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- Aug 23 (First day of class: 23)
- Aug 28 & 30
- Sep 4 & 6
- Sep 11 & 13
- Sep 18 & 20 -- 1st Exam
- Sep 25 & 27
- Oct 2 & 4
- Oct 9 & 11
- Oct 16 (Fall Break: 18-19)
- Oct 23 & 25 -- 2nd Exam
- Oct 30 & Nov 1
- Nov 6 & 8
- Nov 13 & 15
- Nov (T-Giving Break: 17-25)
- Nov 27 & 29
- Dec 4 & 6 (Last day of class: 6) -- Final Exam
- Dec (Reading days and exams 7-15)

- Random Variables: Z
- Sample Space: S = {a, b, c, d}
- Events: a, b, c, d
- Probability of Events: P[Z=a]

- Basic rules for the pass the line bet

- Statistics is about
**estimation** - ... and checking your methods

- RStudio
- Creating functions
- Stylistic preferences: capitalization, indentation, etc.
- See Programming Tips For Statisticians for more

- Using R to perform theoretical experiments.
- The Exact (1-α) level confidence interval for a proportion
- The probability statements that define the method
- Calculating the bounds "by hand", i.e. solving using trial and error in R

- Developing theoretical experiments to test operating characteristics of methods

- Exact interval
- Asymptotic Normal interval (Wald interval)
- Wilson interval
- Add 2 successes and 2 failures interval

- Understand the philosophical justification
- Understand the mathematical justification
- Understand the performance in various simulated settings

- Wald interval (Z interval) with variance known.
- Z interval with variance unknown.
- t interval with variance unknown.
- Likelihood support interval using Normal distribution.

- When X and Y are dependent,
- When X and Y are independent, i.e. Cov(X,Y) = 0.
- When N is large (Frequentist, Likelihoodist, Bayesian).
- When N isn't large but X is Normal-ish.

Intervals for other measures comparing population proportions (RR, OR).

Graphical assessments of Normality: Quantile-Quantile (QQ) Plots

- Delta method
- Numerical approximation of a posterior distribution (ratio of two independent Beta distributions)

- Hypothesis testing vs a point null

- Type I and Type II errors
- Pre-specifying a Type I error rate (α)

- Permuting treatment assignment to generate a null distribution

- Wilcoxon-Mann-Whitney test (wilcox.test)

- one-sample proportions test
- equality of two proportions test (as Z and as Chi-squared)

- Chi-squared test
- ANOVA

- Familywise Error Rate
- Bonferroni procedure
- False Discovery Rate
- Benjamini Hochberg procedure
- Controlling
*pre-experimental*probabilities like Type I error, FWER, and FDR

- Second generation p-values
- Indirect control of Type I error

- P[Ho true | rejected Ho] as opposed to P[reject Ho | Ho true]

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Topic revision: r17 - 15 Nov 2018, RobertGreevy

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