I wholeheartedly agree with John Kulig. I don't even bother
covering
that formula in stat. It makes very questionable
assumptions in an
effort to achieve what looks like great precision in finding
a
percentile. For example, it assumes that the scores within
an
interval are perfectly evenly distributed such that the
interval
can be divided into subintervals, each containing one score;
this
even when all of the measured values are identical. Then
the
subintervals are counted to determine just how far above
the
lower real limit the percentile is. If you are going to do
this
kind of interpolation, why not just do it graphically as
John
describes.
Tim
John Kulig wrote:
Miguel. Just a random or two.
To be honest, I hate those formulas, mostly because getting percentiles and percentile points is useful with big data sets, never small data sets, and with big data sets you don't usually have to mess with interval widths and tied scores to get a _useful_ answer. The most useful way I have taught this (following Richard Lehman's undergradaute text) is to have students plot cumulative proportion on Y, data on X. Do a straight edge line from Y from the percentile you want, hit the line, and then drop straight down. If you plot carefully and use a straightedge, you get as much accuracy as one needs (this sounds like a Tukey (1977) method - I'll check later if I have time). This method also allows you to go in reverse, from a particular X up to the line, then left to the percentile rank.
Miguel Roig wrote:Here is the formula that we are working with:
L + [ (N) (P) - nl ] i
nw
Where L represents the lower real limit of the category containing the percentile of interest.
N is the total number of scores in the distribution
nl is the number of individuals with scores less than L
nw is the number of individuals with scores within the category containing the percentile of interesti represents the interval of the category that contains the percentile of interest.
<snip>
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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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"One word of truth outweighs the whole world."
Russian proverb
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Tim Gaines
[EMAIL PROTECTED]
Professor of Psychology
phone: 864-833-8349
Presbyterian College
fax: 864-833-8481
Clinton, SC 29325
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Tim Gaines
Professor of Psychology
Presbyterian College
Clinton, SC 29325
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