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Up With Fabrication, Appreciating Z, Difficult Dinners, and Other Matters.
By DANIEL SELIGMAN RESEARCH ASSOCIATE Sarah E. Morgenthau

(FORTUNE Magazine) – Z Power Curious letter, Z. We are sitting here frowning over Webster's New World Dictionary, where Z is nonchalantly stated in definition No. 4 to be ''a symbol for the 26th in a sequence or group (or the 25th if J is omitted).'' Puzzling, eh? Why are they hinting that J has a below-average attendance record? And having raised the issue of omissibility, why not forthrightly add that Z would be only 24th if some other character also failed to show for the big party? And yet even more puzzling is the failure of New World, which is now general issue at FORTUNE, to evidence awareness of Z's role on the great stage of public policy, where many a stormy scene has been enacted over its implications for our favorite subject -- affirmative action. As anyone will cheerfully testify after reading Judge John A. Nordberg's 163-page landmark decision in Equal Employment Opportunity Commission v. Sears, Roebuck & Co., the judicator in question would have been hard pressed to fill all that space if he didn't have to keep returning to the social and statistical significance of z values (the z being ordinarily lower-cased in this context). Z values help you get more mileage out of the standard deviation (SD). The SD measures the extent to which your results deviate from the mean expectation. When you have a normal distribution of results -- meaning that they can be represented by the famous bell-shaped curve -- then 68% of your universe is within one SD of the average, 95% is within 1.96 SDs, and 99.9% is within 3.29 SDs. In other words, there is only one chance in 1,000 that results will differ from mean expectations by more than 3.29 SDs. A major virtue of the z- value tables is that they enable you to compose comparable statements about the odds associated with any particular SD. In a passage that has left a generation of statistics students yearning to blow spitballs at the author, mathematician H. T. Hayslett Jr. of Colby College proclaims in his best- selling Statistics Made Simple that the tables of z values ''are a tremendous labor saver and you should be appreciative of this fact each time you use them.'' But about affirmative action. Z values have been endlessly onstage in the back-and-forth on this issue because complainants keep using the values to argue that some employment pattern or other could not have occurred by chance / and so there must have been discrimination. In the Sears case, the EEOC's statistical expert lengthily testified about z values reflecting the fact that female salespersons at the company were heavily underrepresented in the higher-paying ''commission sales'' jobs; on a nationwide basis, he averred, the gap between actual and expected results ranged from 11.9 to 45.1 SDs. The probability of any such gaps occurring by chance is believed to be substantially less than that of your finding a rhinoceros in the bathtub tonight. Wishing to gain the approbation of the New York Times editorial board, the median federal judge generally stops play at this point in the argument and finds in favor of the kvetchers. However, Nordberg did something quite remarkable. He actually looked at the record of sales applicants at Sears and then said out loud that the genders differed behaviorwise. ''Male applicants,'' he wrote, ''were more likely to be interested in . . . hardware, automotive, sporting goods, and the more technical goods, which are more likely to be sold on commission at Sears . . . Men . . . were usually not interested in fashions, cosmetics, linens, women's or children's clothing, and other household small-ticket items . . . Custom draperies . . . was one division in which women were willing to sell on a commission basis . . . Very few men were willing to sell draperies.'' The EEOC started nagging at Sears in 1973. It filed suit in 1979. The trial before Nordberg lasted ten months. And yet the exercise seems not to have been a total waste of time: a federal judge has actually learned that men gravitate more readily to sporting goods than draperies and women prefer cosmetics to hardware. Also that we should curb our appreciation of old number 26.