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## Course: Methods in Biostatistics I

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# Lecture Materials

### »Lecture Number 1: Set Theory Basics and Probability (106 KB)

1. Cover syllabus
2. Abstract the idea of an experiment
3. Develop basic set theory to be used in the development
of probability
4. Start discussing probability

### »Lecture Number 2: Introduction to Probability (134 KB)

1. Define probability calculus
2. Basic axioms of probability
3. Define random variables
4. Define density and mass functions
5. Define cumulative distribution functions and survivor
functions
6. Define quantiles, percentiles, medians

### »Lecture Number 3: Expected Values (115 KB)

1. Define expected values
2. Properties of expected values
3. Unbiasedness of the sample mean
4. Define variances
5. Define the standard deviation
6. Calculate Bernoulli variance

### »Lecture Number 4: Random Vectors, Independence (123 KB)

1. Define random vectors
2. Independent events and variables
3. IID random variables
4. Covariance and correlation
5. Standard error of the mean
6. Unbiasedness of the sample variance

### »Lecture Number 5: Conditional Probabilities, Baye's Rule (133 KB)

1. Define conditional probabilites
2. Define conditional mass functions and densities
3. Motivate the conditional density
4. Baye's rule
5. Applications of Baye's rule to diagnostic testing

### »Lecture Number 6: Likelihood (120 KB)

1. Define likelihood
2. Interpretations of likelihoods
3. Likelihood plots
4. Maximum likelihood
5. Likelihood ratio benchmarks

### »Lecture Number 7: Distributions (193 KB)

1. Define the Bernoulli distrubtion
2. Define Bernoulli likelihoods
3. Define the Binomial distribution
4. Define Binomial likelihoods
5. Define the normal distribution
6. Define normal likelihoods

### »Lecture Number 8: Asymptotics (151 KB)

1. Define convergent series
2. Definte the Law of Large Numbers
3. Define the Central Limit Theorem
4. Create Wald confidence intervals using the CLT

### »Lecture Number 9: Confidence Intervals (154 KB)

1. Define the Chi-squared and t distributions
2. Derive confidence intervals for the variance
3. Illustrate the likelihood for the variance
4. Derive t confidence intervals for the mean
5. Derive the likelihood for the effect size

### »Lecture Number 10: Confidence Intervals (108 KB)

1. Introduce independent group t confidence intervals
2. Define the pooled variance estimate
3. Derive the distribution for the independent group,
common variance, statistic
4. Cover likelihood methods for the change in the group
means per standard deviation
5. Discuss remedies for unequal variances

### »Lecture Number 11: Presentation of Data (171 KB)

1. Histograms
2. Stem-and-leaf plots
3. Dot charts and dot plots
4. Boxplots
5. Kernel density estimates
6. QQ-plots

### »Lecture Number 12: Bootstrapping (107 KB)

1. Introduce the bootstrap principle
2. Outline the bootstrap algorithm
3. Example bootstrap calculations

### »Lecture Number 13: Confidence Intervals for Binomial Proportions (238 KB)

1. Confidence intervals for binomial proportions
2. Discuss problems with the Wald interval
3. Introduce Bayesian analysis
4. HPD intervals
5. Confidence interval interpretation