Which correlation measure is preferred when evaluating bivariate data containing extreme outliers or non-linearly ordered ordinal categories?

Pearson’s coefficient is computed from the actual values of the variables, so a single extreme observation can change it considerably, and it measures only the strength of a linear relationship. Spearman’s coefficient is calculated on the ranks of the observations. An outlier is then just the highest (or lowest) rank, however extreme its actual value, so its influence is much smaller than under Pearson’s r. Spearman’s coefficient is less sensitive to extreme magnitudes, but not completely immune, because the outlier still occupies a rank. It can also be used for ordinal data such as ratings and rankings, and it captures any monotonic relationship, linear or not. Options (C) and (D) are not standard measures of correlation. The autocorrelation function in option (E) measures the correlation of a time series with its own past values. Hence the correct option is (B).