Lexicographers (“harmless drudges,” Dr. Johnson called us) have good reason to thank Chris Anderson, editor of “Wired” and author of “The Long Tail: Why the Future of Business is Selling Less of More,” for invoking “long tail” word-frequency distributions as an analogy more productive than those boring Bell curves that have bedeviled educational discourse these many years. Here's how the “long tail” approach can help limited-English Americans (young learners and forgetful grandparents) to get more mileage out of their crossword puzzles and spelling contests (senior centers are beginning to use these more and more, incidentally).

As described by Anderson , a “long tail” distribution in bookselling primarily takes shape at the end of each day in Amazon statistics as a relatively small number of titles (‘best sellers”), each of which has been purchased by a very large number of customers. But this statistical high point (much like a very tall, thin mouse) is also flanked by a very large number of different special-interest titles (classics, how-to books, etc.).

Anderson points out that these non-mainstream titles, each of which has a relatively small number of buyers, provide our statistical mouse with an extraordinarily long tail that stretches on and on and on, getting progressively smaller and smaller, but weighty enough in the aggregate to justify plenty of attention from booksellers and publishers.

Mainstream consumers and idiosyncratic consumers — internet access encourages vendors to take both categories seriously these days. Observably so, as indicated by the recent spurt in special-target advertising and solicitation.

Our long-tailed American English vocabulary . . . . By way of drawing a statistical parallel, Anderson cites the British National Corpus, which has drawn up a similar “mouse-tail” frequency list on the basis of 600 million word-occurrences involving both mainstream word-consumers (readers, listeners, etc.) and idiosyncratic word-consumers.

Not surprisingly, BNC lists THE as our most frequently occurring “best selling” word, with 61,847 hits for every million occurrences (roughly 6%), followed by OF (29,391), AND (26,817), A (21,626), and IN (18,214). Thereafter, echoing our mouse-tail analogy, the number of occurrences per million grows fewer and fewer, e.g., only 8,412 for DOWN (ranked 114 th ), and 524 for UNDER (ranked 169 th) . As noted on www.comp.lancs.ac.uk , the tabulation stops with ten occurrences for the noun MORALE, which now occupies pride of place as one of the least frequently used words in the language.

Dictionary definitions and word frequencies . . . . American lexicographers, notably E.J. Thorndike and Irving Lorge , have since the thirties recognized that the number of definitions listed for a word matches up quite neatly on the whole with the frequency of its occurrences; the American Heritage Dictionary, for example, lists 28 different definitions for DOWN (114 th ) and 23 for low-frequency UNDER (169 th ). Practically considered, then, the American dictionary has always served as an authoritative source for spelling bee organizers seeking to challenge students with low-frequency , single-definition words like KYMOGRAM and MYOCARDIA.

Relatively short words with lots of definitions shading off in the direction of longer words with fewer definitions and ending up with a long, long sequence of exotic singletons — that's what the vocabulary of American English actually is in word-frequency terms.

Crossword puzzles and low-frequency definitions . . . . Where spelling bees use low-frequency words, crosswords use the low-frequency definitions of high frequency words as a device for challenging (and frustrating) those who try to work them, as in “a four-letter word that starts with D and means ‘afflicted, sick'” (the 23 rd definition listed by AHD for DOWN). As indicated by the FCAT and other tests of language skills, this kind of multiple-meaning challenge is considered a central element in reading comprehension.

It's worth noting that reading-comprehension tests like the Florida Comprehensive Assessment Test are now using crossword-style multiple definition questions, e.g., a quoted sentence followed by “Which meaning of TRIBE best fits John Adams' use of the word in his letter to Abigail — ‘a unit of socio-political organization consisting of a number of families,' or ‘a group of people sharing an occupation, interest, or habit,' or ‘one of the 12 divisions of ancient Israel'?”

Conventional crossword-puzzle construction is still a highly creative art form. But its multiple-meaning challenge can be effectively duplicated if we use a standard desk dictionary as an authoritative source of high-frequency words, low frequency definitions, and spelling clues. By way of illustration Appendix One presents a 23-item crossword-style challenge based on a conventional spelling list.

