STAT675 Methods in Biostatistics II (grad) 2006 JOHNS HOPKINS

Course Description

Presents fundamental concepts in applied probability, exploratory data analysis, and statistical inference, focusing on probability and analysis of one and two samples. Topics include discrete and continuous probability models; expectation and variance; central limit theorem; inference, including hypothesis testing and confidence for means, proportions, and counts; maximum likelihood estimation; sample size determinations; elementary non-parametric methods; graphical displays; and data transformations.

The goal of this course is to equip biostatistics and quantitative scientists with core applied statistical concepts and methods:

1) The course will refresh the mathematical, computational, statistical and probability background that students will need to take the course.

2) The course will introduce students to the display and communication of statistical data. This will include graphical and exploratory data analysis using tools like scatterplots, boxplots and the display of multivariate data. In this objective, students will be required to write extensively.

3) Students will learn the distinctions between the fundamental paradigms underlying statistical methodology.

4) Students will learn the basics of maximum likelihood.

5) Students will learn the basics of frequentist methods: hypothesis testing, confidence intervals.

6) Students will learn basic Bayesian techniques, interpretation and prior specification.

7) Students will learn the creation and interpretation of P values.

8) Students will learn estimation, testing and interpretation for single group summaries such as means, medians, variances, correlations and rates.

9) Students will learn estimation, testing and interpretation for two group comparisons such as odds ratios, relative risks and risk differences.

10) Students will learn the basic concepts of ANOVA. 

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For Lectures 1-14, please visit Methods in Biostatistics I (140.651).

> Lecture Number 15: Hypothesis Testing (294 KB)

1. Introduce hypothesis testing
2. Cover hypothesis testing for a single mean
3. Z and T tests for a single mean
4. Confidence interval equivalences
5. P-values

Also see Hypothesis Testing Graphs

> Lecture Number 16: Power and sample size and two group tests ( 228 KB)

1. Power
2. Power for a one sided normal test
3. Power for t-test

Also see Hypothesis Testing Review Notes

> Lecture Number 17: Power and sample size and two group tests (311 KB)

1. Paired difference hypothesis tests
2. Independent group differences hypothesis tests

Also see Hypothesis Testing Review Notes

> Lecture Number 18: Tests for binomial proportions (909 KB)

1. Tests for a binomial proportion

2. Score test versus Wald

3. Exact binomial test

4. Tests for differences in binomial proportions

5. Intervals for differences in binomial proportions

> Lecture Number 19: Two sample binomial tests, delta method (264 KB)

1. Define relative risk

2. Odds ratio

3. Confidence intervals

> Lecture Number 20: Two sample binomial tests, delta method (182 KB)

1. Review two sample binomial results

2. Delta method

> Lecture Number 21: Fisher's exact tests, Chi-squared tests (238 KB)

1. Introduce Fisher's exact test

2. Illustrate Monte Carlo version of test

> Lecture Number 22: Fisher's exact tests, Chi-squared tests (351 KB)

1. Chi-squared tests for equivalence of two binomial proportions
2. Chi-squared tests for independence, 2 x 2 tables
3. Chi-squared tests for multiple binomial proportions
4. Chi-squared tests for independence, r x c tables
5. Chi-squared tests for goodness of fit

Also see Multinomial Distribution Notes

> Lecture Number 23: Simpson's pardox, confounding (285 KB)

1. Simpson's paradox

2. Weighting

3. CMH estimate

4. CMH test

> Lecture Number 24: Retrospective case-control studies, exact inference for the odds ratio (254 KB)

1. Odds ratios for retrospective studies

2. Odds ratios approximating the prospective RR

3. Exact inference for the odds ratio

> Lecture Number 25: Methods for matched pairs, McNemar's, conditional versus marginal odds ratios (321 KB)

1. Hypothesis tests of marginal homgeneity

2. Estimating marginal risk differences

3. Estimating marginal odds ratios

4. A brief note on the distinction between conditional

and marginal odds ratios

> Lecture Number 26: Non-parametric tests, permutation tests (365 KB)

1. Distribution-free tests

2. Sign test

3. Sign rank test

4. Rank sum test

5. Discussion of non-parametric tests

> Lecture Number 27: Inference for Poisson counts (354 KB)

1. Poisson distribution

2. Tests of hypothesis for a single Poisson mean

3. Comparing multiple Poisson means

4. Likelihood equivalence with exponential model

> Lecture 28: Multiplicity (224 KB)

1. Familywise error rates

2. Bonferoni procedure

3. Performance of Bonferoni with multiple independent

tests

4. False discovery rate procedure