Final answer:
The Phi coefficient is the correct correlation to measure the relationship between two dichotomous variables such as gender (male/female) and performance on a task (success/failure).
Step-by-step explanation:
The appropriate correlation for measuring the relationship between a dichotomous variable like gender (male/female) and another dichotomous outcome such as performance on a task (success/failure) is the Phi coefficient. This coefficient represents a special case of Pearson's chi-squared test and is suitable for variables at the nominal level with two categories each.
The correlation coefficient, r, is a measure of the linear relationship between two continuous variables, thus not suitable for the data types (gender and task performance) concerned in the question. The Pearson correlation measures the degree of linear relationship between two continuous scale variables, and the Spearman rank correlation assesses monotonic relationships, often used for ordinal or non-normally distributed continuous variables. The point-biserial correlation is a special case of the Pearson correlation, used for one dichotomous and one continuous variable, which is not what we have here. Hence, for two dichotomous variables, the Phi coefficient is the best fit.