| 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)
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| 3 | Collecting Data |
- Sampling terminology: convenience sampling, SRS, stratified random sampling, multistage cluster sampling, 1 in K
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| 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
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| 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
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| 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
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| 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
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| 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
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| 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)
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| 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
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| 11 | Multiple Linear Regression |
- Understanding ANOVA regression tables, t-tests on individual regression coefficients
- Multicollinearity
- Logical regression
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| 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
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| Exam 4: Chapters 12, 14 |
Tamhane, Ajit C., and Dorothy D. Dunlop. Statistics and Data Analysis: From Elementary to Intermediate. Prentice Hall, 1999. ISBN: 9780137444267.