Quantitative Methods for Lawyers Class #16: T Stat, ANOVA, F Stat
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
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)
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)
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