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I would like to assess the correlation between a 7-category ordinal variable (X) and a number of other variables some of which are ordinal with 3-6 categories, others are continuous and a couple are dichotomous. The dataset includes only 24 observations and lack of normality and tied observations are therefore issues to take into account.

  • Would it be best to use the Kendall coefficient to assess the correlation between X and each of the other variables? If so, which one (i.e. tau-a or tau-b; I know that Roger Newson favours the former)?
  • Would it be reasonable to use Spearman as well?
  • And what would be the best test to assess the correlation with each of the dichotomous variables?
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Rather than either of those I would use Polychoric correlations which were designed for just this instance. They use maximum likelihood to fit a model an underlying normally distributed continuous variable under each ordinal variable; then calculate the correlation coefficient of the continuous variables. There are implementations available in R and Stata.

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