MATH 4310/BIOL6317 - Fall 2011
Biostatistics
Course Info. View syllabus.
First week. Overwiew. Probability measures. Computing probabilities.
Slides from first class.
Homework Set 1, due Thursday, September 1, 1pm.
Second week. Random variables. Cumulative distribution function. Quantiles.
Mean and variance. Chebyshev inequality. Independence. Optional recap on calculus essentials,
Wed, 10-11am, 646 PGH.
Classroom change. From Tuesday, September 6, we are in Farish Hall, FH 135.
Homework Set 2, due Thursday, September 8, 1pm.
Third week. Variance of the sample mean. Standard error of the sample mean. Sample variance.
Sample standard error. Conditional probabilities. Bayes's rule. Sensitivity and specificity of a diagnostic test.
Homework Set 3, deferred to Tuesday, September 20, 1pm.
Fourth week. Diagnostic likelihood ratios and intepreting the outcome of a test result. Likelihoods. Likelihood ratios.
Example: coin flips and biasedness hypotheses. Binomial distribution and maximum likelihood estimator.
Introduction to R. For the next homework and in the future, you may find the notes on R by Dr. Peters, Basics,
Graphics,
Statistics Functions and Regression, etc
helpful.
Homework Set 4, due Thursday, September 22, 1pm.
Fifth week. Normal and standard normal distributions. Conversion between quantiles.
Computing probabilities in the standardized form. Maximum likelhood estimation of the mean for i.i.d normal random
variables with known variance. MLE for mean and variance. Law of large numbers and consistent estimators.
Central limit theorem.
Homework Set 5, deferred to Tuesday, October 4, 1pm.
Sixth week. Central limit theorem and estimating probabilities for finding sample averages in a given
interval. Confidence intervals for unknown means. Chi-squared distribution and confidence intervals
for the variance.
Homework Set 6, due Thursday, October 6, 1pm.
Seventh week. T-distribution and confindence intervals for small sample sizes.
Confidence intervals for paired observations.
Confidence intervals for the success probability of small sequences of Bernoulli trials.
Summary of lectures.
Homework Set 7, due Thursday, October 13, 1pm.
Midterm exam. October 20, 1pm. Note the date was changed by unanimous vote of all students in class! Bring your ID, a scientific calculator, and a pen. The Summary of the lectures relevant for the midterm has been updated.
Review session on Wednesday, Oct 19, 1:30-3pm, PGH 646.
Eighth week. Hypothesis testing. Z-score. P-value. T-test. Equivalence between hypothesis testing (with two-sided
alternative) and computing the confidence interval. Computing power. Paired observations.
Homework Set 8, due Thursday, November 3, 1pm. For students enrolled
in Biol6317, start working on Project 1 as part of the assignment. The project
is due November 10.
Ninth week. Testing for independent groups. Testing for equal variance.
Testing of binomial proportions. Testing for equality of binomial proportions between
independent groups.
Homework Set 9, due Thursday, November 10, 1pm. For students enrolled
in Biol6317, complete Project 1 as part of the assignment.
Tenth week. Relative risk. Delta method for estimating standard errors. Odds ratio.
Fisher's exact test. Hypergeometric distribution. One and two-sided alternatives.
Computing p-values with the Monte Carlo method.
Homework Set 10, due Thursday, November 17, 1pm. For students enrolled
in Biol6317, complete Project 2 as part of the assignment.
Eleventh week. Chi-squared testing for equality of proportions and for independence, for
2x2 tables from case-control studies and larger tables with more categories/relative proportions.
Homework Set 11, due Thursday, December 1, 1pm. For students enrolled
in Biol6317, complete Project 3 as part of the assignment.
Twelfth week. Familywise error and Bonferroni procedure. False discovery rate. Non-parametric tests
and Monte-Carlo methods.
Review session for the final on Friday, Dec 9, 3-5pm, PGH 646. The duration of the final is
3 hours. The Summary of the lectures has been updated to include material up to the final.
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