Difference between revisions of "Chance News 8"

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11 May 2005</div>
 
11 May 2005</div>
  
==The Poisson Distribution and the Supreme Court==
+
==The Poisson distribution and the Supreme Court==
The Poisson Distributioin and the Supreme Court<br>
+
The Poisson distribution and the Supreme Court<br>
 
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br>
 
''Journal of the American Statistical Association'' 31, no. 195 ,(1936), 376-80<br>
 
W. Allen Wallis
 
W. Allen Wallis
  
Supreme  Court Appointments as a Poisson Distribution<br>
+
Supreme  Court Appointments as a Poisson distribution<br>
 
''American Journal of Political Science'', 26, No.1, February 1982<br>
 
''American Journal of Political Science'', 26, No.1, February 1982<br>
 
S. Sidney Ulmer
 
S. Sidney Ulmer
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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 statistician Allen Wallis suggested that the number of Supreme Court appointments in a given year can be approximated by a Poisson distribution.  In his Table 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 exceptions."
+
In 1936 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year.  In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836  (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which  Wallis called  "negligible exceptions."
  
 
[[Image:wallis1.png|500px|center]]
 
[[Image:wallis1.png|500px|center]]
  
Wallis then restricts himself to the years 1837-1932 and finds that the number of court appoiintments in a year can be approximated by a Poisson distrution with mean .5.  His results are shown in his Figure II:
+
Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year.  His results are shown in his Figure II:
  
 
[[Image:wallis2.png|500px|center]]
 
[[Image:wallis2.png|500px|center]]
  
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 1790--1980. His Table 1 compares the actual number of apointments in a year with the expected number of appointments assuming a Poisson distribution with mean  5.13.
+
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 1790--1980. His Table 1 compares the actual number of appointments 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]]
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[[Image:ulmer2.png|500px|center]]
 
[[Image:ulmer2.png|500px|center]]
  
Testing the goodness of fit, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.
+
Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.
  
 
===DISCUSSION===
 
===DISCUSSION===
  
(1) What is the  probabity that a President will make 2 or more appointments to the Supreme Court during a 4 year term?  What is the probability a President makes no appointments during a 4 year term?
+
(1) What is the  probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term?  What is the probability a President makes no appointments during a 4-year term? Has this ever happened?
  
(2) Do you agree with Umer that there is no reason to limit the data to years with the Supreme Court is the same size?
+
(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?
  
(3) Obtain the data needed to update Ullmer's results to 1980 and provide Tables to correspond to Ulmer's Tables 1 and 2.  Add your data Tables to this Chance News.
+
(3) Obtain the data needed to update Ulmer's results to 1980 and provide Tables to correspond to Ulmer's Tables 1 and 2.  Add your data Tables to this Chance News.
 +
 
 +
(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 Ulmer'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.
  
 
==DISCUSSION==
 
==DISCUSSION==

Revision as of 19:52, 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 distribution 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 statistician Allen Wallis suggested that a Poisson distribution can approximate the number of U.S. Supreme Court appointments in a given year. In his Table 1 Wallis provided the number appointed in each year over the intervals with different numbers of Justices on the Supreme Court: 1790-1806 (6) 1807-1836 (7), and 1837-1932 (9). Actually there were 10 in the years 1963 to 1967 which Wallis called "negligible exceptions."

Wallis1.png

Wallis then restricts himself to the years 1837-1932 and finds that a Poisson distribution with mean .5 can approximate the number of court appointments in a year. His results are shown in his Figure II:

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 1790--1980. His Table 1 compares the actual number of appointments in a year with the expected number of appointments assuming a Poisson distribution with mean 5.13.

Ulmer1.png

In his Table II Ulmer limits the data to the 9 member Supreme Courts: 1837 to 1862 and 1869-1980).

Ulmer2.png

Testing the goodness of fits, Ulmer argues that the fit with the varying size Supreme Courts is just as good as with fixed size Supreme Courts.

DISCUSSION

(1) What is the probability that a President will make 2 or more appointments to the Supreme Court during a 4-year term? What is the probability a President makes no appointments during a 4-year term? Has this ever happened?

(2) Do you agree with Ulmer that there is no reason to limit the data to years with the Supreme Court is the same size?

(3) Obtain the data needed to update Ulmer's results to 1980 and provide Tables to correspond to Ulmer's Tables 1 and 2. Add your data Tables to this Chance News.

(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 Ulmer'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.

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.