Good Example Of Report On Managerial Report Based On Probabilities And Conditional Probabilities

Introduction

In this paper we use the knowledge of probability and conditional probability to examine the effectiveness of the judges and courts given in a data sample. The data represents the results of the judges decisions – how many were disposed, how many were appealed and if appealed, what is the amount of the reversed cases.

Body

We are given with the data of 16 judges of Common Pleas Court (43945 cases), 4 judges of Domestic Relations Court (30499 cases) and 20 Municipal Judges (108464 cases). There are 182,908 cases in total.

For each judge there is following information given:

Disposed – the number of disposed cases
Appealed – the number of appealed cases
Reversed – the number of reversed decisions
Now we fill the table in Excel file.
The probability of reversal, given an appeal for each judge is the ratio of number of reversed cases and number of appealed cases for each judge.

The results of the judges effectiveness is given on the histograms below:

Conclusion
The overall rank shows the effectiveness of the courts for each of three courts considered. According to the calculations, the best judge of Common Pleas Court is John W. Sweeny Jr. with the number of 3452 cases disposed, only 145 appealed and only 2 reversed. There are two judges in Domestic Relations Court with the highest rank - John A. Lahtinen and William E. McCarthy. The first judge is better in the probability of the reversed cases given the case is appealed but the second judge is better in the probability of appellations. Generally, they are both the best judges of this court. The best judge of Municipal Court is Dianne T. Renwick with 5645 cases considered, only 5 of which was appealed and no case was ever reversed.

References

Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., & Cochran, J.J. (2015). Essentials of statistics for business and economics. (7th ed.). Stamford, CT: Cengage Learning.
Gut, Allan (2013). Probability: A Graduate Course (2 ed.). New York, NY: Springer. ISBN 978-1-4614-4707-8.
Gillies, Donald (2000); "Philosophical Theories of Probability"; Routledge; Chapter 4 "The subjective theory"