In recent years, machine learning has propagated into different aspects of psychological research, and supervised machine learning methods have increasingly been used as a tool for predicting human behavior or psychological characteristics when there's a large number of possible predictors and data instances. However, researchers often face practical challenges when using machine learning in psychology. In this article, we identify and discuss four key practical challenges that often arise when applying machine learning to data collected for psychological research. The four challenge areas cover (i) sampling error, (ii) measurement error, (iii) non-independent data, and (iv) missing data. Such challenges are extensively discussed in the traditional statistical literature but are often not explicitly addressed, or at least not to the same extent, in the applied machine learning community. We present how each of these issues is dealt with first in traditional statistics and then in machine learning. We discuss the strengths and limitations of each field's proposed approach, draw attention to the similarities and fundamental differences between approaches, and highlight where each discipline might learn something from the other. Finally, we identify fruitful areas of future research at the intersection of the two fields and the methodological developments that could progress both fields forward.