As will be apparent, it's a dictionary based test, not one based on personal whim. But the format is still flexible enough to offer a number of user-friendly options, ranging from using higher-frequency definitions to using stronger spelling clues, e.g., a complete phonetic transcription of the target word ..

Difficulty-rankings and a national standard vocabulary test . . . . Our 23-item test in Appendix One is actually the tip of a modestly proportioned numerical iceberg. Appendix Two therefore presents its work sheet with five basic measurements: (1) word-frequency familiarity level ; ( 2) spelling-unfamiliarity level as indicated by the number of instances in which its spelling conflicts with its phonetic description in AHD; (3) definition-unfamiliarity (DU) as indicated by ordinal-number position of the selected illustrative definition in the sequence of definitions for that word presented in AHD. . . . (4) clue familiarity level as indicated by the number of initial letters.

The fifth and most important measurement is the formula for determining each word's level of difficulty. Arithmetically we can express it as (“spelling unfamiliarity” TIMES “definition unfamiliarity”) DIVIDED BY ( “ clue familiarity TIMES “word-frequency familiarity”).

The potential usefulness of this four-element difficulty-ranking formula can be summed up in one phrase: A National Yardstick. Quantitative skills aside, most high-stakes tests are fundamentally vocabulary power tests, whether it be reading comprehension or the awareness of figurative language.

In addition it's worth pointing out that test makers are quite secretive about how their questions are constructed and how easy or difficult they are supposed to be. Since the same uncertainty also pervades classroom education (what does an A-grade actually “mean” today?), it's very hard for most of us to understand what's actually going on in a society where, as Yeats put it, “The best lack all conviction while the worst are filled with passionate intensity.” Hence the desirability, especially for parents, of having a clearly defined point of reference by which to measure other vocabulary-related tests and the performance of other test-takers.

Dictionaries and authoritative rankings . . . . The impetus behind this test-construction method is quite modest, namely, the decision of a local senior center to offer a competition involving spelling-bee questions and crossword-style questions, thereby putting two traditional American indoor sports into the same psychometric basket. Equally modest, I feel, is its basic principle of Authoritative Ranking, which calls for using the American dictionary as a tool for constructing questions and ranking their difficulty. As it see it, what's here is an easy lexicographical game which anyone — parent, student, or teacher — can play.

It's also an important game whose seriousness can be summed up by saying that American English is today a large, hostile beast with the longest tail on this planet. Simply put, this means that our total vocabulary, as represented in the current Merriam Webster unabridged dictionary, is now roughly 600,000 words — twice the size of France 's or Germany 's. It also means that our spelling system is unique in being the most learner-unfriendly one on the planet, largely because we have imported over 80% of our vocabulary from Graeco -Latin sources.

Hard to learn, easy to forget — that's an accurate description of the English vocabulary, I feel. What it means for us personally is that we as Americans are unique in facing the prospect of going blank on ordinary words (not just proper names) in our early fifties (Medical Science News has in the last twenty years published a number of cross-cultural comparison studies that support this assertion).

Quite apart from personal concerns, our learner-unfriendly vocabulary, along with the number and diversity of those using it, places the overall Civilizational Literacy of our magnificent nation at considerable risk. Where “culture” is largely a matter of cookery and religion, after all , civilization has a much longer “tail,” as Chris Anderson would put it. It has a bigger vocabulary, dictionaries, more words, longer word-frequency lists, more technical terms (one-definition words) , more spelling problems, more pronunciation problems, more books, and more people who read them.

Like imperial Rome or China, American civilization (is there a better word for it?) is defined by its cuisine-blind, location-blind, status-blind, color-blind, religion-blind vocabulary, just as a civilized American is defined by his or her relative mastery of it — measurably so. As described here, our National Standard Vocabulary Test construction method) is far from being a “ civilizational ” panacea . But as pointed out in Appendix Three, it's authoritative, timely, and very, very cheap. Enough so, I trust, to invite some serious attention — including thoughtful criticism wherever it seems appropriate.

