Re: Help with stats please
On 24 Jun 2001 13:54:56 -0700, [EMAIL PROTECTED] (dennis roberts) wrote: > At 12:20 PM 6/24/01 -0700, Melady Preece wrote: > >Hi. I am teaching educational statistics for the first time, and although I > >can go on at length about complex statistical techniques, I find myself at a > >loss with this multiple choice question in my test bank. I understand why > >the range of (b) is smaller than (a) and (c), but I can't figure out how to > >prove that it is smaller than (d). > > > >If you can explain it to me, I will be humiliated, but grateful. > > > > > >1. Which one of the following classes had > > the smallest range in IQ scores? dr > > of course, there is nothing about the shape of the distribution of any > class ... so, does the item assume sort of normal? in fact, since each of > these classes is probably on the small side ... it would be hard to assume > that but, for the sake of the item ... pretend > [ snip ] Good point, about normality. And who provides the "test bank" of items? The testee has to *assume* a certain amount of normality, which is not stated; and you have to *assume* that the N is greater than 2 -- or else the claim is *not* true. It seems to me that when the reader has to supply unstated technical assumptions like these, the test-validator should be careful: I suspect that success on THIS item is context-dependent. There is less problem, if everyone is always given exactly the same test. That *is* an issue, if different sets of items are extracted for use, at different times -- which is what I think of, when I hear "item bank." Could other items clue this answer? That is, Do other items STATE those assumptions? Do other items REQUIRE those assumptions if you are going to answer them? - If the user has seen items in his selection from the "bank", is he more apt to make the intended assumptions here? I expect that a conscientious scale developer is interested of minimizing the work required for validation; and he would avoid this problem if he noticed it. Answer (b) seems right, if the reader is supposed to describe what you would expect 'for moderate sized samples, with scores that are continuous and approximately normal.' -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Help with stats please
Melady Preece wrote: > > Hi. I am teaching educational statistics for the first time, and although I > can go on at length about complex statistical techniques, I find myself at a > loss with this multiple choice question in my test bank. I understand why > the range of (b) is smaller than (a) and (c), but I can't figure out how to > prove that it is smaller than (d). > > If you can explain it to me, I will be humiliated, but grateful. I'm not sure why you would be humiliated, even if the answer were obvious. You can't prove the range of (b) is smaller than (d). The question isn't even worded clearly. (b) says "a range of from 93 to 119" They range from 93 to 119 and have a range of 26 (subject to any typographical errors I might make!), but "a range from to" is just...sloppy. If (d) were a small class, say 2 students, the upper and lower quartiles could be 90 and 110, depending on the precise definition of quartile being used, and the range would be 20, even with normality, etc. > 1. Which one of the following classes had > the smallest range in IQ scores? > > A) Class A has a mean IQ of 106 >and a standard deviation of ll. > B) Class B has an IQ range from 93 >to 119. > C) Class C has a mean IQ of 110 >with a variance of 200. > D) Class D has a median IQ of 100 >with Q1 = 90 and Q3 = 110. > > The test bank says the answer is b. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Help with stats please
In article <006901c0fce2$d07c7640$[EMAIL PROTECTED]>, Melady Preece <[EMAIL PROTECTED]> wrote: >Hi. I am teaching educational statistics for the first time, and although I >can go on at length about complex statistical techniques, I find myself at a >loss with this multiple choice question in my test bank. I understand why >the range of (b) is smaller than (a) and (c), but I can't figure out how to >prove that it is smaller than (d). >If you can explain it to me, I will be humiliated, but grateful. >1. Which one of the following classes had > the smallest range in IQ scores? > A) Class A has a mean IQ of 106 > and a standard deviation of ll. > B) Class B has an IQ range from 93 > to 119. > C) Class C has a mean IQ of 110 > with a variance of 200. > D) Class D has a median IQ of 100 > with Q1 = 90 and Q3 = 110. >The test bank says the answer is b. >Melady What are the sizes of the classes? What are the distributions of the scores in the various classes? If the scores are random from some probability distribution, and other than the sample data there is no additional information about the actual scores, for other than extremely small classes (10 is large here), not many absolute statements can be made. I CAN tell that class C cannot have a smaller range than 29, because otherwise the variance cannot be 200, and scores are given as integers. If they are not integers, it goes down slightly. Even if the model is the totally untenable normal distribution, the scores are RANDOM, and the samples need not look at all normal. As to what was bothering you, what are the quantiles of the normal distribution? -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Help with stats please
