ANCOVA: overview
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ANCOVA  Spearman's rho 


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 of ordinal level  
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  
  $\rho_s = 0$
$\rho_s$ is the unknown Spearman correlation in the population. In words: there is no monotonic relationship between the two variables in the population  
n.a.  Alternative hypothesis  
  Two sided: $\rho_s \neq 0$ Right sided: $\rho_s > 0$ Left sided: $\rho_s < 0$  
n.a.  Assumptions  
  Sample of pairs is a simple random sample from the population of pairs. That is, pairs are independent of one another
Note: this assumption is only important for the significance test, not for the correlation coefficient itself. The correlation coefficient itself just measures the strength of the monotonic relationship between two variables.  
n.a.  Test statistic  
  $t = \dfrac{r_s \times \sqrt{N  2}}{\sqrt{1  r_s^2}} $ where $r_s$ is the sample Spearman correlation and $N$ is the sample size. The sample Spearman correlation $r_s$ is equal to the Pearson correlation applied to the rank scores.  
n.a.  Sampling distribution of $t$ if H0 were true  
  Approximately a $t$ distribution with $N  2$ degrees of freedom  
n.a.  Significant?  
  Two sided:
 
n.a.  Example context  
  Is there a monotonic relationship between physical health and mental health?  
n.a.  SPSS  
  Analyze > Correlate > Bivariate...
 
n.a.  Jamovi  
  Regression > Correlation Matrix
 
Practice questions  Practice questions  