Math 186/283

Statistics

Rice Virtual Lab in Statistics. Includes an online statistics book, HyperStat Online, and demos of statistical concepts, such as the Normal Approximation to the Binomial Distribution. Note that you would need to install or enable Java to use these.
Birthday problem at Mathworld and at the Mathematical Association of America.
Football games that predict presidential elections, and other bizarre correlations: article 1, article 2 (these are news/opinion articles, not academic/scientific sites).
Gallup poll methodology
xkcd comic strips satirizing P-values (explanation) and statistical significance (explanation).
Spurious correlations

Short readable summary of controversial statistical issues in Mendel's work, by Madan Bhattacharyya, Iowa State University.
Longer paper by Fairbanks & Rytting (2001)
A list of papers about both sides of the controversy.
English translation of Mendel's second paper.
Transcription of Fisher's paper that analyzed Mendel's data in the above paper.

Genome resources at NCBI. Includes the DNA sequences of many organisms, tools for viewing them, and analysis. Sample genomes include SARS (SARS-CoV-1 and SARS-CoV-2) and E. coli.
Mouse Genome Informatics.

Article: Myths of Human Genetics (John McDonald, University of Delaware)
SNPedia: Earwax genetics article and SNP rs17822931.
Ensembl: Overview of SNP rs17822931, genome viewer, and allele frequencies in 1000 Genomes Project Phase 3 populations.
NCBI: Allele frequencies by population in different studies
1000 Genomes Project: Populations studied

Demo 1:

Use default data, or paste in data and click "Use Data".
Click "Show Movable line". Use the square green dots on the line to move it around (center green dot moves it up and down; endpoints change slope).
Click "Show Squared Residuals". Move the line some more. Try to manually minimize SSE (sum of squared errors).
Click "Show Regression Line", the "Show Squared Residuals" under it, and see how close you get to the optimal SSE.
Click "Correlation" and "R-squared".
Note: Using "Show Residuals" instead of "Show Squared Residuals"
minimizes SAE = sum of absolute values of residuals
instead of SSE = sum of squared residuals,
so it doesn't match what we're doing.

Demo 2:

Click on a bunch of points on the grid to create data (blue points). Make it have a linear tendency, but not a perfect line. Alternately, paste a dataset into the coordinates box and hit "Update Plot".
Click BOTH "Fit your own line" and "Move Your Fit Line" and then drag the big green dots to move the line.
Click "Show Residuals" and move the line around some more. Try to collectively minimize the residuals. (It would be better if it gave the sum of squared errors, like SSE in demo 1.)
Click "Display line of best fit" and see how close you got.

Demo 3:

Drag on the red line to move it up or down. Drag on the red dots to change its slope.
Try to manually minimize "Your SSE" (sum of squared errors). The optimal value is shown as "Target SSE".
Click "Show Regression Line" to see how close your line (red) is to the optimal one (blue).
To try it again, you can either drag the blue dots to new positions, or use "Randomize Data".

Nielsen, et al. paper using SVD in a microarray experiment; microarray data.
Orly Alter's publications including many on SVD for microarrays.
Yeung and Ruzzo Bioinformatics paper describing PCA for microarrays as problematic.
Todd Will's tutorial on SVD, including interactive Java applet demonstrations.
Example of PCA with Matlab code.
Armstrong et al (2022), "Applications and Comparison of Dimensionality Reduction Methods for Microbiome Data", Frontiers in Bioinformatics: compares PCA, t-SNE, UMAP, and related methods; authors are from UCSD and include BISB PhD students and faculty!