Schedule of classes and notes
Thursday 9/26: Review of the course information and admin details. Overview of the Statistics discipline.
Tuesday 10/1: Illustration of certain aspects of statistical data analysis using a specific application (overview slides). Design of experiments: controlled experiments and observational studies (lecture notes). Reading: Chapters 1 and 2. (For an additional example on randomized controlled experiments and observational studies, check the recent news articles from NYT and NPR)
Thursday 10/3: Further discussion and examples of randomized controlled experiments and observational studies. The histogram as a graphical summary of data. Constructing a (density scale) histogram. Illustration with the histogram of times between successive eruptions of the Old Faithful Geyser (lecture notes). Reading: Chapters 1, 2 and 3.
Tuesday 10/8: Types of variables: qualitative and quantitative (discrete or continuous) variables and data. Numerical measures of center: the average and the median (lecture notes). Reading: Chapters 3 and 4 (Sections 4.1, 4.2 and 4.3).
Thursday 10/10: no class (all classes at UCSC canceled due to power outage)
Tuesday 10/15: Numerical measures of center and spread (lecture notes). Reading: Chapter 4.
Thursday 10/17: Percentiles and the interquartile range. The normal distribution (normal curve); standard units; the normal approximation for data, using only the data average and data SD (lecture notes). Reading: Chapter 5 (optional reading: chapter 6).
Tuesday 10/22: Computing areas under the normal curve, and precentiles of the normal distribution. Review of methods from chapters 3, 4 and 5 (lecture notes). Reading: Chapters 1-5 (review for the exam).
Thursday 10/24: Further calculations under the normal distribution. Average and standard deviation under change of scale. Review exercises (lecture notes). Reading Chapters 1-5 (review for the exam).
Tuesday 10/29: Exam 1
Thursday 10/31: Probability as a measure of uncertainty. Experiments, sample spaces, and events; general conditions (axioms) for probabilities; conditions for probabilities on finite sample spaces; the addition rule for mutually exclusive events (lecture notes). Reading: Chapters 13 and 14.
Tuesday 11/5: Conditional probabilities. Independent events. The multiplication rule for conditional probabilities, and its special case for independent events (lecture notes). Reading: Chapters 13 and 14.
Thursday 11/7: Probability: summary of definitions and formulas. Examples. The law of total probability and Bayes theorem (lecture notes). Reading: Chapters 13 and 14.
Tuesday 11/12: The law of averages. Random variables; random samples from a random variable (population); motivation of statistical learning using the random sample, focusing on the sum. Average and standard deviation of the random variable. Expected value and standard error for the sum. Illustrations with the net gain from placing multiple times the same roulette bet (lecture notes). Reading: Chapters 16 and 17.
Thursday 11/14: Probability histograms. The Central Limit Theorem normal approximation for sums. Applications to the net gain distribution from placing multiple times the same roulette bet (lecture notes). Reading: Chapters 16, 17 and 18.
Tuesday 11/19: Connecting the law of averages with the Central Limit Theorem. Review exercises (lecture notes). Reading: Chapters 13, 14, 16, 17, 18 (review for the exam).
Thursday 11/21: Exam 2
Tuesday 11/26: Overview of statistical inference (based on simple random samples). Chance errors in sample percentages: expected value, standard error, and normal approximation (lecture notes). Reading: Chapter 20 (optional reading: chapter 19).
Tuesday 12/3: Statistical inference for population percentages: the sample percentage as an estimate; estimated SE for the sample percentage; confidence intervals for the population percentage (lecture notes). Reading: Chapters 20 and 21 (sections 1, 2 and 3 from chapter 21).
Thursday 12/5: Review problems. Bayesian statistical inference for population percentages (lecture notes). Reading: review for the final exam.