## Math 322 Biostatistics

### NEWS

• Article on tests of randomness.
• Confusingly, there is also a function named rpart.plot(), which needs

install.packages("rpart.plot")
library(rpart.plot)

It may be used instead of plot.rpart() and has the same inputs.
• There is an updated r-eg-27.txt example for tree classification. It includes more information about computing misclassification rates with printcp() and predict().
• More tree documentation: Zach's example code for building and pruning Classification and Regression Trees (CART) in R.
• HW 11 Solutions are now available.
• HW 10 Solutions are now available.
• Plotting the output of rpart() should be done with plot.rpart(), which needs

install.packages("plot.rpart")
library(plot.rpart)
and which only works with R versions 4 and higher.
• The tree() function in R does not work in R version 4.0 and higher, namely the latest versions. Use rpart() instead after

install.packages("rpart")
library(rpart)

Example file r-eg-27.txt has been updated to include rpart. Be sure to reload the page in your browser.

### R EXAMPLES

Example R commands for:

• Example Midterm (2016).
• Example Final (2020).
• Open-source software R for statistical computing, and its manual.
• Download old free MatLab (for Windows or Linux PCs) from my website.
• There is an online Octave to R dictionary, useful for those who know MatLab or Octave well and want to learn the corresponding R commands.
• R program in file deduct.R to solve HW 1's DNA sequence counting problem.
• R program in file faker.R. Then "faker(n, mu, sd)" generates n>1 samples with exact prescribed mean mu and exact standard deviation sd.
• Notes (brillouin.pdf) on Brillouin and Shannon diversity, for HW 1.
• Notes (condprob.pdf) on conditional probabilities and continuous densities, for HW 3.
• R program in file bvnpdf.R, to compute bivariate normal pdfs. Read the code for usage instructions.
• R program in file dagopear.R to perform the D'Agostino-Pearson test of normality and compute the associated statistics.
• R program in file cochran.R for Cochran's test of a dichotomous variable without replication.
• R program in file kendall.w.R to compute Kendall's coefficient of concordance (Kendall's W). Call it using
kendall.w(tab)
where tab is a matrix with scores (or ranks) along its rows.
• NCI microarray data on 14 cancers:
• nci.info: some information on the data
• nci.names: just the 64 names identifying 14 cancers, to label the 64 rows of gene expression data.
• nci.data: gene expression data, 64 rows of 6830 gene expression values. HINT: Save this to a file.
• Cleaned-up NCI microarray data, 57 samples of 8 cancers with top 12 expressed genes: nci57x13.R, to be saved into your R folder and read into the R session with load("nci57x13.R"). The result is a data frame named "nci12".
• Download nci57x7.R and load("nci57x7.R") to get the top 6 genes data. The result is a data frame named "nci6".
• Article and Table 1 on ABO blood types and cancer in Northern India, for the term project.
• WinBUGS and tutorials:
• Saed Sayad's notes on classifier evaluation:
• Zach's example code for building and pruning Classification and Regression Trees (CART).
• Article feller.pdf on tests of randomness.

### Syllabus

Topics. This is a second course in applied statistics with examples from biology and medicine. Topics include Bayes rule, Markov chains, maximum likelihood estimation with MCMC, classical statistical inference, ANOVA and MANOVA, multivariate visualization, multiple regression, correlation, and classification. Each student will be required to perform and write a report on a data analysis project.

Prerequisites. Math 3200, or Math 2200 and the permission of the instructor.

Time. Classes meet Mondays, Wednesdays and Fridays, 3:00pm to 3:50pm, in Steinberg Hall, room 105 (the Auditorium). Live and recorded video of the lectures will also be available.

Text. The lectures will follow Statistics Using R with Biological Examples by Kim Seefeld and Ernst Linder, an e-text that you may download freely. (Alternative local link.) If you desire a paper copy, you may have it printed and bound at any copy shop from this PDF file.

Supplementary readings and software may be found in the "LINKS" column above.

Homework. You are encouraged to collaborate on homework, although each student must turn in solutions individually. Please complete your solutions on CrowdMark by 11pm on the due date.

For full credit, homework solutions should be clearly legible with the answers properly labeled. For computations, include the R commands used, the input provided, and the output with labels indicating which part of the solution is thus computed.

Suggestion: copy and paste your R session into a text editing program and delete unnecessary text and space, then comment and annotate as needed. Hand in homework as you would like to get it if you were the grader.

Problem sets will be assigned as follows:
 HW #1, due Mon, Feb 1 (Solutions) HW #2, due Mon, Feb 8 (Solutions) HW #3, due Mon, Feb 15 (Solutions) HW #4, due Mon, Feb 22 (Solutions) HW #5, due Mon, Mar 1 (Solutions) HW #6, due Mon, Mar 15 (Solutions) HW #7, due Wed, Mar 24 (Solutions)
 HW #8, due Wed, Mar 31 (Solutions) HW #9, due Wed, Apr 7 (hw09data.txt) (Solutions) (R codes) HW #10, due Mon, Apr 19 (hw10data.txt) (Solutions) (R codes) HW #11, due Mon, Apr 26 (Solutions) (R codes)
Solutions, via CrowdMark, are due at 11:00pm on the due date. Late homework will not be accepted.

Tests. There will be one Midterm Examination due on CrowdMark on Monday, March 8th, 2021.
There will be one cumulative take-home Final Examination, emphasizing the later material. It is due on Friday, May 7th, 2021, on CrowdMark.

Project. There will be one data analysis project due by Monday, May 3rd, 2021, on CrowdMark. A one-page Project Outline is due Friday April 16th, 2021. Late projects will not be accepted. Projects may be selected from this list, or chosen by the student with the prior approval of the instructor.

Grading. One score will be assigned for homework, one for the midterm examination, one for the final examination, and one for the project. These four will contribute in respective shares of 40%, 20%, 20%, and 20% to the course score. Letter grades, computed from the course score, will be at least the following:

 Course score at least: Letter grade at least: 90% 80% 70% 60% A B C D

Students taking the Cr/NCr or P/F options will need a grade of D or better to pass. Students taking the Audit option will need to attend 36 of the 40 class meetings to obtain a Successful Audit grade.

Computing. Students are encouraged to use R on their own computers or on the computers available in the Arts and Sciences Computing Center for both symbolic and numerical computations.

Office Hours. Mondays and Wednesdays 4:00pm-5:00pm (after class), Fridays 10:00am-11:00pm, or by appointment. All office hours will be held by remote videoconferencing.