Data Lab # 4

June 16, 2008

Ivan Katchanovski, Ph.D.

POL 242Y-Y

Chi-Square Test: Research and Null Hypotheses, Sample, and Weights

• Research hypothesis: Men in Canada are more confident in television than women are

• The null hypothesis: Men and women in Canada have the same confidence in television

• Canadian sample of the 2000 World Values Survey (WVS)– Select Canadian respondents from the 2000 WVS dataset

• Identify value for Canada (12) in “nation” variable (v2)

• Data-Select cases-If: v2=12

– Select Weight: Data-Weight Cases-Weight Cases By: v245

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Chi-Square Test: Dependent and Independent Variables

• Dependent variable– Confidence in Television (v150)• Check if recoding values and defining missing values

needed – Define -4, 8, 9 as missing values

• Independent variable: – Sex (v223)• Check if recoding values and defining missing values

needed– Define -4, 8, 9 as missing values

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SPSS Commands

• SPSS Command:– Analyze=Descriptive Statistics-Crosstabs

– “Row” box: select dependent variable (Confidence in Television)

– “Column” box: select independent variable (Sex)

– “Cells” Option: Column percentages

– “Statistics” Option: Chi-square

• SPSS Output– Check % of cells that have expected count less than 5

• If large %, collapse categories by recoding values

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Results

• SPSS Output: – Pearson Chi-square: Asymp. Significance p =.317>p=.05

• Statistically insignificant

• Accept the null hypothesis

• Reject the research hypothesis: – Canadian male and female respondents do not differ

significantly in their confidence in television

– The gender differences are statistically insignificant

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Modified Hypothesis

• New research hypothesis: Confidence in television in Canada differs significantly by the level of education

• The null hypothesis: Confidence in television in Canada is independent of the level of education

• Select new independent variable: – Education (v226)– Check if recoding values and defining missing values needed

• Define -4, 98, 99 as missing values

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Chi-Square Test: SPSS Command• SPSS Command:– Analyze=Descriptive Statistics-Crosstabs

– “Row” box: select dependent variable (Confidence in Television)

– “Column” box: select independent variable (Education v226)

– “Cells” Option: Column percentages

– “Statistics” Option: Chi-square

• SPSS Output– Check % of cells that have expected count less than 5

• 16.7% of cells that have expected count less than 5– Need to collapse categories

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Collapsing/Recoding the Independent Variable

• Collapse /recode v226 variable into new variable

• SPSS recoding command– Transform/Recode into Different Variables

– SPSS “Old and New Values”:• Range from 1 to 7 = 0

• Range from 8 to 9 = 1

• Label values of the recoded education variable (renamed as university education): – 0“Less than university”

– 1 “University”

– Dummy variable: two values (0 and 1) 8

Results• SPSS Output: – Pearson Chi-square: Asymp. Significance p =.000<p=.001

• Statistically significant

• Reject the null hypothesis

• Accept the research hypothesis: – Confidence in television in Canada differs significantly by

the level of education

– The differences are statistically significant at the .001 or .1% level

– 35% of the respondents without university education, compared to 27% of the respondents with university education, have quite a lot of confidence in television

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Presenting Results

Less than university

University

A great deal 6 3

Quite a lot 35 27

Not very much 46 55

None at all 13 15

Total, % 100 100

N 1363 524

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Table 1. Confidence in television in Canada by education level, 2000 World Values Survey, %

Independent Samples t Test• Hypothesis testing: Comparison of the sample means of

a dependent variable for two groups that differ on an independent variable

• Dependent variable: – interval-ratio

– ordinal variable treated as interval ratio

• Research Hypothesis: Men have lower level of confidence in television compared to women in Japan

• Null hypothesis: Men and women in Japan have the same level of confidence in television

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Independent Samples T-test: Dependent and Independent Variables

• Dependent variable: Confidence in television (v150)• Ordinal but can be treated as interval-ratio:

– If defined as a measure of non-confidence in television because increase in its values means decrease in confidence in television

– If recoded by assigning higher values to higher confidence levels

• Independent variable: Sex• Two categories (groups): Male and Female

– Sampling distribution: Student t distribution– SPSS selects t distribution automatically

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Independent Samples T-test: SPSS Commands

• Select Japan sample in the 2000 WVS dataset– Identify value for Japan (13) in “nation” variable (v2)

• Data-Select cases-If: v2=13

– Check if weights should be used

• SPSS Command: – Analyze-Compare Means-Independent Samples T Test

– Select Confidence in television (v150) as “Test Variable”

– Select Sex as “Grouping Variable”

– Define Groups: “Use specified values”: • 1 (Male) and 2 (Female)

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Results• Compare means of the dependent variable– Men have higher mean level of non-confidence in

television compared to women in Japan: 2.33>2.19

• Select “equal variances assumed” if Leven’s test for equality of variances is statistically insignificant: – Sig.=p=.000>.05

• Select “equal variances not assumed” if Leven’s test for equality of variances is statistically significant: – Sig.=p<.05

• Determine significance in t-test for equality of means– p =.000<p=.001

• Statistically significant14

Interpretation of Results

• Reject the null hypothesis

• Accept the research hypothesis: –Men have lower level of confidence in television

compared to women in Japan

– The differences are statistically significant at the .001 or .1% level

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