On Sun, 24 Jun 2001, Melady Preece wrote in part: > I am teaching educational statistics for the first time, and although I > can go on at length about complex statistical techniques, I find myself > at a loss with this multiple choice question in my test bank. I > understand why the range of (b) is smaller than (a) and (c), but I > can't figure out how to prove that it is smaller than (d). > 1. Which of the following classes had the smallest range in IQ scores? > > A) Class A has a mean IQ of 106 and a standard deviation of ll. > B) Class B has an IQ range from 93 to 119. > C) Class C has a mean IQ of 110 with a variance of 200. > D) Class D has a median IQ of 100 with Q1 = 90 and Q3 = 110. > > The test bank says the answer is b. Right. Since you're happy that range(B) < range(A) and range(B) < range(C), I'll focus on (B) vs. (D). In (B), the entire _range_ is from 93 to 119: 26 (or 27, depending on how you choose to define "range") points. In (D), the central half of the distribution is from 90 to 110: the interquartile range (IQR) is 20 points, symmetric about the median; the full range must therefore be greater than 20. Now, _if_ the distribution is normal (which may be what we were to assume from the allegation that these are IQ scores; although as Dennis has pointed out, ille non sequitur -- unless these are rather large classes AND NOT SELECTED BY I.Q. (or by any variable strongly related to I.Q.)), then 10 points from Q1 to median (or from median to Q3) represents 0.67 standard deviation, which implies a standard deviation of about 15, which is larger than the standard deviation in (A) and slightly larger than that in (C). However, we need not invoke the normal distribution. We observe that the distribution in (D) is at least approximately symmetric (insofar as the quartiles are equidistant from the median). If we may assume also that the distribution is unimodal (which I should think reasonable), it then follows (from the "tailing off" of distributions as one approaches the extremes) that the distance from minimum to Q1 (and the distance from Q3 to maximum) is greater than the distance from Q1 to median (or median to Q3). This implies that the range of the distribution exceeds twice the interquartile range: that is, range(D) > 2*20 = 40. Since the range in (B) is only 26, clearly the range of (B) is less than the range of (D). If any part of this argument remains unclear, I'd be happy to attack it again. A rough sketch should make things pretty obvious, but it's a bit of a nuisance to draw pictures in ASCII characters! --DFB. Donald F. Burrill [EMAIL PROTECTED] 184 Nashua Road, Bedford, NH 03110 603-471-7128 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Help with stats please
At 12:20 PM 6/24/01 -0700, Melady Preece wrote: >Hi. I am teaching educational statistics for the first time, and although I >can go on at length about complex statistical techniques, I find myself at a >loss with this multiple choice question in my test bank. I understand why >the range of (b) is smaller than (a) and (c), but I can't figure out how to >prove that it is smaller than (d). > >If you can explain it to me, I will be humiliated, but grateful. > > >1. Which one of the following classes had > the smallest range in IQ scores? of course, there is nothing about the shape of the distribution of any class ... so, does the item assume sort of normal? in fact, since each of these classes is probably on the small side ... it would be hard to assume that but, for the sake of the item ... pretend in addition, it does not say to assume the population of IQ scores has mean = 100 and sd about 15 ... so, whether this plays a role or not, i am not sure BUT ... > A) Class A has a mean IQ of 106 >and a standard deviation of ll. at least about 2 units of 11 = 22 on each side of 106 ... range about 45 or so or more > B) Class B has an IQ range from 93 >to 119. well, range here is about 26 ... less than in A for sure > C) Class C has a mean IQ of 110 >with a variance of 200. variance of 200 means an sd about 14 ... so 2 units of 14 = 28 on each side of 110 ... range must be 50 or more ... similar to A but, more than C > D) Class D has a median IQ of 100 >with Q1 = 90 and Q3 = 110. 25th PR = 90 and 75PR = 110 ... IF we assumed the class was ND ... then the mean would be about 100 too ... and since -1 for SD below the mean and +1 SD above the mean would give your roughly the 16th PR and 84th PR ... Q1 and Q3 are NOT that far out ... so, the SD must be at least 10 or more ... thus, 2 units of at least 10 = 20 on either side of 100 = range of at least about 40 ... probably less than A or C ... but, more than B ... B is probably the best of the lot BUT, i am NOT sure what the real purpose of this item is ... >The test bank says the answer is b. > >Melady > > > > > >= >Instructions for joining and leaving this list and remarks about >the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ >= _ 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/ =
Help with stats please
Hi. I am teaching educational statistics for the first time, and although I can go on at length about complex statistical techniques, I find myself at a loss with this multiple choice question in my test bank. I understand why the range of (b) is smaller than (a) and (c), but I can't figure out how to prove that it is smaller than (d). If you can explain it to me, I will be humiliated, but grateful. 1. Which one of the following classes had the smallest range in IQ scores? A) Class A has a mean IQ of 106 and a standard deviation of ll. B) Class B has an IQ range from 93 to 119. C) Class C has a mean IQ of 110 with a variance of 200. D) Class D has a median IQ of 100 with Q1 = 90 and Q3 = 110. The test bank says the answer is b. Melady = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
