Difference between revisions of "Chance News 8"

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W. Allen Wallis
 
W. Allen Wallis
  
Supreme  Cout Appointments as a Poisson Distribution<br>
+
Supreme  Court Appointments as a Poisson Distribution<br>
''American Journal of Political Science'', 26,No.1, Feb 1982<br>
+
''American Journal of Political Science'', 26, No.1, February 1982<br>
 
S. Sidney Ulmer
 
S. Sidney Ulmer
  
This is not current news but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.
+
This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.
  
In 1936 Allen Wallis suggested that the number of supreme court  appointments in a given year can be approximated by a Poisson distribution with meen .5He first provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Coourt: 1790-1806 (6) 1807-1836  (7), and 1837-1932 (9).
+
In 1936 Allen Wallis suggested that the number of supreme court  appointments in a given year can be approximated by a Poisson distribution.  In his Figure 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Coourt: 1790-1806 (6) 1807-1836  (7), and 1837-1932 (9). Acually there were 10 in the years 1963 to 1967 which  Wallis called  "negligible exception."
  
 
[[Image:wallis1.png|500px|center]]
 
[[Image:wallis1.png|500px|center]]
  
Wallis then restricts himself to the years 1837-1932 and fits a Poisson distribution providing the following result:
+
Wallis then restricts himself to the years 1837-1932 and finds that the number of court appoiintments in year can be approximated by a Poisson distrution with mean .5.  His results are shown in his Figure 2:
  
 
[[Image:wallis2.png|500px|center]]
 
[[Image:wallis2.png|500px|center]]
  
In his article. Sidney Ulmer suggests that we could include the years with smaller number of Justices and also updates the data to 1980.  He receives the following result:
+
In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 179--1980. His Figure 1 compares actual number of apointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.
  
 
[[Image:ulmer1.png|500px|center]]
 
[[Image:ulmer1.png|500px|center]]
 +
 +
In table 2 Ulmar does the same thing but limited to the 9 year data (1837 to 1980).
 +
 +
[[Image:ulmer2.png|500px|center]]
 +
 +
testing the goodness of fit, Ullmun argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.
 +
==DISCUSSION==
 +
 +
(1)  Find the probability that a president who serves four years will make 2 or more Supreme Court appointments.
 +
 +
(2) Obtain the data from 1790 to 2005 and make tables corresponding to the Ulman's Tables 1 and 2.  Add the tables to this article and also include the data to make it easier to update these results in future years.
  
 
==Item2==
 
==Item2==

Revision as of 18:59, 23 October 2005

Oct 15 to Oct 30

Quotation

One more fagot of these adamantine bandages, is, the new science of Statistics. It is a rule, that the most casual and extraordinary events -- if the basis of population is broad enough -- become matter of fixed calculation. It would not be safe to say when a captain like Bonaparte, a singer like Jenny Lind, or a navigator like Bowditch, would be born in Boston: but, on a population of twenty or two hundred millions, something like accuracy may be had. Ralph Waldo Emerson Fate

Forsooth

Here's another Forsooth from the October issue of RSS News.

Your'e more likely to die in a fire in Strathclyde than anywhere else in the country

BBC1 mews bullietin
11 May 2005

The Poisson Distribution and the Supreme Court

The Poisson Distributioin and the Supreme Court
Journal of the American Statistical Association 31, no. 195 ,(1936), 376-80
W. Allen Wallis

Supreme Court Appointments as a Poisson Distribution
American Journal of Political Science, 26, No.1, February 1982
S. Sidney Ulmer

This is not current news, but since Supreme Court appointments are in the news we felt that these articles might make an interesting class discussion.

In 1936 Allen Wallis suggested that the number of supreme court appointments in a given year can be approximated by a Poisson distribution. In his Figure 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Coourt: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Acually there were 10 in the years 1963 to 1967 which Wallis called "negligible exception."

Wallis1.png

Wallis then restricts himself to the years 1837-1932 and finds that the number of court appoiintments in year can be approximated by a Poisson distrution with mean .5. His results are shown in his Figure 2:

Wallis2.png

In his article, Sidney Ulmer updated the data to 1980 and also includes data from the early Supreme Courts with 6 and 7 members. Thus his data covers the years 179--1980. His Figure 1 compares actual number of apointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.

Ulmer1.png

In table 2 Ulmar does the same thing but limited to the 9 year data (1837 to 1980).

Ulmer2.png

testing the goodness of fit, Ullmun argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.

DISCUSSION

(1) Find the probability that a president who serves four years will make 2 or more Supreme Court appointments.

(2) Obtain the data from 1790 to 2005 and make tables corresponding to the Ulman's Tables 1 and 2. Add the tables to this article and also include the data to make it easier to update these results in future years.

Item2

To be added.