I agree with the general discussion RE meaning communicated by
'frequency density,' but I do want to add something WRT to 'bin' vs.
column.
As originally done, in the day of paper, etc., measured values could
be thought of as being placed into a series of bins, holding the
specified range. People who sorted eggs, apples, or potatoes had
experience. People who saw produce arrayed in a grocer's stall were
exposed to the concept of 'bins.'
It all made visual, conceptual sense. Let's not dismiss the insights
this allowed.
I once visited a small engine production plant. the tolerance stack-
up on the engine parts was such that each engine had a different push
rod length [push rods control the value lifters and valves]. At the
point where they added the push rods they had a long row of perhaps
20 physical bins. On one side an operator would grind down push rods
to lengths that would keep the 20 bins filled. ON the other side the
engine assembler would make a measurement, take a push rod out of the
marked bin and put it into the engine. Near each end of the bins was
a note to not add to the bin unless requested. Clearly (to me) the
extremes of the distribution of push rod lengths.
I wish today I had a photo of that row of bins. Nonetheless, my
students can all visualize those bins, and how a count of numbers in
each would make a histogram, and we could work out the frequency, or
density, of it from those numbers.
Then I tell them that the computer puts counts into those 'bins' in
the spread sheet the same way as they would count them out and put
them into the cells, er, bins of the spread sheet. We sort a few
numbers together from a sample to demonstrate.
The concept has been transferred. We can go on to bigger things.
So, if it's OK with you :), I'll keep talking about bins, until my
students can follow the procedure, do it themselves, and start the
interpretation.
Have you got anything to get the point across better? I'll use that,
too.
Jay
On Oct 12, 2007, at 7:04 AM, R.Thomas wrote:
> The problems highlighted in this discussion seems to stem from the use
> of the word 'bin' in place of column.
>
> The subject matter is charts. Use of the word bin seems to stem from
> the computerisation of charts. It is a bit of computer jargon
> inappropriately imported into statistics
>
> As far as charts are concerned 'bin' has no meaning that cannot be
> better covered by the purely descriptive word column. It makes sense
> to talk and write about column-width. Bin-width just illustrates
> that
> bin is not the right word. Would it make sense to say 'density means
> divided by the width of the bin'?
>
> Statisticians should keep in mind that they need to communicate
> with the
> public. Yes frequency density can be plotted on the vertical axis.
> But 'number of occurrences per ...' is much more intellible.
>
> Ray Thomas, Faculty of Social Sciences, Open University
> ************************************************
>
>
>
> Date: Wed, 10 Oct 2007 17:50:13 +0100
> Reply-To: "Hooper, Richard" <[log in to unmask]
> <http://www.jiscmail.ac.uk/cgi-bin/webadmin?LOGON=A2%3Dind0710%26L%
> 3Dall
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> From: "Hooper, Richard" <[log in to unmask]
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> 3Dall
> stat%26T%3D0%26F%3D%26S%3D%26P%3D10962> >
> Subject: Re: "Frequency density" as a histogram label
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>
>
> 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
> <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]
> <http://www.jiscmail.ac.uk/cgi-bin/webadmin?LOGON=A2%3Dind0710%26L%
> 3Dall
> stat%26T%3D0%26F%3D%26S%3D%26P%3D10962>
> _________________________________________
>
>
> -----Original Message-----
> From: A UK-based worldwide e-mail broadcast system mailing list
> [<mailto:HYPERLINK
> "http://www.jiscmail.ac.uk/cgi-bin/webadmin?LOGON=A2%3Dind0710%26L%
> 3Dall
> stat%26T%3D0%26F%3D%26S%3D%26P%3D10962"[log in to unmask]
> <mailto:HYPERLINK> >] On Behalf Of Allan Reese (Cefas)
> Sent: 09 October 2007 10:40
> To: [log in to unmask]
> <http://www.jiscmail.ac.uk/cgi-bin/webadmin?LOGON=A2%3Dind0710%26L%
> 3Dall
> stat%26T%3D0%26F%3D%26S%3D%26P%3D10962>
> 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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>
> Ray Thomas, Faculty of Social Sciences, Open University
>
>
> ________________________________
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