ANCOVA: overview
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ANCOVA  Pearson correlation 


Independent variables  Variable 1  
One or more categorical with independent groups, and one or more quantitative control variables of interval or ratio level (covariates)  One quantitative of interval or ratio level  
Dependent variable  Variable 2  
One quantitative of interval or ratio level  One quantitative of interval or ratio level  
THIS TABLE IS YET TO BE COMPLETED  Null hypothesis  
  $\rho = \rho_0$
$\rho$ is the unknown correlation in the population, $\rho_0$ is the correlation in the population according to H0  
n.a.  Alternative hypothesis  
  Two sided: $\rho \neq \rho_0$ Right sided: $\rho > \rho_0$ Left sided: $\rho < \rho_0$  
n.a.  Assumptions of tests for correlation  
 
 
n.a.  Test statistic  
  Test statistic for testing H0: $\rho = 0$:
 
n.a.  Sampling distribution of $t$ and of $z$ if H0 were true  
  Sampling distribution of $t$:
 
n.a.  Significant?  
  $t$ Test two sided:
 
n.a.  Approximate $C$% confidence interval for $\rho$  
  First compute approximate $C$% confidence interval for $\rho_{Fisher}$:
Then transform back to get approximate $C$% confidence interval for $\rho$:
 
n.a.  Properties of the Pearson correlation coefficient  
 
 
n.a.  Equivalent to  
  OLS regression with one independent variable  
n.a.  Example context  
  Is there a relationship between physical health and mental health?  
Pratice questions  Pratice questions  