Dr. Gallagher and Edstat newsgroup: Here's my take on the MCAS and boxplots.
(1) I agree with Eugene Gallagher and others in that the question about boxplots on the MCAS is poor, since the correct answer depends on whether you learned the "Tukey" boxplot (that indicates outliers) or the "quick" boxplot (that ignores the possibility of outlers and merely extends the whiskers to the minimum and maximum). It is typical in college-level stat texts to use the Tukey boxplot, but I believe (I may be wrong) that high-school level books tend to use the "quick" boxplot. (2) Gallagher is correct in that most standard software packages (such as SPSS, SAS, S-plus/R, Minitab?) construct the "Tukey" boxplot. However I have not seen anyone mention the fact that the TI-83 graphing calculator can actually construct either of the two types of boxplots. In the StatPlot menu, the TI-83 has a Boxplot option (for what TI-83 calls a "regular" boxplot that I refer to as a "quick" boxplot) and a ModBoxplot option (this is a "modified" or Tukey boxplot). I believe this is pertinent because I assume that many secondary math classes use TI calculators. (3) My solution in my Introduction to Statistics class, therefore, is to discuss both kinds of boxplots. I use the Moore/McCabe text, which describes the Tukey boxplot. However, since many of my students will be teaching at the middle-school or high-school level, I also point out the existence of the "quick" boxplot. I do stress that the Tukey boxplot is superior, since it indicates potential outliers. (4) If the Massachusetts Department of Education really wants to include a boxplot item on the test, it should either be a multiple choice question written so that the correct answer is the same no matter which type of boxplot one was taught, or an open-ended question where the students actually create boxplots for 2 data sets and compare/contrast the 2 distributions. The readers then should be aware of both types of boxplots when assessing the question. That's my two cents, anyway Chris Mecklin At 02:33 AM 10/05/2001 +0000, EugeneGall wrote: >During the last week in August, there was a lengthy thread on sci.stat.edu >about problems with the probability and statistics questions in MCAS, the high >stakes test required for graduating from a MA public high school. > >Shortly after participating in that thread, I wrote up my analyses of 6 of the >41 questions on the 2001 exam and 4 of the 42 questions on the 2000 exam. I >mentioned this group and several people who posted on that thread in my >commentary. Four of the 2000 & 2001 questions were in the area of statistics >and probability. The most severe problems appear to be testing on concepts >intended only for 11th & 12th graders - a violation of the basic principle of >MCAS. My commentary includes cross-references to these learning standards. > >I sent my critique to the Dept. of Education in Aug. so that they could delete >the flawed questions from the scores on which failure decisions are based. As >described in the newspaper article linked below, there are no appeals now >possible in MCAS for failing because of invalid questions. Students must pass >this MCAS math test, or one of 4 retakes, to graduate in 2003. 45-50% of MA >10th graders failed the tests offered from 1998 through 2000. > >The MA Dept of Education's Press spokesman, Heidi Perlman, is quoted in a >Berkshire Eagle story that DOE stands behind all of the questions I discussed: > "But the Department of Education dismisses the professor's analysis > of the >test and stands by all its questions. In fact, the department changed its >scoring policy on the 10th-grade tests this year to safeguard against errors, >officials said. .. "Some of the questions could've been slightly better >worded, >but in total none of them are invalid questions," said department spokeswoman >Heidi Perlman. She said it was reviewed by department staff, but >officials did >not agree with Gallagher's analysis. "We don't believe his criticisms are >valid," Perlman said. > >Ms Perlman's comments can can be read in the following news article from the >Berkshire Eagle, by Jennifer Fenn: >http://search.newschoice.com/ArchiveDisplay.asp?story=d:\index\newsarchive >s\ne\nebe\fpg\20011002\1122674_mcaserrors.txt&source=www%2Eberkshireeagle% >2Ecom&puid=2269&paper=Berkshire+Eagle+Online > >One reporter told me that he wasn't sure how to handle my analysis of these >questions because DOE says the questions are all valid, and I say that they >aren't. He said that he's not a mathematician and can't judge who is >correct. >I said publish the questions, and let the mathematically literate readers >respond. > >I would appreciate what the members of this group think about the questions, >especially about the statistics and probability questions. I realize that my >28-p commentary is a bit much, but the issue is very important to the Class of >2003 and other citizens of MA. > >The math/stats questions, with my analysis can be viewed at: >http://www.es.umb.edu/edg/MCAS/mcasproblems.pdf > >Gene Gallagher >UMASS/Boston > > >================================================================= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >================================================================= Christopher J. Mecklin, PhD Assistant Professor Department of Mathematics and Statistics Murray State University Murray, KY 42071 Phone: 270 762-5437 Fax: 270 762-2314 http://campus.murraystate.edu/academic/faculty/chris.mecklin/index.htm ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
