By the time we reach voting age, almost all Americans have at least a high school education. That means we have been exposed to numerous math courses, and hopefully passed them. But that does not mean we have a good sense of numbers. Innumeracy in the modern sense means that one does not have a good grasp of statistics and probability and how they impact one’s worldview. This article by FiveThirtyEight discusses a recent study of how little the blue and red teams know about each other, a prime example of how innumeracy is causing real problems in America.
Language of Statistics
It seems that a many intro statistics students struggle with the “language” of stats. I am working on a micro-course on that topic and I ran across this article: Statistics for people in a hurry. It is well worth the read the 8-minute read.
One kind are “natural” pairings, such as spouses, siblings, and especially twins. This type of pairing is often used in medical observational research when it is difficult to construct a true experiment. (PennState, 2017)
But even more common are other types of pairing. A more accurate label for this two-sample test is a test for dependent samples. Samples are dependent when there is a relationship of some kind in play which causes the samples to not be independent.
I like this definition from the Minitab blog:
If the values in one sample affect the values in the other sample, then the samples are dependent. [Read more…] about Paired samples are not always obvious