Chi-Square in SPSS

Using Survival Data from the Titanic

Getting Chi-Square StatisticsData: Survival on the Titanic by Gender

Analyze →Descriptive Statistics

→Crosstabs

Move one variable into ROW and the other into COLUMNS.

CLICK on CELLS

Select Percentages Within Categories of the Independent Variable

• Independent Variable (Gender) is in the Rows

• Always show Observed count• Optionally, show Expected

count• Percentage across the Rows• Click CONTINUE• In main dialogue box,

Click STATISTICS

Selecting Chi-Square Statistics

• Choose Chi-Square for hypothesis test

• Click Phi and Cramer’s V for measure of strength of the relationship

• Click CONTINUE• On main dialogue box,

Click OK

Crosstabs Table

• Observed count(yellow highlight)

• Expected count(blue highlight)

• Percent within each Gender who Died or Survived(pink highlight)

• Report: “Most men on the Titanic (80.2%) died while most women (71.6%) survived.”

gender * survival Crosstabulation

680.000 168.000 848.000

529.4 318.6 848.0

80.2% 19.8% 100.0%

126.000 317.000 443.000

276.6 166.4 443.0

28.4% 71.6% 100.0%

806.000 485.000 1291.000

806.0 485.0 1291.0

62.4% 37.6% 100.0%

Count

Expected Count

% within gender

Count

Expected Count

% within gender

Count

Expected Count

% within gender

1 Men

2 Women

gender

Total

1 Died 2 Survived

survival

Total

Chi-Square Tests

332.205b 1 .000

330.003 1 .000

335.804 1 .000

.000 .000

331.948 1 .000

1291

Pearson Chi-Square

Continuity Correctiona

Likelihood Ratio

Fisher's Exact Test

Linear-by-LinearAssociation

N of Valid Cases

Value dfAsymp. 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 166.43.

b.

Chi-Square Test

• Pearson chi-square is the default test• When Sig < alpha, variables are related.• Report:

“The relationship is significant (χ2(1) = 332.205, p < .005).”

Symmetric Measures

.507 .000

.507 .000

1291

Phi

Cramer's V

Nominal byNominal

N of Valid Cases

Value Approx. Sig.

Not assuming the null hypothesis.a.

Using the asymptotic standard error assuming the nullhypothesis.

b.

Measures of Relationship• Phi for 2x2 tables Cramer’s V for larger tables• Both range from 0 to 1 with 0 = no relationship• For df = 1

– V = 0.10 is a small effect– V = 0.30 is a medium effect– V = 0.50 is a large effect

• Report: “Genderhad a large effecton chance of survival for the Titanic passengers.”

Survival by Social Class on the Titanic

Class Social Class * Survived Died or Survived on Titanic Crosstabulation

117 187 304

189.8 114.2 304.0

38.5% 61.5% 100.0%

163 112 275

171.7 103.3 275.0

59.3% 40.7% 100.0%

526 186 712

444.5 267.5 712.0

73.9% 26.1% 100.0%

806 485 1291

806.0 485.0 1291.0

62.4% 37.6% 100.0%

Count

Expected Count

% within Class Social Class

Count

Expected Count

% within Class Social Class

Count

Expected Count

% within Class Social Class

Count

Expected Count

% within Class Social Class

1 Upper

2 Middle

3 Lower

Class SocialClass

Total

0 Died 1 Survived

Survived Died orSurvived on Titanic

Total

Chi-Square TestSurvival by Social Class on the Titanic

Chi-Square Tests

115.246a 2 .000

114.292 2 .000

114.311 1 .000

1291

Pearson Chi-Square

Likelihood Ratio

Linear-by-LinearAssociation

N of Valid Cases

Value dfAsymp. Sig.

(2-sided)

0 cells (.0%) have expected count less than 5. Theminimum expected count is 103.31.

a.

Effect Size and Write-UpSymmetric Measures

.299 .000

.299 .000

1291

Phi

Cramer's V

Nominal byNominal

N of Valid Cases

Value Approx. Sig.

Not assuming the null hypothesis.a.

Using the asymptotic standard error assuming the nullhypothesis.

b.

Gender was not the only factor that affected the chance of survival when the Titanic sank in the North Atlantic. Social class was significantly related to survivorship (χ2(2) = 115.246, p < .005). More than half of the upper class passengers (61.5%) and many of the middle class (40.7%) passenger survived while only one fourth (26.1%) of the lowest class passengers survived. Social class had a moderate relationship (V = .299) to survival, not as great as the effect of gender.

For df(2): V = .07 is a small effect V = 0.21 is a medium effect V = .035 is a large effect