  Z-scores are often employed in outlier detection in a dataset. For small
samples, the presence of multiple outliers forces a finite supremum on the
absolute value of possible z-scores that decreases with an increasing number of
outliers, creating a "masking effect" that hinders identification of true
outliers. We give an illustrative case study in which the accurate detection of
the number of outliers is critical, and provide a closed form expression of the
maximum possible z-score in terms of the sample size and number of outliers. In
addition, a corresponding analysis on the $t-$statistic is performed.
