At 03:55 PM 7/24/01 -0400, Donald Burrill wrote: >Hi, Dennis! > Yes, as you point out, most elementary textbooks treat only SRS >types of samples. But while (as you also point out) some more realistic >sampling methods entail larger sampling variance than SRS, some of them >have _smaller_ variance -- notably, stratified designs when the strata >differ between themselves on the quantity being measured. sure ... i know that (then i said) ... but, we KNOW that most samples are drawn in a way that is WORSE than SRS and you responded >I don't think _I_ know this. I know that SOME samples are so drawn; >but (see above) I also know that SOME samples are drawn in a way that >is BETTER than SRS (where I assume by "worse" you meant "with larger >sampling variance", so by "better" I mean "with smaller sampling >variance"). i think we do know this ... if you enumerate all the situations you know of where sampling from some larger population has been done ... i would bet a dollar to a penny that ... the sampling plan is WORSE than SRS ... so, i would suggest that the NORM is worse ... the exception is SRS or better i don't think books spend nearly enough time ... on the fact that most day in day out samples are taken in a pretty pathetic way ... >I perceive the "basic problem" as the fact that sampling variance is >(relatively) easily calculated for a SRS, while it is more difficult >to calculate under almost _any_ other type of sampling. sure ... but, books ONLY seem to discuss the easy way ... and i do too ... because it seems rather straight forward ... but, given time constraints ... it never goes further than that ... > Whether it is enough more difficult that one would REALLY like to avoid >it in an elementary course is a judgement call; but for the less >quantitatively-oriented students with whom many of us have to deal, we >_would_ often like to avoid those complications. Certainly dealing with >the completely _general_ case is beyond the scope of a first course, so >it's just a matter of deciding how many, and which, specific types of >cases one is willing to shoehorn into the semester (and what "previews >of coming attractions" one wishes to allude to in higher-level courses). however, we do become sticklers for details ... and force students to use the correct CVs, make the right CIs, ... do the t tests correctly ... and heaven forbib if you get off a line or two when reading off the values from the t table ... >Seems to me the most sensible "adjustment" (and of a type we make at >least implicitly in a lot of other areas too) is > = to acknowledge that the calculations for SRS are presented > (a) for a somewhat unrealistic "ideal" kind of case, i would stress ... really unrealistic ... > (b) to give the neophyte _some_ experience in playing this game, and then leave them hanging???? >Some textbooks I have used (cf. Moore, "Statistics: Concepts & >Controversies" (4th ed.), Table 1.1, page 40) present a table giving the >margin of error for the Gallup poll sampling procedure, as a function of >population percentage and sample size. Such a table permits one to show >how Gallup's precision varies from what one would calculate for a SRS, >thus providing some small emphasis for the cautionary tale one wishes to >convey. but ... in moore and mccabe ... the stress throughout the book ... is on SRSes ... and no real mention is made nor solutions to ... the problems that it will be a rare day in analysis land ... for the typical person working with data ... to be doing SRS sampling ... it's just not going to happen the bottom line, IMHO, is that we glide over this like it is not a problem at all ... when we know it is > ------------------------------------------------------------------------ > Donald F. Burrill [EMAIL PROTECTED] > 184 Nashua Road, Bedford, NH 03110 603-471-7128 _________________________________________________________ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
