1. Cross Tabulation with Chi Square
Inferential Statistics
Parametric
Non-parametric

2. Parametric Statistics
Statements about unobserved data from a population
Population Parameters
how does the statistic (e.g. a mean) compare to the true population statistic?
interval or ratio

3. Non-parametric Statistics
1. No assumption of normal distribution
2. NON-sample
3. Tests for INDEPENDENCE
4. Asks if the observed non-zero relationships is statistically significant

4. Chi Square 1. nominal (sometimes ordinal)
2. uses a cross tabulation or contingency table
3. Asks: Is there a relationship?

5. Formula for Chi Square
chi square =
∑ (observed - expected)2
expected

6. Examples
Frequency of sex during last year
Happiness

7. Interpreting the Output
Chi square value
degrees of freedom (d.f.)
(r-1, c-1)
significance level
the larger the chi square value, the more likely that the relationship is statistically different from zero

8. Other Measures of Association
 other tests allow prediction
 measures from 0 to 1 
lambda, phi, rho, gamma
example: gamma
ordinally measured
more than 2X2 tables
range from to +1