Which non-parametric test of correlation is suitable for data with tied ranks, such as a Likert scale?

Kendall's correlation is particularly suitable for data with tied ranks because it effectively accounts for the ranks of data points, particularly when there are many ties. In situations where you are working with ordinal data, such as responses from a Likert scale, tied ranks can frequently occur since respondents may select the same rating. Kendall’s tau correlational coefficient specifically embraces and adjusts for these ties through its calculation method, which focuses on concordant and discordant pairs of ranks.

This makes it a robust choice for analyzing the strength and direction of association between two ordinal variables. By using this method, researchers can achieve a more accurate representation of the correlation, mitigating the impact of tied ranks that could distort results if analyzed with other correlation methods.

In contrast, while Spearman's correlation also accommodates tied ranks, it is generally less preferable to Kendall's in situations with extensive ties, as it can assign equal values which might misrepresent the underlying data distribution. Pearson's correlation, on the other hand, is not appropriate for ordinal data or tied ranks since it assumes interval data and a linear relationship. The Chi-square test is unrelated to correlation and is used for categorical data analysis, making it unsuitable in this context.