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Castaneda v Partida: frequentist treatment is contained of An interesting and celebrated example of application of a Ztest for a proportion in a verdict of the U.S. Supreme Court. The beginning of the story a lower court Partida seeks habeas is told in s document s relief contending that he was denied due process and equal pro- e grand jury of Hidalgo County, Teras, which indicted him, was onal underrepresented by Mexican-Americans. This went to the U.S. Supreme court which ru CASTANEDA .PARTIDA, Decided March 23, 1977 eld: Based on all the facts that bear on the grand jury discrimination issue, astial disparities (the county population was 79% Merican-American, but, orer an 11-yer period only 39% ofthose summoned for grand jury service were Merican-American), the methd ef jury selection, and any other relevant testimony as to the manner in which the se- ient to demonstrate a prima facie case of intentional diserimination in grand jury selection, Under this standard, the proof offered by respondent was sufficient to demonstrate a prima facie case of discrimination in grand jury selection. The statistical evidence is given in a footnote. We again cite the original text and we will then reproduce the reasoning using our mathematical notation. l Footnote 17 | if the jurors wore drawn randomly from the gemoral population, then the mumber of Mexican-Amcricans in the sample could be modeled by a binomial distribution. See Finkelstein, The Application of Statistical Decision Theory to the Jary Discrienination Cases, 80 Harv. L. Rev. 338, 353-356 (1966). See generally P. Hoel, Introduction to Mathematieal Statistics 58-61, 79-86 (4h ed. 1971); F. Mosteiler, R. Rourke, & G. Thomas, Probability with Statistical Application, 130-116, 270-291 (2d ed. 1970). Given that 79.1% f the popalation in Mexican-Americas, the expected aumber of Mexdean-Americans among the 870 persons summoned to serve as graad jarors over the 11-year period is approaximately ES5. The obeerved aumber is 339. Of course, in any given drawing some luctuation from the expected number is prodictod. The important point, however, is that the statistical model shows that the results of a random drawing aro likely to fall in the vicinity of the expocted value. Scc F. Mosteller, R. Rourke, & G. Thomas, supra, at 270-290. The measure of (430 U.S. 482, 497] the predicted fuctuations from the expected value is the standard deviation, defined for the hinouial distribution as the square root of the produet of the total mmher in the sample (here 870) times the probsbility of selecting a Mexican-American (0.791) tiames the probability of selecting a hou-Mexicad-Anerican (0.209). Id, at 213. Thus, in this case the staudard deviation is approxinuately 12. As a general rule for such large samples, if the difference between the expected value and the observed number is greater than two or three standard deviation, thea the hyp bere reflect a diference between the expected and observed number of Mexican-Americans of approxim othesis that the jury drawing was random would be suspect to a social scientist. The 11-year data ately 29 standared deviations. A detailed caleulation reveals that the lkelihood that such a substantial departure from the expected value would occur by chance is less than 1 in 10140. The data for the 2 1/2-year period during which the State District Jndge supervised the selection process similarly support the inference that the exclusion of Mexican-Americans did not occur by chance. Of 220 persons called to serve as grand jurors, only 100 were Mexican-Americans. The expected Mexican-Americau representation is approximately 174 and the staudard deviatiou, as calculated fron the binonial odel, is approximately six. The discrepancy between the expected and obscrved valucs is more than 12 standard http://cases,justia.com/us-court-of-appeals/F2/524/481/ only coueln

what is the use of statistics in the article. i need it to be detailed

Answer 1

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