Psychology is a puzzle

A blessing of retirement is that it frees up more time for crossword puzzles.

In 2013, my colleague Chris Gruber retired. Chris was vice president of research and development at Western Psychological Services (WPS, the test publisher, and my employer) for many years. He was also a fellow of Div. 5, and long-time editor of The Score. He was the one who encouraged me to join Div. 5 and seek out opportunities with its leadership group.

Chris presided over the transition of The Score from a print publication to an electronic document. Now, as I conclude my service as editor, the newsletter has evolved again from PDF to HTML format on the Div. 5 website. In this inaugural edition under new Editor Sara Rzepa, The Score offers another first — a crossword puzzle. (PDF, 662KB) It's one I created for Chris' retirement, a parting gift for a devotee of puzzles and tests. For me, the occasion unleashed an ambition: to ascend from mere consumer of crosswords to actual constructor of them.

Why is it that research psychologists are often crossword enthusiasts as well? Puzzle fascination may not be unique to our profession, but the interest certainly fits the profile of a cerebral, introverted psychometrician. And the nature of the “work” is similar: both activities are about making sense of tables; rows and columns, across and down.

Test developers are table jugglers, poring over counts of persons in demographic categories, parsing grids full of test scores. Crosswords are just another kind of table for a brain accustomed to them.

Within data sets and puzzles, cell values depend upon one another. In the tables of a test, dependencies are relatively weak. For example, test scores are somewhat constrained by, among other things, demographic factors and developmental trends (i.e., an expected score for a four-year-old is an outlier for a 16-year-old).

In puzzles, the inter-cell dependencies are stronger, the degrees of freedom smaller. Puzzles obey symmetry: placing a black square determines its mirror image on the opposite side of the grid. Once a letter enters a cell, English spelling rules (e.g., “i before e, except after c”) limit the possibilities for adjacent cells. For the constructor, constraints multiply as the grid fills fitting the last few words can be excruciating, I learned.

A crossword is an amusement, the solver's experience a function of the puzzle's difficulty. Some solvers like to breeze through easy crosswords; others enjoy struggling for hours with a difficult grid. But a puzzle is also a test, of vocabulary and knowledge of obscure facts. A psychometrician contemplates a puzzle and wonders: “Can I calibrate this, can I attach numerical estimates of difficulty to the clues, and to the puzzle as a whole?” The investigator might start by deconstructing the puzzle: removing its grid, transforming it into a list of questions and answers. Then it begins to look more like a conventional test, which might submit to a conventional analysis.

A constructed crossword puzzle, on the other hand, does not yield to conventional methods. Within the grid, “item” difficulties are moving targets: solving one clue makes the next one easier, filling in letters helps identify the desired word. Deconstructing a puzzle into a list of clues eliminates the dependencies among the answers; in a constructed puzzle, the answers are intertwined physically and semantically. A test of crystallized verbal knowledge becomes, in addition, a measure of a fluid ability, one that merges visual and verbal skills. It is the capacity to manipulate words in a mental grid, to locate letter strings along crosswise and downward vectors, all before actually committing pen to paper. This fluid, visual-verbal intelligence drives performance on crosswords, especially when solvers are timed, as they are in tournaments.

Can one impose a quantitative solution on a constructed puzzle by changing the level of analysis, calibrating individual cells instead of whole words? Seen in this way, my puzzle, a 21 × 21 grid with 71 black squares, becomes a 370-item test, with each answer a single character. But one-letter answers are just as context-dependent as whole-word answers. The “difficulty” of any certain cell depends on a partially random factor: the order of entry of letters into surrounding cells. The solver's unpredictable approach makes precise measurement unlikely, if not impossible.

Crossword puzzles, viewed as tests, thereby resist the quantitative methods of item calibration. As New York Times puzzle editor Will Shortz wrote: “Calibrating puzzle difficulty is an art, not a science, and on some days I may have miscalculated.”

Times solvers are left with the editor's intuitive, ordinal scale of difficulty. Monday's puzzle is the easiest, and the challenge rises as the week advances, culminating in Saturday's baffling grid. Sunday's large puzzle, the format I chose for my own, has a “Wednesday − Thursday” level of difficulty, and it offers the added intrigue of a theme. For Chris, the one who kindled my fascination with tests and helped me turn it into a career, the theme would express my gratitude. And if this puzzle ends up testing your confidence, I am all the more thankful.