Sybil Shaver writes:
Reading Stephen White's novel Line of Fire I encountered the following: (in the middle of a discussion of a death which is either accidental or suicide, p. 51 of the hardcover)
"What do you mean 'if she intends to die'? Isn't dying always intent?"
I shook my head. "It helps to think about suicidal behavior having two pairs of defining variables. Picture a simple chi square – a two-by-two graph. On one axis is the dichotomy of intent – the person intends either to die or to survive. On the other axis is the dichotomy of lethality – the person chooses either a method of high lethality or one of low lethality.
"The two-by-two chi square allows for four possible combinations." I turned over our grocery list and sketched a chi-square with four boxes. "People with low intent sometimes choose methods of high lethality. They can end up dying, almost by accident, because death wasn't what they were seeking. The opposite is people who intended to die, but they chose a low-lethality method. They're the ones who believed that five aspirin and two shots of vodka would kill them. But they end up surviving, again, almost by accident."
"You drew four boxes. What are the other two?"
I squeezed water from a rag to use to wipe the counter. "I described low intent/high lethality, and high intent/low lethality. The other two are low intent/low lethality, and high intent/high lethality. People in both those categories get the outcome they intended. Low intent/low lethality is the classic 'cry for help' suicide attempt-someone who intends to survive but is eager for someone else to know about the gesture. That person doesn't wish to die, and she chooses a method that makes death unlikely. High intent/high lethality is the guy who puts a shotgun barrel in his mouth and pulls the trigger with his toes. He intends to die and chooses a method that is damn near certain to do it.'
The first-person narrator uses "a chi-square" to refer to what I have always called "a contingency table". [In fact, the description of the four possibilities is very close to the way I describe the four possible results of doing a classical hypothesis test: two are errors, of different natures, and two give correct results.]
The narrator is Alan Gregory, a clinical psychologist (Ph. D.) and presumably at least a partial alter-ego for the author, who is also a clinical psychologist.
There is certainly some overlap between the usage of contingency tables and the usage of Chi-square tests, but I've never seen or heard of a contingency table being referred to as "a chi square" before. So is this an idiosyncracy of Stephen White (or possibly, of his teacher whom he thanks in the acknowledgments) or is it a common usage in some circles?
I don't intend to embarrass anyone by this question. (I'm quite sure that 30 years after my last heard lecture in PDEs, I'd badly mangle the terminology today.) But I'm curious. I hope you can find a way to put this out to the LL commenters.
I agree with Sybil — a matrix of (e.g.) intents and choices is called a "contingency table", while a "Chi square(d) distribution" is "the distribution of a sum of the squares of k independent standard normal random variables", used in various sorts of "Chi-square(d) test".
It's true that the contingency table described in White's novel is a square matrix (with the same number of rows and columns), and it's also true that the Χ2 distribution plays a role in the analysis of contingency tables, e.g. via Cramér's V. So it's plausible that someone might get confused, fictionally or in reality, and misunderstand or misremember a square contingency table as a "Chi square".
On the other hand, maybe some sub-tribe of statisticians has taken this terminological nexus as the basis for reducing the six syllables of "contingency table" down to the two syllable of "Chi square". Comments?