Conducting analyses based on synthetic texts, we created ideal conditions to uncover the hidden properties of a range of distinctiveness measures. Through our experiment, we tested the sensitivity of these measures to variations in the frequency and dispersion of a specific word. We found that LLR and chi-square tests are even more sensitive to frequency variation than RRF, which is simple and relies only on word frequency. Both Zeta variations and the rank-sum test demonstrated similar scores and abilities to detect distinctive words. Moreover, we discovered that TF-IDF is more sensitive to slight dispersion differences of the target word compared to other dispersion-based measures. Finally, we found that Eta does not detect a word with a clear contrast in dispersion when its frequency is the same in both the target and comparison corpora.