Quantitative Methods for Lawyers - Class #16 - More T Stat, ANOVA, F Stat - Professor Daniel Martin Katz

1. Quantitative
Methods
for
Lawyers Class #16
More T Stat,
ANOVA & the F Stat
A
n
o
v
a
@ computational
computationallegalstudies.com
professor daniel martin katz danielmartinkatz.com
lexpredict.com slideshare.net/DanielKatz

2. Some Additional
Thoughts on the
“T” Statistic

3. Assumptions Associated
with the “T” Statistic
Normality in the Underlying Data Being Tested
Independent Samples
(as opposed to paired samples)
Equal Variances ( Roughly Equal Variances)~

4. Equal Variances
(Roughly Equal Variances)
How Do We Know Whether the Variances
Are Equal or Equal Enough?
Bartlett’s or Levene’s Test for Equality of Variances
Conducted like other statistical test with the typical
pvalue > .05 than reject criteria

5. Wilcox Rank Sum Test
This is a Non-Parametric Test
(like Chi Squared - Does not scale with magnitude of the observation)
Conducted By Ranking the Data and Comparing
those ranks from each group
Normality in the Underlying
Data Being Tested
Diagnostic = Shapiro-Wilk Normality test

6. T Test Typically Assumes Independence
If Not True - than used the Paired Samples Version
of the T-Test
Independent Samples
(as opposed to paired samples)

7. ANOVA and the
F-Statistic

8. 2500
1500
1500
1300
2000
1500
1500
2000
2000
1500
1400
1500
2000
800
3000
1500
2000
2000
1700
2500
2299
1900
2050
2101
1160
2101
1300
3500
900
995
1299
1900
995
771
1250
900
749
1200
950
1200
995
1300
1600
1601
1000
1371
2400
1500
1325
1500
1799
2780
1800
1399
2225
1700
3800
2299
1800
1450
1500
1000
1500
1799
1600
1600
2000
2500
1200
2500
2000
1500
Northern
District
Western
District
Southern
District
Eastern
District
Attorneys Fees in
Chapter 7 BK’s in Texas
Districts
(From Lawless, et al)

9. Pairwise Comparison Might Not Make Sense If We Are
Interested in Answering Questions Such as is there a
statistically significant difference across all four judicial
districts
Limitation of “T Test”
in this Context
Note: Given a 5% Threshold and a Total of Six
Comparisons - {(W,N)(S,N)(E,N)(S,W)(E,W)(E,S)}
~26% Chance of Generating Stat Significance in
at least 1 Comparison

10. ANOVA and F stat
Comparing Multiple Means at Once

11. ANOVA
Analysis of Variance = ANOVA
Conceptually ANOVA Relies on a Ratio of two
different measures
(1) Between Group Difference
Weighted Difference between the mean of
each group and the overall mean of all groups
(Squared to eliminate Negative Signs)
called the between group sum of squares

12. ANOVA
Analysis of Variance = ANOVA
Conceptually ANOVA Relies on a Ratio of two
different measures
(2) Within Group Difference
Difference between observations and the
overall mean
(Squared to eliminate Negative Signs)
called the Within group sum of squares

13. ANOVA
Between group sum of squares (SSb)
(number of observations in each group) x (mean of each
group - overall mean)2
Within group sum of squares (SSw)
(each observation - group mean)2

14. ANOVA
Mean group sum of squares
Mean Within group sum of squares
(SSb)
degrees of freedom
(MSb) =
(SSw)
degrees of freedom
(MSw) =
F =
(MSb)
(MSw)
_______
_______

15. http://www.psych.utah.edu/stat/introstats/anovaflash.html

16. Take a look at this
page for a moment as
it may help build your
intuition about how the
Fstatistic is calculated

17. http://www.physics.csbsju.edu/stats/anova.html
Can Use R But in the Meantime this
Might be easier for our purposes

18. http://www.physics.csbsju.edu/stats/anova.html

21. Other Uses for
F Tests
http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm

22. Daniel Martin Katz
@ computational
computationallegalstudies.com
lexpredict.com
danielmartinkatz.com
illinois tech - chicago kent college of law@