Cross Tabulation with Chi Square Inferential Statistics Parametric Non-parametric

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

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

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

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

Examples Frequency of sex during last year Happiness

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

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 -1 to +1