"G. Marc Turner" wrote:
> I need some advice on how to handle an issue in my stats course...
>
> I'm currently using the Essentials of Statistics (by Gravetter & Wallnau)
> as the textbook. In the chapter on variability, it uses the real limits for
> the calculation of the range, inter-quartile range, etc. This is actually
> how I learned to do the calculations by hand, and haven't really thought
> much about it until now.
>
> I'm also teaching the students how to use SPSS (v9) to get the same
> information after going over the hand-calculations. BUT, SPSS does not use
> the real limits when calculating the range, quartiles, etc. (For example,
> for one data set we get a range of 9 and an interquartile range of 1.89 by
> hand. SPSS calculates the range as 8 and the interquartile range as 2.)
>
> So, tomorrow afternoon when I go over this in class, and the students ask
> me to explain why the scores are different, what should the answer be? My
> immediate reaction is to say that we shouldn't trust the values of SPSS,
> and this points out why it is important to know how to do the calculations
> by hand. However, I'm not sure how far that will get me in convincing the
> students.
I don't mess with the upper and lower limits anymore (except when I teach
them how to graph). I don't think it's worth the effort. With a _small_ data
set, knowing that the IQR is 3.1 as opposed to 3.0 is rarely useful. Indeed,
with a small data set many of our descriptive statistics are not needed anyway.
You just look at the numbers. As the sample size gets larger and larger, the
practical significance of using limits and factoring in "tied" scores
diminshes. While I don't ordinarily condone imprecision - medians, ranges, and
IQRs are usually done as part of exploratory data analysis (EDA) in which case
nobody every does them anyway - and all the attention payed to the limits and
tied scores deflects the students _away_ from the real message which is the
approriate use of these statistics.
Given the numerous challenges of the stats course and all the hurdles that
lie ahead, I "choose my battles", do a quick example by hand (no limits or
ties) and then tell them to have the computer do it. When else in their
professional life will they need to get a IQR to that precision?
I have seen some stats books (Lehman?) that have students plot the
cumulative freqency, and then with a straight edge draw in Q1 and Q3, and then
"eyeball" where the line hits. If done properly this is quite accurate and
potentially useful in an exploratory data analysis (EDA) context. The stats
book I use now (Moore's Basic Practice of Statistics - EDA oriented) doesn't
mess with the limits at all.
From the standpoint of the software developers, I think it would be easy to
adjust for tied scores (though I have never tried to write the code!), but it
might being a stretch to figure the limits. When you have the numbers 3,4,5 -
_you_ know the unit of measurement is .5 and the limits of 5 are 4.5 to
5.49999...., but how would the code know? I suspect (but don't actually know)
that when the enter the number 5, it is represented as 5.0000000 - or something
like that. On most programs you can change the number of digits past the period
to display on the monitor, but this is cosmetic (though I'd love to hear from a
real programmer on this issue).
--
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John W. Kulig [EMAIL PROTECTED]
Department of Psychology http://oz.plymouth.edu/~kulig
Plymouth State College tel: (603) 535-2468
Plymouth NH USA 03264 fax: (603) 535-2412
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"What a man often sees he does not wonder at, although he knows
not why it happens; if something occurs which he has not seen before,
he thinks it is a marvel" - Cicero.
