Newsgroups: sci.med.dentistry

Subject: Re: Periostat and statistics
Date: Fri, 20 Apr 2001 15:09:15 GMT
Organization: EarthLink Inc. -- http://www.***.com/

Joel, how do they deteremine the P value?  ie. (P>0.05) I was under the
impression that P values were of more value because the took into
consideration standard deviation.  This is what all the clinical trial
studies seem to use.  Is there something you know that the reviewers don't?

******

Information on standard deviation posted below: Way below!

*****

what if N=9999?

Same. If a pocket is measuring 6 mm, and the improvement is 0.25 mm, One
needs negative numbers to balance out a putative 3 mm improvement!

Really, is that the only way you could come up with that number? Had no
idea.

I am a miniature golf player ... I am just faking this part .....

I assume the same way you would judge the efficacy of of a new cement or
impression material.

Right. I have a vague impression that cement A works well in my hands. As
for patient response to cement A, how would I eliminate confounding
variables?

If you can't trust the research, and you can't trust you own observations,
what can you do?

Read Reality, CRA, etc.

*****

Same with golf scores, same with Periostat data.
Std. Deviation - an unknown to your golfing buddy!

How about printing this out and handing it to him?

  ***

Hypothetical case:

New York City and Duluth, MN both have average
household incomes of $78,343. Which city would be the
better location for your brand new BriteSmile Dental
Whitening Center?  PS- It costs the patients from $500-
$700 for an hour's whitening treatment.  Better get a
good grip on household income distribution first!

The Std. Dev. (Standard Deviation) could supply the
missing information needed to make an informed choice.
The "average" for both cities could be identical
however the data could be -- would be --- vastly
different!

Same with golf scores, same with Periostat data.

Joel M. Eichen, D.D.S.

[background post - posted 7/24/99]

Hello!

I received an e-mail from Bob Kehoe asking for some
more information about standard deviation with regards
the article about staff salaries.  His magazine has
supplied the mean and the range, but had omitted the
standard deviation. It is a statistic that is readily
available if your data is in an Excel spreadsheet or
any database program. If your data is on 3 by 5 cards,
then you must calculate standard deviation separately.
This is not just a concept for mathematicians and for
scientists.  It works for everybody.

It comes down to this:

Some statistics, such as the mean and the range, are
easily calculated, but hide the true pattern of
the numbers that produce them.

The mean describes a set of numbers with a single
central number. In contrast, the range reveals how the
numbers in a set vary from each other. But often these
two statistics do not fairly represent the numbers in
their sets.

It needs a second statistic, the standard deviation, to
make sense of these contradictions.

  **  **  **

Standard deviation (meaning plain old deviation from
the mean) tells us how much variation there is in the
numbers. How far away from the mean does the "regular"
(whatever regular is) number lie?

Lets say that the data shows that the average hygienist
gets $25. and hour with a std. deviation of $4. an
hour. Two standard deviation units indicates (2 times
$4 or $8) meaning that 95% of all of the doctors
reporting will pay their hygienists between $17. an
hour and $33. an hour (mean plus or minus 2 std. dev).
99% of all of the doctors reporting will pay their
hygienists between $13. an hour and $37. an hour (mean
plus or minus 3 std. dev).  The other 1% are known as
outliers. They affect the mean but do not affect the
standard deviation.

The mean (arithmetic average) is a very poor statistic.
Does this statement surprise you?

Here's the temperatures for 3 U.S. cities.

Normal Monthly Mean Temperatures
(Fahrenheit) for 1961-1990

                           January  July  Yearly Mean
Fairbanks, AK               -1.6    72.3     36.5
Phoenix, AZ                 65.9   105.9     85.9
Honolulu, HI                80.1    87.5     84.4

The annual mean temperature for Fairbanks, Alaska is
36.5, but it is a balmy 72.3 degrees in July.

The mean for Phoenix, Arizona is 85.9, yet it is a cool
65.9 in January.

The mean is a poor predictor in these 2 cities, but in
Honolulu, Hawaii the mean of 84.4 is typical of
temperatures year round.

Clearly the mean is not enough.

Suppose that you are in some course and have just
received your grade on an exam. It is natural to ask
how the rest of the class did on the exam so that you
can put your grade in some context. Knowing the mean or
median tells you the "center" or "middle" of the
grades, but it would also be helpful to know some
measure of the spread or variation in the grades.

