StatJdy3
Dear Engineering Student,
Nothing will ever be attempted if all possible objections
must be first overcome.
Samuel Johnson
Subject: A statistical engineering study to determine if a
negative focal state of the eye (nearsightedness) can be
prevented.
These remarks are addressed to engineering students entering
a four-year college, such as Embry-Riddle. It is assumed that
they would have, or can develop the engineering and scientific
insights necessary to make this preventive effort work properly.
The entire work of judgment evaluation would depend completely on
their scientific understanding.
As a engineering student entering a four year college I am
certain you must take a course in college statistics.
Participation in this type of study would occur in the first year.
In the following three years you could form a judgment about your
involvement in this type of analytical work.
There are two types of studies. Engineering studies where we
wish to determine the behavior of a mechanical or electrical
control system. Since your background is in engineering, I think
you will understand the nature of this testing of the null
hypothesis.
Medical studies do require the use of a placebo group. Since
the Internet has become wide-spread and a great deal of
information is available to you about the effect the minus and
plus lens have on the focal state of the eye, it would be
impossible to maintain a "placebo group" at an engineering college
such as Embry Riddle. Indeed the instructions and data collection
requirements would prohibit a medical study.
The following constitutes a medical review of the statistical
analysis designed to show that the eye functions as an
auto-focused camera.
When we attempted to institute a preventive effort at the
Naval Academy, it was necessary to provide a statistical analysis
to show that preliminary results would be meaningful. We
suggested that 100 motivated pilots be offered a tutorial on the
subject, and if properly motivated be trained to make all the
critical measurements of their focal state.
The study would run for 4 months should be sufficient to
demonstrate the basic separation of focal states for the test
group relative to the control group. At the end of this work, the
engineers who must be privy to their own study would evaluate the
results and decide to continue with the effort or quit.
The numbers are representative. It is assumed that there
would be attrition in both the test group and the control group
for various reasons. Any engineer could quit the study, but could
not re-enter the study.
I have used standard college statistics for this analysis.
In my judgment, the pilot-students must understand this type of
technical analysis, and would appreciate the type of intellectual
and physical control they would use to protect their distant
vision -- through their four years at the college.
The difference of 0.2 diopters between the test and control
groups in 4 months would be sufficient to reject the null "optical
bench", or "box camera" hypothesis.
These are "talking points" for our proposal.
Since you have the technical background I would think that
both you and the engineer-pilots would be interested in conducting
this type of study as an engineering effort.
Best,
Otis
**************************
A TEST TO DEMONSTRATED THAT THE FOCAL STATE OF THE
EYE "FOLLOWS" THE ACCOMMODATION SIGNAL
Test the hypothesis that there is absolutely no neurological
linkage between the accommodation system of the eye and the focal
state of the eye.
The mean focal state of 100 midshipmen with 20/20 eyes is +
0.3 diopters with a standard deviation of 0.25 diopters.
[It had been previously established that the focal state goes
downward at a rate of to -0.33 diopters per year for the average
focal state of all eyes. Ref: Gemlin, West Point Study.]
Using random number assignments, the group is divided into a
test group and a control group. The control group will keep
accurate records of their visual environment. The test group, who
use a positive lens (read at the blur-point) will change their
visual environment by +1.0 diopter (average).
This use of the plus lens will produce an accommodation delta
of at least +0.75 diopters.
At the end of six months, 45 students remain in the control
group and 35 in the test group. The control group has a focal
state of +0.1 diopters, and the test group, a focal state of 0.3
diopters. Both test and control groups have a standard-deviation
of 0.25 diopters.
QUESTION:
Are these results significant, and if so, what is the level
of significance of the results.
NOTE: Standard testing states that a level of 0.05 is
significant, and a level greater than 0.01 (1 in 100) is
highly significant.
SOLUTION:
The pilot-engineers must decide between the hypothesis:
Ho: The null hypothesis is the belief that the eye is a box
camera, and there must be no relationship between the visual
environment and focal state of the eye.
The Ho Hypothesis: Focus of Test group = Focus of Control Group
The null hypothesis states that there will be no significant
difference will develop between the two groups.
Ha: Test-group (will develop a more positive focal state) than
Control-group (The single-tailed test.)
The alternative hypothesis (Ha) states that the natural eye
behaves as an auto-focused camera, and will control (change) its
focal state based on the "delta" produced by the assiduous use of
a plus lens.
%%%%%%%%%%%%%%%%%%%%%%%%%
The values in this equation are translated as follows:
X-Bar = Average of Test and Average of Control:
At the start of the test, the average refractive status is
identical for the group -- considered to be homogeneous.
After the group of 100 is randomly divided in half, then a
difference in refractive status (measured by the pilots with
trial-lens kit) will develop. In this specific example the
difference between the two groups was projected as 0.2 diopters
after four months.
Sigma = Standard deviation:
In statistics, "Sigma" is a required calculation. Before the
start of this test, Standard-deviation will be calculated for the
group of 100.
After four months, standard-deviation will be calculated for
the test-group and the control-group. This value is required for
this calculation.
T = Test Group:
The group that does not wear the a strong plus lens during
the four month of the study. This group will, monitor their focal
status with a trial-lens kit.
C = Control Group:
This group will wear a proper-strength plus lens, as detailed
elsewhere on this site. They must understand how they must wear
the plus lens. The detailed instructions required will prevent
the use of a "blind study". It is felt that that the engineers
will understand this need for detailed instructions and
understanding of both the method and goals of this study, as an
engineering, rather than a "medical" study.
N = Number in group:
100 people will start the test, with 50 in each group. It is
expected that a number of pilots will not be able to complete the
test for various reasons. In this example, 45 people reported
their measurements in the control group, and 35 reported their
measurements in the test group, thus meeting the protocol of this
engineering study.
%%%%%%%%%%%%%%%%%%%%
The null hypothesis Ho, assumes that the means of the
two groups are identical. The following "Z" static is calculated
as described below.
[ X-Bar(Test) + X-Bar(Control) ]
Z = ----------------------------------------------------------
Square Root [ Sigma-T ^2 / N(test) + Sigma-C ^2 / N(Control) ]
Z = ( 0.3 ) - ( 0.1 ) / SQRT [ (0.25^2 / 35) + (0.25^2 / 45) ]
Z = 3.549
Notes: X-Bar = Average of Test and Average of Control
Sigma = Standard deviation
^2 = Squared
T = Test Group
C = Control Group
N = Number in group
SQRT = Square Root of [ ]
Since the result, 3.549, exceeds 2.33, which is the 0.01 (99
percent) confidence level, we can say that it is highly probable
that the eye is a control-system, and that this result is in
agreement with the previous experiments that demonstrate that all
eyes will go negative when forced to wear a minus lens.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
LEVELS OF SIGNIFICANCE:
------------ Percent -----------
Significance Level: 0.05 0.01 0.005 0.002
Critical "Z" values 1.645 2.33 2.58 2.88
for the one-tailed
test
^^^^^^^^^^^^^^^^^^^^
The values chosen for this review are representative numbers.
The results of an a formal study will produce similar outcome. It
is worth the effort to establish the above suggested relationship.
On the basis of this test, using the one-tailed test at a
level of significance of 0.01 we should reject the null
hypothesis, Ho, that the natural eye is a rigid box camera, and
that there is NO RELATIONSHIP between the eye's visual environment
and its focal status.