STATISTICS FOR LAWYERS. “Nonparametric” Statistics “Distribution-Free” Statistics. Distributional Violations. Treat data as nominal Chi Square Tests Binomial Sign test (for matched samples) Use specialized tests that do not make assumptions about the underlying distribution of the data
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STATISTICS FOR LAWYERS
“Nonparametric” Statistics
“Distribution-Free” Statistics
Large Sample:
R = 17
critical value from table is 9 (or less)
(16 males and 12 Females)
E{R} = 15
σ{R} = sqrt(27)/2 = 2.6
Z = (12-15)/2.6) = -1.15
Uniform Distribution
Central Limit Theorem applies and variance is known
Number of Hours Devoted to Civil Cases by Hourly Fee Lawyers
All Cases
Drop cases requiring more than 500 hours
Drop cases requiring more than 100 hours
State Federal
Compare Lawyer Effort for Federal and State Cases
State Federal
Alternative to the two sample t-test
State Federal
Taking the logarithm will sometimes cure nonnomality issues
If there are values of 0, need to add 1 to do log
State Federal
t-test on original data produced a t of -5.590
Rank tests would not change using log transform because the log transformed data are monotonically identical to the original data.
State Federal
State Federal
State Federal
State Court
Federal Court
Alternative to the matched pair t-test
beforeafterdifferrank
7665-11(-)6
3224-8(-)5
6570+5(+)4
8785-2(-)1
2225+3(+)2.5
912+3(+)2.5
3725-12(-)7
T = 2.5 + 2.5 + 4 = 9
critical value at .05 level is 2
Alternative to one analysis of variance
Ni = number of observations in ith group
M = number of sets of ties
Tj = tj3 - tj
tj = number of observations tied for the jth set of ties
Replace original values of each variable with ranks, and then compute Pearson’s product moment correlation using the ranks as the data.
C is number of concordant pairs; D is number of discordant pairs
Specialized version to use with contingency table formed from two ordinal variables
gamma
Somer’s assymetric D
- inf
+ inf
τ1
τ2
τ3
τ4
Y*
Y=1
Y=2
Y=3
Y=4
Y=5
- inf
+ inf
τ1
τ2
τ3
τ4
Y*
Y=1
Y=2
Y=3
Y=4
Y=5