reliability

[razina khayat]

Hi all,
   I'm trying to do a test-retest reliability analysis on attachment loss measurement. Attachment loss is measured in millimeters ranging from 0 to about 14. my question is how to do this within ± 1 mm accuracy. Also for validity assessment (using gold standard), how could we measure the same variable within 1 mm accuracy.
  thanks,
  razina



---------------------------------
Talk is cheap. Use Yahoo! Messenger to make PC-to-Phone calls.  Great rates starting at 1¢/min.

[Stevan Nielsen]

Dear Colleagues,

I have stumbled upon an interesting phenomenon: I have discovered that
consumption of a valuable resource conforms to a very regular, reverse
J-shaped distribution.  The modal case in our large sample (N = 16,000)
consumes one unit, the next most common case consumes two units, the
next most common three units, the next most common four units -- and
this is the median case, and so on.  The average is at about 9.7 units,
which falls between the 72nd and 73rd percentile in the distribution --
clearly NOT an indicator of central tendency.

I used SPSS Curve Estimation to examine five functional relationships
between units consumed and proportion of consumers in the sample,
testing proportion of consumers in the sample as linear, logarithmic,
inverse, quadratic, or cubic functions of number of units consumed.  I
found that the reciprocal model, estimating proportion of cases as the
inverse of units consumed, was clearly the best solution, yielding a
remarkable, and very reliable R2 = .966.  All five models were reliable,
but the next best was the logarithmic solution, with R2 = .539; worst
was the linear model, with R2 = .102.

These seems like a remarkably regular, quite predictable relationship.
I've spent my career so enamored with normal distributions that I'm not
sure what to make of this distribution.  I have several questions for
your consideration:

Do any of you have experience with such functions?  (I believe it would
be correct to call this a decay functions.)

Where are such functions most likely to occur in nature, commerce,
epidemiology, genetics, healthcare, and so on?

What complications arise when attempting to form statistical inferences
where such population distributions are present?  (We have other
measurements for subjects in this distributions, measurements which are
quite nicely normal in their distributions.)

Your curious colleague,

lars nielsen

Stevan Lars Nielsen, Ph.D.
Brigham Young University

801-422-3035; fax [phone]

[Anthony Babinec]

Here are a couple general comments.

While the normal distribution might be a useful
assumed distribution for errors in regression, there
is no reason to think that it is necessarily useful for
summarizing all phenomena out there in the world.

As you have described your data, they are counts.
In other words, values are 1, 2, 3 etc., and not
real values in some interval.

Are you looking at consumption in some fixed unit of time -
say week, month, year? Given some assumptions, there
are distributions such as the poisson that might
be appropriate. It also could be the case that
what you are studying represents a mixture of types,
say usage types (low, medium, high), though that may or
may not be the case here.

Pete Fader(Wharton) and Bruce Hardie(London Business School)
have a nice course on probability models in marketing that is
regularly given at AMA events.

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Stevan Nielsen
Sent: Thursday, July 13, 2006 10:12 AM
To: [hidden email]
Subject: A Distinctly Non-Normal Distribution

Dear Colleagues,

I have stumbled upon an interesting phenomenon: I have discovered that
consumption of a valuable resource conforms to a very regular, reverse
J-shaped distribution.  The modal case in our large sample (N = 16,000)
consumes one unit, the next most common case consumes two units, the
next most common three units, the next most common four units -- and
this is the median case, and so on.  The average is at about 9.7 units,
which falls between the 72nd and 73rd percentile in the distribution --
clearly NOT an indicator of central tendency.

I used SPSS Curve Estimation to examine five functional relationships
between units consumed and proportion of consumers in the sample,
testing proportion of consumers in the sample as linear, logarithmic,
inverse, quadratic, or cubic functions of number of units consumed.  I
found that the reciprocal model, estimating proportion of cases as the
inverse of units consumed, was clearly the best solution, yielding a
remarkable, and very reliable R2 = .966.  All five models were reliable,
but the next best was the logarithmic solution, with R2 = .539; worst
was the linear model, with R2 = .102.

These seems like a remarkably regular, quite predictable relationship.
I've spent my career so enamored with normal distributions that I'm not
sure what to make of this distribution.  I have several questions for
your consideration:

Do any of you have experience with such functions?  (I believe it would
be correct to call this a decay functions.)

