ANCOVA: overview
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ANCOVA  Chisquared test for the relationship between two categorical variables 


Independent variables  Independent /column variable  
One or more categorical with independent groups, and one or more quantitative control variables of interval or ratio level (covariates)  One categorical with $I$ independent groups ($I \geqslant 2$)  
Dependent variable  Dependent /row variable  
One quantitative of interval or ratio level  One categorical with $J$ independent groups ($J \geqslant 2$)  
THIS TABLE IS YET TO BE COMPLETED  Null hypothesis  
 
 
n.a.  Alternative hypothesis  
 
 
n.a.  Assumptions  
 
 
n.a.  Test statistic  
  $X^2 = \sum{\frac{(\mbox{observed cell count}  \mbox{expected cell count})^2}{\mbox{expected cell count}}}$
where for each cell, the expected cell count = $\dfrac{\mbox{row total} \times \mbox{column total}}{\mbox{total sample size}}$, the observed cell count is the observed sample count in that same cell, and the sum is over all $I \times J$ cells  
n.a.  Sampling distribution of $X^2$ if H0 were true  
  Approximately a chisquared distribution with $(I  1) \times (J  1)$ degrees of freedom  
n.a.  Significant?  
 
 
n.a.  Example context  
  Is there an association between economic class and gender? Is the distribution of economic class different between men and women?  
Pratice questions  Pratice questions  