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Re: Hearing Loss "False Positives"

Dear list,

As someone who has been trained in basic statistics, I find the
discussion about statistical error a bit misleading.

1.  Maybe it's my mistake in reading, but I didn't catch how big the
deviation from normal (in decibels) counts as having hearing loss.
Without this figure, all the rest of the discussion is meaningless.
So for the moment, let's call it D (representing a worrisome deviation
from normal threshold).

2.  If there is sufficient error of measurement to cause 10% of
children with normal hearing to be classified as having hearing loss,
because their measured threshold happens, on one occasion, to deviate
by D dB from normal, then, assuming error to be symmetrical, then the
following is true as well.  In the population of children with true
deviations of D, 10 percent of them will be measured as having normal
hearing.  So error cuts both ways, labeling normals as having hearing
loss and those with true hearing loss as normal.

3.  So what's the best approach?  The mean measured hearing loss (in
dB) in a random sample is an unbiased estimate of the mean in the
population from which it was drawn.  So you should report the observed
mean of your sample as your "best guess" of the true hearing status of
the population and also report a confidence interval around that mean,
based on the error of measurement.  This confidence interval is a
fuzzy region in which 95 or 99 percent of the possible true estimates
of the mean will lie (with decreasing probability as they deviate from
the measured value).  So the reporting of the observed mean doesn't
represent a biased account of the truth.  A more exact estimate can be
obtained by increasing the sample size.

4.  In the face of such error, how do you get a reliable estimate for
an individual child, if the question of special treatment for that
child is involved?  If the child's measured deficit is large enough,
it may not matter whether the true value is a few dB higher or lower.
However, if the score lies near the boundary of the acceptable range,
and a more exact estimate is needed, then we should just repeat the
test a few times, separated by sufficient intervals, and use the
average as the child's score.  (The error in this average will be
lower than that of a single score by an amount that can be

All this implies that there is no need for alarm, despite the
existence of error of measurement, which is always with us.  There are
standard ways of dealing with it.

Best to all,
Albert S. Bregman, Emeritus Professor
Psychology Department, McGill University
1205 Doctor Penfield Avenue
Montreal, QC, Canada H3A 1B1.
Office:  Phone: (514) 398-6103, Fax: (514) 398-4896
On Thu, Sep 23, 2010 at 3:01 PM, Jeffrey Willson <willsonj@xxxxxxxxxxx> wrote:
> I think you're misreading this.  The paper says that a reasonable
> statistical model reveals that the method used in previous studies will find
> roughly 10% of children with normal hearing to have a measured hearing loss
> that isn't real.  You subtract that from the 14.9% figure and you get less
> than 5% of children with high-frequency hearing loss, and probably the
> majority of these are from causes other than loud noises.
> On Thu, Sep 23, 2010 at 7:58 AM, reinifrosch@xxxxxxxxxx
> <reinifrosch@xxxxxxxxxx> wrote:
>> Dear Kevin,
>> From a non-professional: 10 percent of 14.9 percent is about 1.5 percent;
>> that leaves 13.4 percent of teenagers with hearing loss, which is still
>> frightening. From "Molecular Biology of the Cell", Part V, Chapter 22:
>> "Auditory Hair Cells Have to Last a Lifetime".
>> Reinhart.
>> Reinhart Frosch,
>> Dr. phil. nat.,
>> r. PSI and ETH Zurich,
>> Sommerhaldenstr. 5B,
>> CH-5200 Brugg.
>> Phone: 0041 56 441 77 72.
>> Mobile: 0041 79 754 30 32.
>> E-mail: reinifrosch@xxxxxxxxxx .
>> ----Ursprüngliche Nachricht----
>> Von: kevin.austin@xxxxxxxxxxxx
>> Datum: 21.09.2010 23:41
>> An: <AUDITORY@xxxxxxxxxxxxxxx>
>> Betreff: Hearing Loss "False Positives"
>> Would anyone in the professional community care to comment on this?
>> Begin forwarded message:
>> A new study from the University of Minnesota says that we're
>> overestimating the amount of teens with hearing loss.
>> http://www1.umn.edu/news/news-releases/2010/UR_CONTENT_254452.html
>> Thanks in advance.
>> Kevin