Hamilton County judges try thousands of cases per year. In an overwhelming major
ID: 3134255 • Letter: H
Question
Hamilton County judges try thousands of cases per year. In an overwhelming majority of the cases disposed, the verdict stands as rendered. However, some cases are appealed, and of those appealed, some of the cases ae reversed. Kristen DelGuzzi of The Cincinnati Enquirer conducted a study of case handled by Hamilton County judges over the years 1994 through 1996 (The Cincinnati Enquirer, January 11, 1998). Shown in Judge.xls are the results for 182,908 cases handled (disposed) by 38 judges in Common Pleas Court, Domestic Relation Court, and Municipal Court. Two of the judges (Dinkelacker and Hogan) did not serve in the same court for the entire three-year period. The purpose of the newspapes study was to evaluate the performance of the judges. Appeals are often the result of mistakes made by judges, and the newspaper wanted to know which judges were doing a good job and which were making too many mistakes. You are called in to assis in the data analysis. Use your knowledge of probability and conditional probability to help with the ranking of the judges. You also may be able to analyze the likelihood of appeal and reversal for cases handled by different courts.
a. The probability of cases being appealed and reversed in the thee different courts.
b. The probability of a case being appealed for each judge.
c. The probability of a case being reversed for each judge.
d. The probability of reversal given an appeal for each judge.
e. Rank the judges within each court. State the criteria you used and provide a rational for your choice.
Common Pleas Court Judges Total Cases Disposed Appeals Cases Reversed Cases Fred Cartolano 3037 137 12 Thomas Crush 3372 119 10 Patrick Dinkelacker 1258 44 8 Timothy Hogan 1954 60 7 Robert Kraft 3138 127 7 William Matthews 2264 91 18 Willian Morrissey 3032 121 22 Norbert Nadel 2959 131 20 Arthur Ney, Jr. 3219 125 14 Richard Niehaus 3353 137 16 Thomas Nurre 3000 121 6 John O'Connor 2969 129 12 Robert Ruehlman 3205 145 18 J. Howard Sunderman 955 60 10 Ann Marie Tracey 3141 127 13 Ralph Winkler 3089 88 6 TOTAL 43,945 1,762 199 Domestic Relations Court Judges Total Cases Disposed Appeals Cases Reversed Cases Penelope Cunnungham 2729 7 1 Patrick Dinkelacker 6001 19 4 Deborah Gaines 8799 48 9 Ronald Panioto 12970 32 3 TOTAL 30,499 106 17 Municipal Court Judges Total Cases Disposed Appeals Cases Reversed Cases Mike Allen 6149 43 4 Nadine Allen 7812 34 6 Timothy Black 7954 41 6 David Davis 7736 43 5 Leslie Isahia Gaines 5282 35 13 Karla Grady 5253 6 0 Deidra Hair 2532 5 0 Dennis Helmick 7900 29 5 Timothy Hogan 2308 13 2 James Patrick Kenney 2798 6 1 Joseph Luebbers 4698 25 8 William Mallory 8277 38 9 Melba Marsh 8219 34 7 Beth Mattingly 2971 13 1 Albert Mestmaker 4975 28 9 Mark Painter 2239 7 3 Jack Rosen 7790 41 13 Mark Schweikert 5403 33 6 David Stockdale 5371 22 4 John A West 2797 4 2 TOTAL 108,464 500 104Explanation / Answer
Please find the excel file on which the calculation has been done on the link given below.
https://www.dropbox.com/s/qogt3w622ea93v8/Judge.xlsx?dl=0
Now I will tell you the methodolgy/formulas involved in doing the calculations.
Probability of a case being appealed = number of cases appealed/ total number of cases disposed.
Probability of a case being reversed = number of cases reversed/ total number of cases disposed.
Probability of a case being reversed given they have been appealed = number of cases reversed/ number of cases appealed
The judge having lesser probability of a case being appealed/ reversed has been given a higher rank.
Note : the calculations for all the three courts has been done on seperate sheets in the excel file whose link has been given at the beginning of this question. In case you are not clear with any step or formula, please ask in comments.
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