Quantitative
Methods
for
Lawyers Class #16
More T Stat,
ANOVA & the F Stat
A
n
o
v
a
@ computational
computationallegalstu...
Some Additional
Thoughts on the
“T” Statistic
Assumptions Associated
with the “T” Statistic
Normality in the Underlying Data Being Tested
Independent Samples
(as oppose...
Equal Variances
(Roughly Equal Variances)
How Do We Know Whether the Variances
Are Equal or Equal Enough?
Bartlett’s or Le...
Wilcox Rank Sum Test
This is a Non-Parametric Test
(like Chi Squared - Does not scale with magnitude of the observation)
C...
T Test Typically Assumes Independence
If Not True - than used the Paired Samples Version
of the T-Test
Independent Samples...
ANOVA and the
F-Statistic
2500
1500
1500
1300
2000
1500
1500
2000
2000
1500
1400
1500
2000
800
3000
1500
2000
2000
1700
2500
2299
1900
2050
2101
116...
Pairwise Comparison Might Not Make Sense If We Are
Interested in Answering Questions Such as is there a
statistically sign...
ANOVA and F stat
Comparing Multiple Means at Once
ANOVA
Analysis of Variance = ANOVA
Conceptually ANOVA Relies on a Ratio of two
different measures
(1) Between Group Differ...
ANOVA
Analysis of Variance = ANOVA
Conceptually ANOVA Relies on a Ratio of two
different measures
(2) Within Group Differe...
ANOVA
Between group sum of squares (SSb)
(number of observations in each group) x (mean of each
group - overall mean)2
Wit...
ANOVA
Mean group sum of squares
Mean Within group sum of squares
(SSb)
degrees of freedom
(MSb) =
(SSw)
degrees of freedom...
http://www.psych.utah.edu/stat/introstats/anovaflash.html
Take a look at this
page for a moment as
it may help build your
intuition about how the
Fstatistic is calculated
http://www.physics.csbsju.edu/stats/anova.html
Can Use R But in the Meantime this
Might be easier for our purposes
http://www.physics.csbsju.edu/stats/anova.html
Other Uses for
F Tests
http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm
Daniel Martin Katz
@ computational
computationallegalstudies.com
lexpredict.com
danielmartinkatz.com
illinois tech - chica...
Quantitative Methods for Lawyers - Class #16 - More T Stat, ANOVA, F Stat - Professor Daniel Martin Katz
Quantitative Methods for Lawyers - Class #16 - More T Stat, ANOVA, F Stat - Professor Daniel Martin Katz
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Quantitative Methods for Lawyers - Class #16 - More T Stat, ANOVA, F Stat - Professor Daniel Martin Katz

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

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

  1. 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. 2. Some Additional Thoughts on the “T” Statistic
  3. 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. 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. 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. 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. 7. ANOVA and the F-Statistic
  8. 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. 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. 10. ANOVA and F stat Comparing Multiple Means at Once
  11. 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. 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. 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. 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. 15. http://www.psych.utah.edu/stat/introstats/anovaflash.html
  16. 16. Take a look at this page for a moment as it may help build your intuition about how the Fstatistic is calculated
  17. 17. http://www.physics.csbsju.edu/stats/anova.html Can Use R But in the Meantime this Might be easier for our purposes
  18. 18. http://www.physics.csbsju.edu/stats/anova.html
  19. 19. Other Uses for F Tests http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm
  20. 20. Daniel Martin Katz @ computational computationallegalstudies.com lexpredict.com danielmartinkatz.com illinois tech - chicago kent college of law@
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