We encounter variables with little variation often in educational data mining (EDM) due to the demographics of higher education and the questions we ask. Yet, little work has examined how to analyze such data. Therefore, we conducted a simulation study using logistic regression, penalized regression, and random forest. We systematically varied the fraction of positive outcomes, feature imbalances, and odds ratios. We find the algorithms treat features with the same odds ratios differently based on the features' imbalance and the outcome imbalance. While none of the algorithms fully solved how to handle imbalanced data, penalized approaches such as Firth and Log-F reduced the difference between the built-in odds ratio and value determined by the algorithm. Our results suggest that EDM studies might contain false negatives when determining which variables are related to an outcome. We then apply our findings to a graduate admissions dataset. We end by proposing recommendations that researchers should consider penalized regression for datasets on the order of hundreds of cases and should include more context about their data in publications such as the outcome and feature imbalances.