Below, Dr. Jeremy Orloff and Dr. Jennifer French Kamrin describe how probability and statistics relate to one another, and why they are well suited to being taught together as a single subject.
Statistics is applied probability, and probability is the mathematical description of random events. While probability is a deductive science—starting from definitions we can prove mathematical theorems such as the law of large numbers—statistics is as much art as science. The students in 18.05 are typically not math majors, and their interests lie in the application more than the theory. Accordingly, the class is roughly 1/3 probability and 2/3 statistics. We provide the essential underpinnings of probability necessary to understand the meaning and justification of statistical methods. Statistics uses probability to describe and draw inferences from data. However, there are myriad ways that statistics are misunderstood and even abused—lies, damn lies, and statistics. This happens in both popular and technical presentations of experimental results. By providing enough of the underlying “why,” we are arming students with not only the knowledge of how to perform statistics, but perhaps more importantly, the ability to read and understand statistical arguments in research papers and media. This allows them to avoid common statistical pitfalls and to understand precisely what the statistics are suggesting.
