Which correlation coefficient is similar to Spearman's but preferred for small datasets with many tied ranks?

Kendall's Tau is indeed the appropriate correlation coefficient to use when dealing with small datasets that contain many tied ranks. This non-parametric measure assesses the ordinal association between two variables, providing a way to evaluate the strength and direction of a relationship.

Unlike Spearman's rank correlation, which can be sensitive to the number of tied ranks present in the data, Kendall's Tau is specifically designed to handle ties more effectively. It does this by calculating the difference between the number of concordant and discordant pairs of observations, providing a more nuanced understanding of the relationship in cases where data contains tied rankings. This makes it particularly valuable for datasets where the assumptions of normality and homoscedasticity generally required for parametric tests are not met.

In contrast, Pearson's r is used for assessing linear relationships in continuous data and does not handle ranks or tied values. The point-biserial correlation measures the relationship between a continuous variable and a binary variable, while the phi coefficient is appropriate for assessing the relationship between two binary variables. Both of these are less applicable in the context of small datasets with many tied ranks compared to Kendall's Tau, which is specifically tailored for such situations.