The following demonstration in SPSS syntax shows that the conservative bias of using t at all times in estimating the CI of a percentage usually doesn't pass the "so what test". If one is doing HT, perhaps the best bet is to do both tests and see if the different p's result in differences in material/clinical/theoretical conclusions.
In these types of analysis, the uncertainty due to sampling is only part of total error. (perhaps only a small part). The conventional margin of error around an obtained percentage is t*se or z*se where the t or z if for the 95% confidence level. This demo assumes an obtained percentage of 50% because 50% has the widest CI. This demo follows the convention that CIs around a sample percentage are rounded away from the mean to whole percentage points. new file. input program. loop df = 8 to 50. compute t_05 = idf.t(.05,df). compute z_05 = idf.normal(.05, 0,1). end case. end loop. loop df = 55 to 300 by 5. compute t_05 = idf.t(.05,df). compute z_05 = idf.normal(.05, 0,1). end case. end loop. end file. end input program. formats t_05 to z_05 (f6.2). compute se= 100* sqrt((.5*.5)/(df+1)). formats se (pct5.2). compute mart_05 = abs(t_05 * se). compute marz_05 = abs(z_05 * se). formats mart_05 to marz_05 (pct5.0). execute. hope this helps put the situation in perspective. Art [EMAIL PROTECTED] Social Research Consultants University Park, MD USA In Ethics I.3, Aristotle says, "we must be satisfied to indicate the truth with a rough and general sketch: when the subject and the basis of a discussion consist of matters which hold good only as a general rule, but not always, the conclusions reached must be of the same order. . . . For a well-schooled man is one who searches for that degree of precision in each kind of study which the nature of the subject at hand admits: it is obviously just as foolish to accept arguments of probability from a mathematician as to demand strict demonstrations from an orator." Alan McLean wrote: > In practice the population is almost always a model - at best it is > ill defined. So the value of sigma is virtually never meaningfully > 'known'. At the same time, a role of statistical analysis is to save > one from jumping to unwarranted conclusions - so one should be > conservative. On this basis, it is preferable to use t even when you > might think z is reasonable. > > Further, with computers to do the analysis, it is just as easy to use > t as to use z. > > So - always use t, never z. > > And, yes, p values are better than critical values. (Unless you are > stuck out in the desert without a computer....) > > Alan > > > On Sunday, November 24, 2002, at 06:03 AM, Jay Warner wrote: > >> the "two question" question was beaten to death, but I can't help >> sticking myself >> into this one. It's too old to ignore :) >> >> when we compare two groups, i.e., one indep. categorical variable of >> two levels, >> near continuous & interval or ratio scale response, we have a z or t >> test on our >> hands. >> >> the 'party line' is that if sigma is 'known' you can use the z, if >> not use t. And >> often, to help 'simplify' things, the book will say that when the >> sample size is >> over 30, you can use z anyway - the estimate of sigma is 'close enough.' >> >> Please don't side track now on the population size - it is most often >> effectively >> infinite. >> >> What is meant by 'known sigma'? It means that you have measured a >> heck of a lot >> of items (30 or more, if you believe the book) to estimate sigma of the >> population, or you have been handed sigma from someone else who has >> made the >> measurements. In a manufacturing environment, that someone is >> typically the QA >> dept., if they follow this logic. In typical business-related >> analyses the >> origins of 'known' sigmas may be less clear. >> >> How good (accurate, precise, unbiased) is this estimate of sigma? >> When it comes >> from someone else, we don't know, a nd often can't know. So we call >> it 'known' >> and proceed. But the number we have is still an estimate of the >> population sigma, >> which in principle we can never measure exactly (most cases). And >> often, we have >> no way of assessing how well that number applies to the current >> situation. Did >> the original sigma estimate come from the same defined population as >> the current >> data? Did these samples use a different paint? Did this survey >> contact people >> from the same part (statistically identical group of people) of town? >> >> May I try a different dichotomy? >> >> When I am given the estimated sigma from somewhere else, so that I >> can't assess >> the validity of it, I call this an _external_ estimate of sigma. I >> accept it with >> the usual reservations, and proceed to do the problem. The equation >> will be a z >> test type. >> >> When I am not handed sigma on a platter, but must estimate it from >> the sample >> data, I call that an _internal_ estimate of sigma. The estimate >> definitely >> applies to the population at hand, to be considered & evaluated as >> ever. the >> equation will be a t test. >> >> Notice: No n >= 30. As some mentioned recently, with machines we >> have p-values >> for t tests, that were not feasible in the dark past without the >> machines. >> therefore, there is no need to decide when n is 'close enough' to use >> a z test. >> >> Using this method to split between the two test types, there is less >> confusion, >> and we can retain a healthy skepticism about the validity of that >> external >> estimate of sigma. >> >> What are the holes in this approach? >> >> Cheers, >> Jay >> >> "Robert J. MacG. Dawson" wrote: >> >>> Paul Bernhardt wrote: >>> >>>> Now, if we can only get over the arbitrariness of the n<30 cut-off for >>>> use of t vs z and teach: use z when you know sigma and t when you >>>> don't. >>>> (Triola, as much as I like some of its choices, still retains this) >>>> <sigh> >>> >>> >>> How about (at least for social & health sciences): use t >>> when you don't >>> know sigma, and speak to a statistician when you think you do? >>> >>> -Robert Dawson >>> .. >>> .. >>> ================================================================= >>> Instructions for joining and leaving this list, remarks about the >>> problem of INAPPROPRIATE MESSAGES, and archives are available at: >>> .. http://jse.stat.ncsu.edu/ . >>> ================================================================= >> >> >> -- >> Jay Warner >> Principal Scientist >> Warner Consulting, Inc. >> 4444 North Green Bay Road >> Racine, WI 53404-1216 >> USA >> >> Ph: (262) 634-9100 >> FAX: (262) 681-1133 >> email: [EMAIL PROTECTED] >> web: http://www.a2q.com >> >> The A2Q Method (tm) -- What do you want to improve today? >> >> >> >> >> .. >> .. >> ================================================================= >> Instructions for joining and leaving this list, remarks about the >> problem of INAPPROPRIATE MESSAGES, and archives are available at: >> .. http://jse.stat.ncsu.edu/ . >> ================================================================= > > > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
