Editing 3/11/21

**Part II: The Capacity to Benefit from
Formal Academic Schooling:
two ideologies of distribution
**by Edward G. Rozycki, Ed.D.

Q: Where do priors originally come from?
A: Never ask that question. -- Eliezer Yudkowsky,

"An Intuitive Explanation of Bayesian Reasoning" at
http://yudkowsky.net/rational/bayes/

The "gold standard" or "priors" one
chooses as a basic reference points for test accuracy
comparisons can have a substantial effect on estimated test
performance characteristics.[**15**]
An educational philosophy or organizational
ideology -- not infrequently viewed by some practitioners as
dispensible verbiage -- can importantly determines what
the priors will be. [**16**] For
example, for public education in the U.S., let us consider two
ideologies: a) DuBois' *Talented Tenth* , or TT*; *also,
what I will call *public school ideology, *PS. [**16b**]

Let us suppose that W.E.B. DuBois had it
right: every human group has at best a "talented tenth" who both
need and can use a formal, theoretical education in order to
maximize their social contribution.[**17**]
Assuming a *normal distribution of
talent* (ND) in a group, this would restrict academic
schooling to students with an IQ of about 119 and above.[**18**]
But public school ideology -- with recent amendments from
Special Education Law -- has it that students with IQ's above 85
(-1 s.d.) should be in the regular classroom with no special
support.

Let us use DuBois' theory of prevalence to generate the "true" and "false" numbers, the gold standard for identifying those "in need" of academic schooling. Public school placement (PS) procedures, which assume the validity of ND, we will treat as a sorting test. That test must have an sensitivity that identifies students from -1s.d. on up as talented. So the sum of true positives + false positives must equal about 84% of the total population. (This is a shift of 74% of the population to the "in need" group.)

However, in the real world of
educational politics, it is difficult to persuade parents and
their advocates that a test that rejects students from a desired
category is to be preferred to a test that admits them. This
consideration may help explain, despite parental objection, the
inclination of school boards to let Gifted Education, admittance
to which is often premised on an IQ of 135, languish unfunded.[**20**]

**REFERENCES**

[**15**] See Lucas M.
Bachman *et
al* "Consequences
of different diagnostic 'gold standards' in test accuracy
research: Carpal Tunnel Syndrome as an example" in *International
Journal of Epidemiology* 2005; **34***:*953-955
available online as pdf at https://academic.oup.com/ije/article/34/4/953/692975

[**16**]
See Edward G. Rozycki, "Philosophy and Education: What's The
Connection?" at http://www.newfoundations.com/EGR/PhilEdCon.html.

Despite the fact that PPV is a function of three variables,
i.e. PPV = F(s, __sp__, p) where s = sensitivity, __sp__
= specificity, and p = prevalence, s and __sp__ may -- by
empirical determination -- be independent variables. However,
the working assumptions in public education tend to disregard
false positives and false negatives and are biased toward
treating s and __sp__ as somehow dependent on each other
(assuming, perhaps, that 1-sp = s .) Also, the error of
disregarding the effects of p is far from uncommon. I will
speculate why this situation exists:

a. There are few uncontroversial "gold standards" in, for example, public education, for identifying either educational goals or deficits -- estimates tend to be based on tradition and anecdote; such dissensus is generally found in many publicly influenced institutions, national defense policy or national health policy.

b. Separate testing for s and

spmay be seen as repetitive, unnecessarily increasing costs, especially since the classifications involved are binary -- also, letting s stand in forspmay be thought to be inconsequential;c. There is a bias toward maximizing inclusion, especially if the treatment outcome is seen as desirable, or,

mutatis mutandis, the need for treatment dire.

[**16b**]
See Lynn Fendler and Irfan Muzaffar, "The History of the Bell
Curve: sorting and the idea of the normal" in Educational Theory
Vol 58, No 1 (2008)pp. 63 - 82.

[**17**]
W. E. B. DuBois "The Talented Tenth" Chapter Two in *The
Negro Problem *(New York: James Pott and Company, 1903)

[**18**]
The normal IQ distribution covers 90% of the population at
approximately +1.3 standard deviations from the mean of 100.
Using 15 points = 1 s.d., we get an IQ of approximately 119 as
the lower limit of the "talented tenth."

[**20**]
See Edward G. Rozycki, "Justice Through Testing" available at http://www.newfoundations.com/EGR/Justice.html