Statistical Thinking and Data Analysis

Calendar

This class will cover the following topics from the course textbook:

Tamhane, Ajit C., and Dorothy D. Dunlop. Statistics and Data Analysis: From Elementary to Intermediate. Prentice Hall, 1999. ISBN: 9780137444267.

CHAPTERS	TITLES	TOPICS
2	Review of Probability	Computing probabilities: conditional probabilities and Bayes’ rule Quantiles/percentiles, CDF’s, mean, median, variance, standard deviation, covariance, various distributions and what they are used for (particularly Bernoulli, Binomial, Multinomial, Hypergeometric, Poisson, normal)
3	Collecting Data	Sampling terminology: convenience sampling, SRS, stratified random sampling, multistage cluster sampling, 1 in K
4	Summarizing and Exploring Data	Summarizing univariate data: numerically (sample mean, IQR, etc.) and by plotting (pie/bar/pareto chart for categorical data, histogram, box plot, normal plot) Summarizing bivariate data: Simpson’s paradox, scatter plot, sample correlation coefficient Time series: MA, EWMA, forecast error and MAPE, auto-correlation coefficient
Exam 1: Chapters 2-4
5	Sampling Distributions of Statistics	Normal approximation to binomial distribution (which relies on the CLT), computing probabilities with chi-square distribution, t-distribution, F-distribution
6	Basic Concepts of Inference	Bias, MSE, setting up hypotheses, Type I error, Type II error, power For z-test: z-scores, p-values, confidence intervals
7	Inferences for Single Samples	Sample size calculation for confidence intervals on z-test, sample calculation for z-test, sample size calculation for power on z-test, t-test, chi-square test for variance
8	Inferences for Two Samples	QQ plots Comparison of two means for independent samples design (large samples z-test, small sample t-test using either a pooled variance or the Welch-Sattethwaite method) Comparison of two means for matched pairs design (t-test, power and sample-size calculation for power) Comparison of variance using the F-test
Exam 2: Chapters 5-8
9	Inferences for Proportions and Count Data	Comparison to a given proportion using large sample z-test, sample size calculation for confidence intervals Comparison of two proportions using large sample z-test Chi-square test (multinomial and goodness of fit)
10	Similar Linear Regression and Correlation	Computing the least square line, computing r^2, hypothesis testing on beta_1, understanding ANOVA regression tables Checking model assumptions and transforming data
11	Multiple Linear Regression	Understanding ANOVA regression tables, t-tests on individual regression coefficients Multicollinearity Logical regression
Exam 3: Chapters 9-11
14	Nonparametric Statistical Methods	Comparison to a given median using: sign test, Wilcoxon signed rank test (these tests can also be used on the di’s for matched pairs) Comparison of two distributions using Rank Sum test or MWU test Rank correlation methods: Spearman’s rank coefficient, Kendall’s Tau
Exam 4: Chapters 12, 14