Hi
First, thanks to Mike for taking the time to track down this
information. Just a couple of points ... I've reordered relevant parts
of Mike's posting (prefaces by MP:) before my comments (prefaced by
JC:). [apologies if this is duplicate or triplicate or ... I've had to
send it a number of times because of some computer glitch]
MP:
Note that 4.5% of this group have doctorates. In
previous posts on this topic, estimates of the
percentage in the general population were calculated
using the Census* Community Survey data. In retreospect,
this is the wrong calculation to do, that is, one should
not take the number of Ph.D. estimated in the population
and divide it by the total number of people in the sample.
This does give one the percentage of the general population
that have Ph.D. but for purposes of comparison, the
denominator should the number of people between 24 to 94
years of age, that age range of the richest groups. Children,
which would be included in the total sample number will
inflate the denominator and not provide the appropriate
number for comparison. In other words, to determine
whether the 4.5% of Ph.D.s in this richest group is an
*overrepresentation* or *underrepresentation* requires
one to compare 4.5% to the percentage of Ph.D.s in the
age range of 24 to 94 (excluding the richests).
JC:
The tables Mike and I used earlier DO limit the denominator to adults
(18 and over or 25 and over in the case of Mike's earlier estimate of
.0125). So the earlier estimates hold.
MP:
(3) Given that this dataset represents that richest
400minus2 people in the U.S. in 2008 and under the
assumption that is exhaustive, this group is not a
sample but a population. Consequently, the usual tests
of statistical significance would not apply (e.g.,
testing whether the correlation between networth in
$billions and educational level is zero or not would
not be appropriate since we are dealing with the
population rho and not the sample r). Bootstrapping
and re-sampling techniques can be used to estimate
standard errors for various statistics/parameters
but one would do so under specific explicit assumptions.
Note also that the usual formula for the variance
and standard deviation which correct for sample
estimates/sampling error would provide overestimates
of the true variance and standard deviation
JC:
But some statistical tests would be valid, such as the likelihood of
getting 18 or more PhDs among 400 billionaires if p = .0125. Although
the current proportion of .045 is close to that of the earlier 100
billionaires, the statistical probability is MUCH reduced because of the
larger group. Below is the exact probabilities of 0 to 20 or more PhDs
in a group of 400 if p = .0125. The likelihood of 18 or more PhDs is
extremely small, .0000011. Indeed the chance of just 9 or more PhDs is
less than .05. I used SPSS to generate these exact probabilities, but
it might be interesting to use the normal approximation as well.
x px cpx upx
0 .0065289 .0065289 .9934711
1 .0330579 .0395868 .9604132
2 .0834815 .1230683 .8769317
3 .1401926 .2632609 .7367391
4 .1761281 .4393890 .5606110
5 .1765740 .6159630 .3840370
6 .1471450 .7631079 .2368921
7 .1048375 .8679454 .1320546
8 .0651917 .9331371 .0668629
9 .0359425 .9690796 .0309204
10 .0177893 .9868688 .0131312
11 .0079837 .9948525 .0051475
12 .0032760 .9981285 .0018715
13 .0012377 .9993662 .0006338
14 .0004331 .9997993 .0002007
15 .0001411 .9999403 .0000597
16 .0000430 .9999833 .0000167
17 .0000123 .9999956 .0000044
18 .0000033 .9999989 .0000011
19 .0000008 .9999997 .0000003
20 .0000002 .9999999 .0000001
MP:
(3) Mean Networth in $Billions for each level of
education: using the Degree.2 above (separates MA/MS
from MBA), here are the descriptive statistics (standard
errors are provided but they may not be meaningful):
Estimates for NetWorth$Bil
Degree.2 Mean Std.Er
00 High School 6.076 0.776
10 Associate 2.600 3.680
20 Bachelors 3.330 0.404
30 Masters 8.817 1.227
31 MBA 3.545 0.575
40 MD or JD 3.389 0.855
50 Doctorate 3.189 1.227
JC:
As Mike correctly notes, this is an excellent dataset for making some
good points in statistics (and other) classes. One such point might be
about restriction of range. As noted by Rick, we are looking at a tiny
proportion of the population defined by the very, very highest of
incomes. Is it reasonable to expect any relationship with such a
restricted sample/population?
Again, thanks to Mike P for taking the time.
Take care
Jim
James M. Clark
Professor of Psychology
204-786-9757
204-774-4134 Fax
j.cl...@uwinnipeg.ca
Department of Psychology
University of Winnipeg
Winnipeg, Manitoba
R3B 2E9
CANADA
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