Quantifying association in ordinal data.

What is non-parametric correlation? A non-parametric (or ordinal) correlation coefficient for two variables quantifies the extent to which there is, in the study sample, a consistent relationship between the values for the two variables. The correlation coefficient indexes the strength of the relationship found, from zero (no discernible relationship) to a maximum value of 1 (denoting a perfect relationship). There are two main methods for obtaining non-parametric or rank correlation coefficients: Spearman rho (ρ) and Kendall tau (τ). The general principles are the same (both are based on calculations using ranked data) and for most purposes the interpretation is very similar.2 This Noteworthy Statistics (NS) explanation will focus on Spearman rho, as used in the Kulczycki et al. paper.1 An ordinal association might be manifested in two ways: direct or inverse. The most straightforward association to envisage is a direct relationship, where an individual who gives a ‘higher’ response (relative to group) on the one variable, tends also to give a ‘higher’ response on the other variable (or in the case of other individuals, mid-responses with mid, or lower with lower). An example might be the association between parity and ‘wish for permanent contraception’. Alternatively, the true situation might be an inverse relationship, where higher values on the one variable tend to be found in association with lower values on the other variable (and vice versa) (e.g. between ‘degree of concern about hormone use’ and ‘acceptability of hormonal implant contraception’). Direct and inverse relationships will be distinguishable from analysis output because, under conventional numerical coding schemes for responses, direct relationships result in positive correlation coefficients (>0 to 1), and indirect relationships in negative correlation coefficients (<0 to –1). This is why inverse relationships are also commonly termed negative associations/correlations. [In Table 2 in the Kulczycki et al. paper, all the correlations with ‘experience in diaphragm fitting’ are negative (i.e. the more experience, the less the perceived barrier).1]