Lets look at a small example. Suppose three classes of
5 students each write the same exam and the grades are:

 Class 1
        Class 2
               Class 3
   82
          82
                 67
   78
          82
                 66
   70
          82
                 66
   58
          42
                 66
   42
          42
                 65

Each of these classes has a mean, of 66 and yet there
is great difference in the variation of the grades in
each class. One measure of the variation is the range,
which is the difference between the highest and lowest
grades. In this example the range  for the first two
classes is 82 - 42 = 40 while the range for the third
class is 67 - 65 = 2. The range is not a very good
measure of variation here as classes 1 and 2 have the
same range yet their variation seems to be quite
different.  One way to see this variation is to notice
that in class 3 all the grades are very close to the
mean, in class 1 some of the grades are close to the
mean and some are far away and in class 2 all of the
grades are a long way from the mean. It is this concept
that leads to the definition of the standard deviation.

Lets look at class 1. For each student calculate the
difference between the students grade and the mean.

 Class 1  scores
        Difference from the mean

   82
         16
   78
         12
   70
          4
   58
         -8
   42
         -24

The average of these differences could now be
calculated as a measure of the variation, but this is
zero. What is really needed is the distance from each
grade to the mean not the difference. You could take
the absolute value of each difference and then
calculate the mean. This is called the mean deviation,
i.e. mean deviation = , where n is the number of
students in the  class. For class 1 this is 64/5 =
12.8. Another way to deal with the negative differences
is to square each difference before adding.

 Class 1  scores
       Difference from the mean
              Difference from the mean squared

   82
         16
               256
   78
         12
               144
   70
          4
               16
   58
         -8
               64
   42
         -24
               576

The sum of this column is 1056. To find what is called
the standard deviation, s, divide this sum by n-1 and
then, since the sum is in square units, take the square
root. For class 1 this gives std. deviation.

To see some practical examples, look at the following:

http://www.***.com/
(Medical school admissions, University of British
Columbia, showing mean scores, range and standard
deviation).

http://www.***.com/
le.html

(This one is a standard deviation calculator on the
internet. You can also use a scientific calculator, but
if you do not have one, then go here.)

http://www.***.com/ ~dmason/stat/stat2.html
(A second internet standard deviation calculator)

Cheers,

Joel

Joel M. Eichen, D.D.S.

*******************************************

[This post from 2/16/99]

A community

Some folks wonder why I post about so many different topics.
I frequently include such diversity as local politics or the
state of the economy.  It is because I posit that a strong
dental profession relies on an entire cadre of patients,
friends, and neighbors for its continuing existence. We hope
that you are enjoying the fruits of a strong financial
position.  We need you to be fairly secure in your own
finances to help us support our dental practices.  We, in
turn will do our best to care for the state of your teeth.

Corporate consolidators who buy practices and owe fealty to
shareholders are currently presenting a real challenge for
privately owned dental practices.  Managed care dental plans
contain challenging aspects too.  Perhaps the biggest threat
of all to today's dentistry is the pandemic practice of land
speculation.

The 1998 U.S. average family income is around $34,000.
Unfortunately, this does not begin to tell the story of what
the "average family" has available as income. To determine
that, one needs to know the shape of bell curve and how
steeply family income falls away from the mean (or average).

The concept of "standard deviation" or "variance from the
mean" tells us how many people fall ...

read more »

deviation.  You clearly have a vast knowledge of statistical calculation,
could you please explain the P value?

 I have a vague impression that cement A works well in my hands. As

I don't understand your question.

Please be more specific.  What is the "etc?"  Are these publications that
can be trusted to provide more accurate and reliable clinical information
than those that typical dentists and periodontists rely on?

Did a little research on my own....standard deviation takes on importance
only when you lack a control....double blind study,  and the control is
valid, Std. Deviation takes on far less significance.

Your analogy fails because the golf scores have no control to compare.  When
the control and the subject are both placed under the same conditions, then
measured by the same standard, the control is considered zero and the
variance between the control and the test subject is the result.

P value is the probability of a given variance happening as a result of the
tested hypothesis.

Well Joel, which is it?