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APPENDIX ONE. . . . A Ranked-Difficulty Crossword-Style Vocabulary Test . . . . Overall this is a difficult vocabulary test. Even though the word-targets are familiar, their definition-clues are going to be puzzling, very much like asking a friend for a five-letter word meaning “the presiding officer of a meeting,” instead of the more familiar definition,” a piece of furniture for one person to sit on.”

By way of balancing matters we'll give you stronger spelling clues to work with, namely, the first three letters and the total number of letters. Thus the clue “ACT5” accompanied by the dictionary definition, “someone who does something,” would lead many of us to guess “actor”— especially if we're told via the abbreviation “1/2” that our definition is the first one in a two-definition entry.

Our word-targets are taken from a standard spelling list of 507 words ( www.esl.desk.com ) and their definitions are taken from the American Heritage Dictionary. They are presented in a sequence that reflects their frequency of use, their level of spelling difficulty, and the relatively unfamiliarity of the illustrative definition. Based on these elements, the overall difficulty of this particular test has been computed as 1.107.

1 ...CAL8...A schedule of events...3/6

2 ...YAC5... Any of various relatively small sailing or motor-driven vessels, generally with smart graceful lines, used for pleasure cruises or racing...1/2

3 ...GUA5... To offer as a stake in a bet; wager...4/5

4...FAC9....duplicate...4/4

5 ...NAR9... Consisting of or characterized by the telling of a story...3/4

6 ...SAC12... Grossly irreverent...1/2

7 ...WAR7... To provide adequate grounds for; justify...12/14

8 ...MAG8...Any of various compartments attached to machines, used for storing or supplying necessary materials...7/8

9 ...VAC6... Operating by means of suction...10/11

10 ...BAL7... To increase or rise quickly...10/10

11 ...LAB10... A place for practice, observation, or testing...4/4

12 ...PAM8... A short essay or treatise, usually on a current topic, published without a binding...2/2

13 ...TAN8... Something palpable or concrete...7/7

14 ...OBE9... A sphere of ecclesiastical authority...3/4

15 ...ABS7... Inattentiveness. ..4/4

16...DEC7 .. To give a false impression...4/4

17 ...EAS6... In all likelihood...3/3

18 ...HAN12... A large piece of cloth worn as a decorative article; a scarf...2/2

19 ...JEA8... Close vigilance...2/4

20 ...QUA8... The exact character of a proposition in reference to its universality, singularity, or particularity...7/7

21 ...REA9... Of or relating to the representation of objects, actions, or social conditions as they actually are...3/3

22 ...IDE7... In theory or imagination; theoretically...2/2

23 ...KNO9... Specific information about something...5/6

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APPENDIX TWO . . . . Illustrative preliminary work sheet for constructing the ranked-difficulty crossword-style vocabulary test in Appendix One .

Preliminary notes . . . . The target words on this work sheet have been excerpted from www.ESL.Desk.com , contains an alphabetized list of 507 frequently misspelled words. A random selection procedure has been used, namely, the first word in each alphabetical group. Appendix Three presents a point-by-point discussion of the general reasoning behind this test-construction method.

ENTRY FORMAT. . . . (a) target word. . . . (b) target-word clue. . . . (c) illustrative definition selected from those listed for the target word in the American Heritage Dictionary (AHD). . . . (d) word-frequency familiarity level (WF) as indicated by the number of definitions listed for the target word in (AHD). . . . (e) spelling-unfamiliarity (SU) level as indicated by the number of instances in which its spelling conflicts with its phonetic description in AHD. . . . (f) definition-unfamiliarity (DU) as indicated by ordinal-number position of the selected illustrative definition in the sequence of definitions for that word presented in AHD. . . . (g) clue familiarity level (CF) as indicated by the number of initial letters. . . . (h) level of test-item difficulty ID as indicated by the formula (SF/WF) times (DU/CF).

