Rank correlation coefficients are ways of looking at correlations between variables, i.e. the systematic relationship between paired values of each variable, e.g. correlation of weight with height perhaps. Or, more typically for our area, of values on one measure with another say of CORE-OM scores against PHQ-9 scores. That would be a typical exploration of convergent validity.
Details #
The point about rank correlation coefficients is that they look at the correlation between the ranks of the values of the variables, not the raw values. This makes then “non-parametric” statistics, i.e. not dependent on assumptions about the distributions of the scores.
There are two main rank correlation coefficients used in our fields: the Spearman and the Kendall ones. To confuse things a bit further, there are actually two widely used Kendall correlation coefficients. One complication for rank correlation is the presence of ties: more than one observation having the same variable. Ties may be in one or both of the variables. Ties complicate the calculation of statistical significance for rank correlation coefficients and of confidence intervals around observed values but there are fairly robust ways of getting both p-values and confidence intervals even in the presence of ties.
See more details for all of this via the links below, either within the glossary, or beyond.
Try also #
- Confidence intervals
- Convergent validity
- Correlation
- Estimation
- Kendall correlation coefficient
- Non-parametric tests
- Null hypothesis significance testing (NHST) paradigm
- Parametric tests
- Ranking
- Spearman correlation coefficient
- Ties
- Validity
Chapters #
Not covered in the OMbook.
Online resources #
- In my shiny apps, one that gives you confidence intervals around a reported Spearman correlation coefficient given the dataset size.
- In my Rblog entries:
- Correlation coefficients (1): a general introduction to correlation coefficients
- Correlation coefficients (2): “Significance testing and confidence intervals for correlation coefficients … and back to why!”
- Confidence interval around Spearman correlation coefficient: background to that interval, see shiny app above
- Bootstrap_Spearman: “A quick exploration of bootstrapping a Spearman and why you might, or might not, want it.”
Dates #
First created 7.i.25.
