Numbers certainly rule my world. Statistics is one of my most important research tools. So why not having a look at another pop-statistics book?
Kaiser Fung’s Numbers Rule Your World manages to introduce some fundamental concepts of statistics without actually doing any statistics. Each concept is introduced in the context of two case studies that highlight different aspects of the concept. Showing that different objectives lead to a different approach to the data, utilizing the same statistical concept in different ways. Further, instead on giving another introduction to the standard basics like central tendency, random processes and so on Fung focuses on a few central, more general concepts. Thus, he intends rather to instill some statistical thinking than to instruct the reader in specific methods.
Let me single out two statistical concepts from his list of five that I believe to be the most important.
First, heterogeneity matters (Fung writes ‘variability matters’), the mean hides all the interesting stuff. Much of my research interest can be summarized with this exact same statement. There is no real representative agent in economics. Differences in preferences and behavior, in the intensity of reactions to a stimulus (or treatment in an experiment) are the really interesting part of the story. Studying human behavior without this heterogeneity would be rather boring.
Second, there are two types of errors in statistical tests – false negatives and false positives – and we attach different costs to these errors. There is always a trade-off. You cannot decrease the error rate of one without increasing the other error (keeping the data constant and just moving the decision threshold around). Indeed asymmetric costs can also be attached to errors in a continuous model. And these asymmetric costs often exit in real life, a negative deviation from a target may have a considerably different impact on a decision than a positive deviation.
Both ideas seem often neglected in applied work. It is not the differences between individuals that is studied, it is often the general tendency of the whole group that is reported. Between-subject heterogeneity is hidden. And, often only one type of error is explicitly mentioned. Mr. P tells you only about the false positive. (Too often, I have to plead guilty on the second charge, too.)
In the end, however, Fung’s book is not for the (applied) statistician or the seasoned researcher applying statistics in his work. It is for lay-people and it may be well worth their time to have a look at it.