FYSigLe2.txt           


Dear Student,


Subject:  Calculating the significance level of the Oakley-Young
     study


     Majority-opinion ODs generally deny ANY significance for the
Oakley-Young study.

     But the reality is that the results are highly significant.

     I have taken the time to go through Frank Young's "Plus", or
so-called bifocal study.

     He stated that is results were significant -- but did not
supply the calculation nor some of the data to prove how
significant his results were for the large number of individuals
involved in this study.

     I wonder if you could review these calculations and either
state your support, or supply questions about the data.

     Here are the data from the study:

Nt = 225 wearing a plus (ages from 6 to 17)

Sigma-T = I am forced to estimate this, but the Standard Deviation
     (from the Eskimos) was about 1.4 diopters. ###

Nc = 192 wearing a “single minus”.

Sigma-C = Again, forced to estimate, the Standard Deviation
     (Sigma) was about 2.0 diopters.  The Eskimo data is VERY
     accurate.


     Here is the classic equation from statistics:


	    Xt	-  Xc

Z =  ---------------------------------------------------

    Square Root of [ ( Sigma^2/ Nt ) + (Sigma^2 / Nc )	]


Xt = 0 diopters (the Plus group did not go down)

Xc = -1/2 diopters across the 192 people in the control group.
     (the single-minus went down at a rage of -1/2 diopters per
     year, for the kids wearing the single minus.)

     After one year with 0.5 diopters difference:


	   0.0 - ( -0.5 )

Z = ---------------------------------

  Square Root of [ ( 1.4^2 / 226 ) + ( 2.0^2 / 192 )]


Z =   0.5 / 0.172

Z = 2.91


Highly Significant is above Z = 2.33

     This is substantially above highly significant after one
year!!

     After two years:

     Z = 1.0 / 0.172


     Z = 5.82

     This is in fact “off the map” of the Probability Curve.  ***

     Please check this math, and the significance level.


     In order to plan for FUTURE studies, (with motivated pilots,
for instance) it is truly necessary that they understand the real
implications of this type of scientific test, and verification of
the significance of these results.

     That is why selecting engineering students who know what they
are doing is so essential -- and have the personal motivation to
do it right!

     If we ever were to propose this type of study to the National
Eye Institute, then this would be the "core" of the argument to
support a preventive study or effort, with respect to educated
engineers and scientists.


     Best,

     Otis

========================


*** Significance levels, from the text book.

"Areas Under the Normal Probability Curve"

Z is the horizontal.  The probability is the area under the curve.


Z    Probability, or significance

Z= 2.33  P= 0.01
Z= 3.08  P= 0.001
Z= 3.61  P= 0.0001
Z= 3.86  P= 0.00001


     After one year, given the number of eyes involved, the
results, in terms of science, were highly significant, and 
after two years, were far above Z = 3.86, and P = 0.00001.

     I would expect that engineers, who had the motivation to do this 
right would achieve the same scientific results.

=========================


####  Standard Deviation (Sigma) from:

"Ocular Biometry of Eskimo Familes"
By Francis A. Young and George A. Leary

Group		# of Eyes	Mean	Sigma

Grand Parents	N = 96		+2.21	1.31 Diopters

Parents		N = 180		+1.19	1.55 Diopters

Older Children	N = 194		-0.93	1.97 Diopters

Young Children	N = 218		+1.40	1.70 Diopters