This paper identifies key concepts and issues associated with the reasoning of informal statistical inference. I focus on key ideas of inference that I think all students should learn, including at secondary level as well as tertiary. I argue that a fundamental component of inference is to go beyond the data at hand, and I propose that statistical inference requires basing the inference on a probability model. I present several examples using randomization tests for connecting the randomness used in collecting data to the inference to be drawn. I also mention some related points from psychology and indicate some points of contention among statisticians, which I hope will clarify rather than obscure issues. (Contains 7 figures and 3 tables.)