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