Engineering, Science and Statistics (t-test)


t_test.txt


Dear Mike,

Subject: How to use statistics to establishe the dynamic behavior of
the fundamental eye.

Please don't insult my intelligence -- to the effect that engineers
and scientists don't
understand statistics. I think it is you that has a very hard time
understand analysis
of the eye's behavior, and the use of statistics "t-test" to establish
the accuracy of
the correlation coefficient calculation:

===========


Otis> I have no problem with statistics.


Mike> That's nonsense. If you knew the first thing about statistics
you wouldn't
swallow all the myth and nonsense you do.

==========

Here is the calculation:



STUDENTS "T" CALCULATION FOR THE CORRELATION COEFFICIENT

Was the correlation coefficient from this experiment accidental?
Did
Dr. Young randomly obtain 0.972 for the monkeys in the test when the
actual
population correlation coefficient was zero? This assertion can be
checked
by use of the students "t" distribution:

r
t = ------------------------
___________________
/ 2
/ 1 - r
\ / ---------
\/ n - 2

Where:

n = 23 (Number of measurements made)

r = 0.97 (Correlation coefficient from the experiment)

for v = 21 (Degrees of freedom = 23 - 2)

t = 3.819 (Value for 99.9 percent confidence limit)
..001

2
t = 0.97 / SQRT [ ( 1 - 0.97 ) / ( 23 - 2 ) ]

t = 18.28


Since 18.28 exceeds 3.819 (the 99.9 percent confidence limit) we
can
reject the idea that the Helmholtz-passive concept is correct. There
is a
very high correlation between the average value of accommodation and
the
focal state of the fundamental eye.


Preventive, second-opinion best,

Otis
.

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