Where are such functions most likely to occur in nature, commerce,
epidemiology, genetics, healthcare, and so on?

What complications arise when attempting to form statistical inferences
where such population distributions are present?  (We have other
measurements for subjects in this distributions, measurements which are
quite nicely normal in their distributions.)

Your curious colleague,

lars nielsen

Stevan Lars Nielsen, Ph.D.
Brigham Young University

801-422-3035; fax [phone]

[Hector Maletta]

The phenomenon you are describing seems to follow a Poisson distribution.
There are also other asymmetrical distributions that apply to multiple
phenomena in nature and society. The Poisson distribution was first tried by
Bortkiewicz in the early 20th century to predict the number of Prussian
soldiers killed annually by a horse-kick (or was it the number of times an
average soldier would be kicked by a horse during his service time? I do not
remember precisely), and applies to any event that could happen multiple
times with decreasing probability of repetition.
Another famous asymmetrical distribution, first rising to a maximum in some
low value and then decreasing gradually towards higher values, is the Pareto
equation for the distribution of income. He found few people with
implausibly low incomes, then a maximum frequency around the most common
wage level, and then a very long tail with decreasing frequencies as income
increases all the way up to Bill Gates level.
There is no reason to expect these phenomena to follow a symmetrical, let
alone a normal Gaussian, distribution.
Hector


-----Mensaje original-----
De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de
Stevan Nielsen
Enviado el: Thursday, July 13, 2006 12:12 PM
Para: [hidden email]
Asunto: A Distinctly Non-Normal Distribution

Dear Colleagues,

I have stumbled upon an interesting phenomenon: I have discovered that
consumption of a valuable resource conforms to a very regular, reverse
J-shaped distribution.  The modal case in our large sample (N = 16,000)
consumes one unit, the next most common case consumes two units, the
next most common three units, the next most common four units -- and
this is the median case, and so on.  The average is at about 9.7 units,
which falls between the 72nd and 73rd percentile in the distribution --
clearly NOT an indicator of central tendency.

I used SPSS Curve Estimation to examine five functional relationships
between units consumed and proportion of consumers in the sample,
testing proportion of consumers in the sample as linear, logarithmic,
inverse, quadratic, or cubic functions of number of units consumed.  I
found that the reciprocal model, estimating proportion of cases as the
inverse of units consumed, was clearly the best solution, yielding a
remarkable, and very reliable R2 = .966.  All five models were reliable,
but the next best was the logarithmic solution, with R2 = .539; worst
was the linear model, with R2 = .102.

These seems like a remarkably regular, quite predictable relationship.
I've spent my career so enamored with normal distributions that I'm not
sure what to make of this distribution.  I have several questions for
your consideration:

Do any of you have experience with such functions?  (I believe it would
be correct to call this a decay functions.)

Where are such functions most likely to occur in nature, commerce,
epidemiology, genetics, healthcare, and so on?

What complications arise when attempting to form statistical inferences
where such population distributions are present?  (We have other
measurements for subjects in this distributions, measurements which are
quite nicely normal in their distributions.)

Your curious colleague,

lars nielsen

Stevan Lars Nielsen, Ph.D.
Brigham Young University

801-422-3035; fax [phone]

[Antoon Smulders]

Well,
I think you can measure millimeters (distances) quite accurately using
precise instruments, but I don't think attachment loss can be measured in
millimeters.
Antoon Smulders

-----Oorspronkelijk bericht-----
Van: SPSSX(r) Discussion [mailto:[hidden email]] Namens razina
khayat
Verzonden: donderdag 13 juli 2006 16:24
Aan: [hidden email]
Onderwerp: reliability

Hi all,
   I'm trying to do a test-retest reliability analysis on attachment loss
measurement. Attachment loss is measured in millimeters ranging from 0 to
about 14. my question is how to do this within ± 1 mm accuracy. Also for
validity assessment (using gold standard), how could we measure the same
variable within 1 mm accuracy.
  thanks,
  razina



---------------------------------
Talk is cheap. Use Yahoo! Messenger to make PC-to-Phone calls.  Great rates
starting at 1¢/min.