I don't think that "frequency density" is an oxymoron, since "density"
just means "divided by the width of the interval".
The kind of density with which statisticians are most familiar is a
PROBABILITY DENSITY. A histogram can be viewed as an estimate of the
probability density function - in this case the vertical axis should
show the RELATIVE FREQUENCY DENSITY (relative frequency is an estimate
of probability). When Stata includes the "density" option in its
histogram command, this is a short-hand for relative frequency density.
FREQUENCY DENSITY is another alternative that can be plotted on the
vertical axis of a histogram. Frequency and relative frequency (not in
density form) can only be shown unambiguously on the vertical axis if
all the bins have equal width. Of course, since this is overwhelmingly
the most common situation we come across, these are what we most
commonly see.
Richard Hooper
_________________________________________
Dr Richard Hooper,
Lecturer in Medical Statistics
Respiratory Epidemiology & Public Health Group,
NHLI @ Imperial College London
Emmanuel Kaye Building
Manresa Road
London. SW3 6LR
http://www1.imperial.ac.uk/medicine/nhli/respiration/popgenetics/reph
tel: +44 (0)20 7352 8121 ext. 3502
fax: +44 (0)20 7351 8322
email: [log in to unmask]
_________________________________________
-----Original Message-----
From: A UK-based worldwide e-mail broadcast system mailing list
[mailto:[log in to unmask]] On Behalf Of Allan Reese (Cefas)
Sent: 09 October 2007 10:40
To: [log in to unmask]
Subject: Re: "Frequency density" as a histogram label
Sandy MacRae suggests: If examinations demand this type of labelling,
textbooks will obviously use it and it is appropriate for histograms
with variable bin size or vanishingly narrow bin size. But does anyone
else use it when reporting data?
However, I had commented to him off-list that I would regard the label
"frequency density" as an oxymoron. In terms of usage, Stata histogram
command offers options:
" density, fraction, frequency, and percent specify whether you
want the histogram scaled to density
units, fractional units, frequencies, or percentages. density
is the default."
The distinction I would draw is that density units imply the sum of
column areas is normalized as 1, while frequency units imply the sum is
the number of observations.
Who examines the examiners?
Allan
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