In this a-b-c-d-e-f-g-h sequence, the last five (all numerical expressions) appear within enclosures: parentheses for WF and brackets for SU, both of which are basic vocabulary features. These are followed by braces for DU and angles for CF, both of which represent test-maker decisions. Last to appear are the virgules, which enclose the results of our item-difficulty (ID) formula. The average level of test-item difficulty for these 23 items is 1.107, ranging from a low of 0.333 for CALENDAR to a high of 1.944 for KNOWLEDGE.

By way of illustration: The entry for ABSENCE is followed by its 3-letter spelling cue and then by a one-word definition from AHD. After this comes (d) its word-frequency familiarity level in parentheses, followed by (e) its spelling unfamiliarity level in brackets, (f) its definition-unfamiliarity level in braces, (g) its clue-familiarity level in angles, and (h) its overall level of test-item difficulty in virgules, as determined by our formula involving the preceding defg -variables.

TEST CONSTRUCTION WORKSHEET — 23 Test Items

Absence, ABS Inattentiveness. . . . ( 4 ) [3] {4} <3> /1.333\.

Balloon, BAL To increase or rise quickly. . . . (10) [2] {9} <3 > / 1.000\.

Calendar, CAL A schedule of events. . . . ( 6 ) [1] {3}<3> /0.333\.

Deceive, DEC To give a false impression. . . . ( 4 ) [4] {4}<3> /1.333\.

Easily, EAS In all likelihood. . . . (3) [4] {3} <3 > / 1.333\

Facsimile, FAC duplicate. . . . (4) [2] {4} <3> /0.667\.

Gauge, GUA To offer as a stake in a bet; wager. . . . (5) (4) {5} <3> /0.533\.

Handkerchief, HAN A large piece of cloth worn as a decorative article; a scarf. . . . (2) [4] {2} <3> /1.333\.

Ideally, IDE In theory or imagination; theoretically. . . . (2) [5] {2 }< 3> /1.667\.

Jealousy, JEA Close vigilance. . . . (2) [4] {2} <3> /1.333\.

Knowledge, KNO Specific information about something. . . . (6) [7 ]{ 5}<3> /1/944\.

Laboratory, LAB. . . . A place for practice, observation, or testing (4) [3] {4 }< 3> /1.000\.

Magazine, MAG Any of various compartments attached to machines, used for storing or supplying necessary materials. . . . (8) [3] {7} <3> /0.875\.

Narrative, NAR Consisting of or characterized by the telling of a story. . . . (4) [3] {3} <3> /0.750\

Obedience, OBE A sphere of ecclesiastical authority. . . . (4) [5] {3} <3> /1.250\.

Pamphlet, PAM A short essay or treatise, usually on a current topic, published without a binding. . . . (2) [3] {2} <3> /1.250 \ .

Quantity, QUA The exact character of a proposition in reference to its universality, singularity, or particularity. . . . . (7) [4 ]{ 7}<3> /1.333\.

Realistic, REA Of or relating to the representation of objects, actions, or social conditions as they actually are. . . . . (2)[3] {2 }< 3> /1.500\ .

Sacrilegious, SAC Grossly irreverent. . . . (2) [5] {1 }< 3> /0.833\.

Tangible, TAN Something palpable or concrete. . . . (7) [3] {7 }< 3> /1.000\.

Vacuum, VAC Operating by means of suction (11) [3] {10 }< 3> /0.909\

Warrant, WAR To provide adequate grounds for; justify. . . . (14) [3] {12 }< 3> /857\

Yacht, YAC Any of various relatively small sailing or motor-driven vessels, generally with smart graceful lines, used for pleasure cruises or racing. . . . (2) [3] {1 }< 3> /0.500\ .

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APPENDIX THREE . . . . General Discussion . . . . This follows the a-b-c sequence of points covered at the beginning of Appendix Two . It's intended as a guide for parents and educators who want to constructed their own tests. So it covers some of the problems involved. Overall, though, I think what's here makes a strong case for the National Standard Vocabulary Test construction method as a practical tool for redemocratizing and relegitimizing the assessment of what, next to aging, is a crucial element for all Americans, young and old — namely vocabulary power.

