Non-parametric Tests e.g., Chi-Square

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Non-parametric Testse.g., Chi-Square
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When to use various statistics

• Parametric
• Interval or ratio data
• Name parametric tests we covered Tuesday

• Non-parametric
• Ordinal and nominal data

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Parametric Tests
To compare two groups on Mean Scores use t-test.
For more than 2 groups use Analysis of Variance
(ANOVA)
Nonparametric Tests
Cant get a mean from nominal or ordinal data.
Chi Square tests the difference in Frequency
Distributions of two or more groups.
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Chi-Square X2

• Chi Square tests the difference in frequency
  distributions of two or more groups.
• Test of Significance
• of two nominal variables or
• of a nominal variable an ordinal variable
• Used with a cross tabulation table

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Chi-Square
Chi-Square
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Logic of Chi-Square Analysis

• If the observed values are different enough from
  the expected values, you reject the null
  hypothesis
• If the observed values and the expected values
  are similar, you fail to reject the null
  hypothesis

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Example Work Pregnancy

• The impact of working on pregnancy

• Ha Working during pregnancy increases the risk
  of miscarriage
• H0 Working during pregnancy has NO impact on the
  risk of miscarriage

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Example Work Pregnancy

• Suppose in general population 5 in 100 pregnancy
  results in miscarriage
• Probability(p) .05 or 5

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Example Work Pregnancy
Miscarriage
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Example Work Pregnancy

• H0 Working during pregnancy has NO impact on the
  risk of miscarriage

?
Miscarriage
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Example Work Pregnancy

• If NULL hypothesis TRUE, both work no work
  groups would have same probability of
  miscarriage. EXPECTED values

Miscarriage
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Example Work Pregnancy

• The actual values in your data OBSERVED VALUES

Miscarriage
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p .001
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(No Transcript)
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Tourist Expenditure Mainlander vs. Japanese
Chi-Square x2 7.34, df 2, plt.001
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Excel
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Finished Chart
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The Stats for Chart
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Use SPSS Crosstabs (for nominal and
ordinal data)

• Click. Analyze
• Descriptive statistics
• Crosstabs
• Highlight variables for row
• Highlight variable for column
• Click statistics, click chi-square or correlation
• Etc.

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Both chi square (non-parametric test) and t-test
(parametric test)

• Examines if observed difference between groups in
  your data is true difference
• True difference difference that exists in the
  population
• H0 says there is no difference in the population

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Which values are compared?
Chi-Square
Frequencies in each cell
t-test
Mean and Standard Deviation of each group
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If H0 is true
Chi-Square
The values in the frequency table will look like
Expected Values
t-test
The distribution of both groups will look like
Population Distribution
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Chi- square If H0 is trueMales Females
(No difference)
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t-test If H0 is true
of cases
Test score
Mean
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t-test If H0 is NOT true
of cases
Test score
Mean
Mean
Mean
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t-test If H0 is NOT true
of cases
Test score
Mean
Mean