# Mini Calendar

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

# Topics Covered

## Week 1 (Aug 23)

Review of Probability.
• Random Variables: Z
• Sample Space: S = {a, b, c, d}
• Events: a, b, c, d
• Probability of Events: P[Z=a]
Craps
• Basic rules for the pass the line bet
Big Picture
• ... and checking your methods

## Week 2 (Aug 28 & 30)

Intro to coding in R.
Detecting a weighted die.
• 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

## Week 3 (Sept 4 & 6)

How good is the exact interval?
• Developing theoretical experiments to test operating characteristics of methods
At least three (1-α) level confidence intervals for a proportion
• Exact interval
• Asymptotic Normal interval (Wald interval)
• Wilson interval
• Add 2 successes and 2 failures interval
P[LB < θ < UB] < 1-α Central Limit Theorem. Normal approximation for the Binomial.

## Week 4 (Sept 11 & 13)

What makes x/n a "good" estimator for θ? Unbiasedness - definition, proof for x/n. Likelihood function L[θ]. Maximum likelihood estimator (MLE). Values that are well supported by the data. Likelihood Support interval for a proportion. Big Picture - when examining a statistical method:
1. Understand the philosophical justification
2. Understand the mathematical justification
3. Understand the performance in various simulated settings

## Week 5 (Sept 18 & 20)

Sensitivity, Specificity, Positive Predictive Value, Negative Predictive Value. Bayes theorem Prior probability distribution and posterior probability distribution. Bayesian Credible interval for a proportion.

## Week 6 (Sept 25 & 27)

Interval methods for the population mean. Wald interval (Z interval) with variance known. Z interval with variance unknown. t interval with variance unknown. Likelihood support interval using Normal distribution.

## Week 7 (Oct 2 & 4)

Bayesian credible interval using Normal distribution. Estimating Power by hand. Interval methods for the difference of two population means.
• Wald interval (Z interval) with variance known.
• Z interval with variance unknown.
• t interval with variance unknown.
• Likelihood support interval using Normal distribution.
Estimating sample size needed to achieve a given level of precision, e.g. SE < 0.001. Interval methods for the difference of two population means.
• 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.

## Week 8 (Oct 9 & 11)

Interval methods for the difference of two population proportions (RD).
Intervals for other measures comparing population proportions (RR, OR).
Graphical assessments of Normality: Quantile-Quantile (QQ) Plots

## Week 9 (Oct 16)

Intervals for other measures comparing population proportions (RR, OR).
• Delta method
• Numerical approximation of a posterior distribution (ratio of two independent Beta distributions)

2nd Exam

## Week 11 (Oct 30 & Nov 1)

Inference.
• Hypothesis testing vs a point null
Power curves
• Type I and Type II errors
• Pre-specifying a Type I error rate (α)

## Week 12 (Nov 6 & 8)

Randomization Inference
• Permuting treatment assignment to generate a null distribution
Nonparametric tests
• Wilcoxon-Mann-Whitney test (wilcox.test)
When the null shapes the variance
• one-sample proportions test
• equality of two proportions test (as Z and as Chi-squared)

## Week 13 (Nov 13 & 15)

Omnibus Tests
• Chi-squared test
• ANOVA
Multiple comparisons
• Familywise Error Rate
• Bonferroni procedure
• False Discovery Rate
• Benjamini Hochberg procedure
• Controlling pre-experimental probabilities like Type I error, FWER, and FDR

## Week 15 (Nov 27 & 29)

Statistical vs Clinical Significance
• Second generation p-values
• Indirect control of Type I error
Estimating post-experimental probabilities
• P[Ho true | rejected Ho] as opposed to P[reject Ho | Ho true]

## Week 16 (Dec 4 & 6)

Final Exam
Topic revision: r17 - 15 Nov 2018, RobertGreevy

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