(a) target word . . . . To be authoritative a word list should come from an external source, ideally one that's publicly accessible, e.g., an internet spelling list ( googling GRE VOCABULARY will produce 37,000 hits, for example), flash cards, etc. . . . Senior centers now offer anti-Alzheimer's programs that combine spelling challenges with crossword “offbeat definition” challenges.

(b) target-word clue . . . . The choice of a three-letter clue makes the test item easier, along with compensating for the absence of conventional crossword puzzle clues like visual design and word-letter juxtaposition. If desired, a do-it-yourself phonetic transcription could be substituted, e.g., aeb”sehns for ABSENCE, bael-oon ” for BALLOON, etc. My experience, even with first graders, indicates that simple exposure is enough to produce a pronunciation mastery of a system that in effect duplicates the “natural spelling” of most orthographically illiterate intelligent eighth graders.

This “natural spelling” system is what's used today in many foreign-language teaching programs and in the Scholastic Children's Dictionary.

And it's certainly far better suited to computer keyboards than the “Noah Webster” system used by AHD and other desk dictionaries today. . . . Though more time-consuming to construct, phonetic-transcription clues are well worth using, especially with non-native speakers of English.

(c) illustrative definition selected from those listed for the target word in the American Heritage Dictionary (AHD) . . . . In crossword puzzle terms defining ABSENCE as “inattentiveness” comes across as somewhat sneaky. But it certainly underscores the point that an American English word is apt to have several definitions listed for it, not just one. Also, the current emphasis upon “choosing the word-meaning that fits” in reading-comprehension tests like the FCAT certainly legitimizes choosing a further-on AHD definition (#4) from AHD.

It should be noted here that dictionaries vary in their use of numerals and letters ( a,b,c , etc.) in identifying elements in a definition sequence, thereby requiring, for example, that “1a, 1b, 2, 3, 4a, 4b, 4c” be renumbered as “1, 2, 3, 4, 5, 6, 7. . . . In general the sequence of dictionary definitions is from basic, e.g., “the state of being away” to secondary, e.g., “inattentiveness.” But a shift to another part of speech can often bring the basic sense back in a higher numerical position, as in high-frequency words like RUN or CAP.

(d) word-frequency familiarity level (WF) as indicated by the number of definitions listed for the target word in (AHD) . . . This construction procedure uses a word's number of definitions as an indication of how frequently it's actually used TODAY in speech and writing. The common sense justification for this is that frequency of use and multiple meanings go together in both speech and in a dictionary.

But even theoretically, it's worth noting that the British National Corpus, which contains 600 million word items, and the Global English 15,000 word list, have had to “massage” vocabulary elements like the possessive (‘S), which is listed as a separate word. . . . In the interests of both accessibility and authority, the American dictionary is actually a better “invisible” word-frequency list than current computer constructs.

(e) spelling-unfamiliarity (SU) level as indicated by the number of instances in which its spelling conflicts with its phonetic description in AHD . . . . Determining this number requires a comparison of target word's spelling with its phonetic transcription in AHD. For consonants the comparison is easy and quick.

For vowels and diphthongs , on the other hand, one must stick resolutely with five basic letter-sound correspondences, namely, A as in CAT and AT, E as in PET and GET, I as in IT and SIT, O as in OH and ROAD, and U as in MUTE and SUIT. All the other correspondences (the U-sound of MOON, etc.) should be counted as irregularities. . . . This is not to say that English spelling is a complete disaster. It does have “rules” (Paul Hanna of Stanford has enumerated 600 of them). But most of us have to learn it by rote, with the result that our spelling usually gets worse, not better, as we grow older.

(f) definition-unfamiliarity (DU) as indicated by ordinal-number position of the selected illustrative definition in the sequence of definitions for that word presented in AHD . . . . It's worth noting here that the sequence of definitions represents an informal “definition frequency list,” since the opening definitions are more frequently used in speech (and hence more familiar), along with being closer to the original meaning of the word, etymologically considered.

