Chi square Test Using SPSS

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

Outline

• Introduction

• Dataset

• Chi-square

• Exercise

12/7/2016 2DR ATHAR KHAN - LCMD

Introduction

• The chi-square test for independence, also

called Pearson's chi-square test or the chi-

square test of association, is used to

discover if there is a relationship between

two categorical variables.


BMI

• Body mass index (BMI) is a measure of body fatbased on height and weight that applies to bothadult men and women.

– Under & normal weight: BMI <25

– Overweight & obesity: BMI ≥ 25


Question 1

• Is there any association between living ina suburban area and being overweight?

– Under & normal weight: BMI <25

– Overweight & obese: BMI ≥ 25

Chi Square test


Dataset

• 30 adults aged 18+ (males and females) were recruited to

study the difference in BMI according to their area of

residence.

• Variables

– Sex (female=1, male=0)

– BMI

– Urban or rural (urban=0, rural=1)


Area of Residence

Total

Urban Rural

BMI Categories

Normal and Underweight

7 11 18

Overweight and Obesity

10 2 12

Total 17 13 30


Assumptions

• Assumption #1:

• Two variables should be measured atan ordinal or nominallevel (i.e., categorical data).


Assumptions

• Assumption #2:

• Two variable should consist of two or morecategorical, independent groups. Exampleindependent variables that meet this criterioninclude gender (2 groups: Males and Females),ethnicity (e.g., 3 groups: Caucasian, AfricanAmerican and Hispanic), physical activity level(e.g., 4 groups: sedentary, low, moderate andhigh), profession (e.g., 5 groups: surgeon, doctor,nurse, dentist, therapist), and so forth.


Hypothesis Testing– Step by Step

• Step 1: Stating the null hypothesis

– H0: Area of residence and BMI categories areindependent

– Ha: Area of residence and BMI categories aredependent

OR

– H0: There is no association between living in anurban area and being overweight

– Ha: There is an association between Living in anurban area and being overweight are dependent

• Step 2: Significance level

– Alpha = 0.0512/7/2016 10DR ATHAR KHAN - LCMD


• Step 3: Critical value

– Sampling distribution = χ2 distribution

– Df = (r-1)(c-1) = 1 (a 2-by-2 table)

– χ2 (critical) = 3.481



• 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 ResidenceTotal

Urban Rural

BMI Categories


7 11 18


10 2 12

Total 17 13 3012/7/2016 12DR ATHAR KHAN - LCMD

Hypothesis Testing– Step by Step• Step 4: Calculated Value

• 4.Calculate the Expected frequencies (E) a. For each cell: Column total xRow total/N b. Write the Expected frequency into the appropriate boxin the table.

• CHECK: Expected frequencies (E) marginal totals are the same as forObserved frequencies (O)Eyeball the contingency table, noting wherethe differences between O (observed) and E (Expected) values occur. Ifthey are close to each other, the levels of the independent (predictor) variable arenot having an effect.


Urban Rural

BMI Categories


7 11 18


10 2 12

Total 17 13 30

10.2 7.8

6.8 5.2


Important Point:

Chi-square can be used if no more than 20% of

the expected frequencies are less than 5 and none

is less than 1 (see note 'a.' at the bottom of SPSS

output to see if this is a problem).

It is possible to 'pool' or 'collapse' categories into

fewer, but this must only be done if it is meaningful

to group the data in this way.




Urban Rural

BMI Categories


7 11 18


10 2 12

Total 17 13 30

10.2 7.8

6.8 5.2



O E O-E (O-E)2



• Step 5: Decision

• Step 6: Conclusion



Step 4: computing the test statistic in SPSS



• Step 5: making a decision and interpreting the results of the test

overweight_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

79.699b 1 .000

78.301 1 .000

82.696 1 .000

.000 .000

79.619 1 .000

1000

Pearson Chi-Square

Continuity Correctiona

Likelihood Ratio

Fisher's Exact Test

Linear-by-Linear

Association

N of Valid Cases

Value df

Asymp. Sig.

(2-s ided)

Exact Sig.

(2-s ided)

Exact Sig.

(1-s ided)

Computed only for a 2x2 tablea.

0 cells (.0%) have expected count less than 5. The minimum expected count is 98.

25.

b.

Result(χ2 obtained)12/7/2016 19DR ATHAR KHAN - LCMD

Exercise

• Does a significant relationship exist between

Gender and BMI categories ?


BMI Categories * Gender Crosstabulation

Gender

TotalMale Female

BMI Categories

<25

Count 7 11 18

Expected Count 7.2 10.8 18.0

% within Gender 58.3% 61.1% 60.0%

>25

Count 5 7 12


% within Gender 41.7% 38.9% 40.0%

Total

Count 12 18 30


% within Gender 100.0% 100.0% 100.0%


Chi-Square Tests

Value dfAsymp. Sig.

(2-sided)Exact Sig. (2-

sided)Exact Sig. (1-sided)

Pearson Chi-Square .023a 1 .879

Continuity Correctionb.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


Chi square Test Using SPSS

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