Physical activity counteracts some of the negative consequences associated with chronic neurological diseases. Here, we describe the levels of physical activity and sports activity in patients with multiple sclerosis and chronic stroke and test compliance with the recommendation for health-promoting physical activity of the World-Health Organization. Secondly, we tested for differences between the groups of patients, and thirdly, we examined relationships between PA and Sport with psychological indicators of perceived energy and self-beliefs. Psychological constructs were assessed with validated measures from (...) different disciplines in Psychology. A statistical aim was to describe interpretations gained by parametric Bayesian and Null-Hypothesis-Significance Testing statistics on the example of the conducted tests for differences and relationships. Descriptive analyses revealed that pMS and pStroke complied with recommendations of the WHO, but with large variance indicating that patient groups are not homogenous. Tests for differences showed that the PA difference between pMS and pStroke can be attributed to the higher proportion of women in the pMS sample as they engage more in household chores. Tests for relationships showed that for pStroke, vitality, self-control, and self-efficacy were positively related to the level of sports activity. Furthermore, pStroke who were sport active had lower fatigue and higher self-control and self-efficacy scores than sport inactive people. Although they address slightly different questions, the Bayesian and the NHST approach led to similar general conclusions. (shrink)