(g) clue familiarity level (CF) as indicated by the number of initial letters . . . . This choice represents a major construction option for the test designer, especially one who wants to produce an encouraging experience for anxious test takers, young and old.

(h) level of test-item difficulty ID as indicated by the formula (SF/WF) times (DU/CF) . . . . Every home computer can make this computation. . . . It should be emphasized, though, that with small groups our first three items — target word, clue, and definition — are all that's required. The remaining five are there to establish the credibility of the test and its results, especially when used to compare, say, the performance of a group of senior citizens with that of a high school honors English class.

TEST CREDIBILITY. . . . Cheapness . . . . Leaving elements d-e-f-g-h aside, this kind of test is disgracefully cheap to construct, especially with the in-the-computer capacity of AHD to search, copy, and paste.

By way of illustration. here are [starting at 8:30AM ] ten word-clues chosen in sequence from the Gettysburg Address, each followed by a numbered definition from the American Heritage Dictionary: FAT6.... 5. An early form; a prototype. NAT6 .... 2. The government of a sovereign state. EQU5 .... 6. Tranquil; equable. CIV5 .... 6. Being in accordance with or denoting legally recognized divisions of time , GRE5.... 11. Grand; aristocratic. FIE5 .... 5a. An area of human activity or interest, PRO6 .... 8. Worthy of the name, GRO6 3. To move with noisy friction. NOT4 .... 4. A comment or an explanation, as on a passage in a text., CAU5.... 6. A subject under debate or discussion. [ finished at 8:53 AM (broken by one short phone call).

With ten items taking 25 minutes, we can fairly state our basic item-construction time as 2.5 minutes per topic, thereby permitting a nonprofessional test designed to construct a 100-item test in 250 minutes, as opposed to the 50 hours a professional psychometrist would need for a conventional multiple choice test with at least three distractors (or “foils”) per item.

Our cheapness feature extends into actual test taking, since only one-word answers are required (just like Jeopardy), and these can be translated into a multiple choice framework via asking for the first omitted vowel letter in each word, i.e., A, E, I, O, U, Y, or “none of these.” Best of all, it reduces the cheating problem by permitting multiple versions of the “same” basic test.

Authority . . . . Thanks to their use of a nationally respected dictionary, tests using this construction method can fairly lay claim to the same authority as any “high stakes test” (e.g., FCAT, SAT, ACT, GED, etc). As Richard Phelps has pointed out in Killing the Messenger, such tests are EXTERNAL, which means they're not depended upon local design and interpretation. They are also STANDARDIZED, thanks to each test's use same numerically comparable elements item by item.

Finally, and most important, these test results are SIGNFICANT. In past-tense terms, this means that their results can be used to measure the productive impact of vocabulary building activities like reading, poetry memorization, direct vocabulary study, etc. . . . In present-tense terms this means their results can be compared with other tests and conclusions drawn regarding the predictability of future scores on tests other tests that attempt to measure vocabulary power.

Timeliness . . . . Education reform is today in the position of a physician trying to take a patient's temperature with a broken thermometer. Day by day and year by year, students need to know exactly where they stand on a vocabulary scale just as much as their parents need to know where they stand on a battery of cholesterol tests. These tests are above all PUBLIC instruments that can be explained and imitated in any setting , be it a senior citizen's center, a home schooling program, or the Los Angeles Unified School District . They are also PRODUCTIVE, since they focus upon the primary building blocks of reading comprehension, namely, word recognition and multiple-meaning fluency. Finally, they can justifiably be called PATRIOTIC by virtue of their emphasis upon American English as a national, complex, civilized language.

TO SUM UP . . . . This project started with a recognition that spelling bees and crossword puzzles are, and have been for many years, central elements in American society. It has attempted to fuse them together into a single, flexible testing instrument that anyone can use as a “silent, crossword-style spelling bee.” It's fundamentally a very simple idea and so, I hope, is the arithmetic.

National Standard Vocabulary Test, I must admit, is a rather pretentious label for “silent, crossword-style spelling bee.” But I feel it's accurate, enough so focus our attention upon what's truly a national problem, not just a local one.