ANCOVA: overview
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ANCOVA  KruskalWallis test 


Independent variables  Independent 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 variable  
One quantitative of interval or ratio level  One categorical of ordinal level  
THIS TABLE IS YET TO BE COMPLETED  Null hypothesis  
  Formulation 1:
 
n.a.  Alternative hypothesis  
  Formulation 1:
 
n.a.  Assumptions  
  Group 1 sample is a simple random sample (SRS) from population 1, group 2 sample is an independent SRS from population 2, $\ldots$, group $I$ sample is an independent SRS from population $I$. That is, within and between groups, observations are independent of one another  
n.a.  Test statistic  
  $H = \dfrac{12}{N (N + 1)} \sum \dfrac{R^2_i}{n_i}  3(N + 1)$  
n.a.  Sampling distribution of $H$ if H0 were true  
  For large samples, approximately the chisquared distribution with $I  1$ degrees of freedom. For small samples, the exact distribution of $H$ should be used.  
n.a.  Significant?  
  For large samples, the table with critical $X^2$ values can be used. If we denote $X^2 = H$:
 
n.a.  Example context  
  Do people from different religions tend to score different on social economic status?  
Pratice questions  Pratice questions  