Basic statistics
My entire book AP Stats and Business Stats published on Lulu.com is given here in the form of posts. If you prefer to have a pdf book, it is just $1.99. See the book review on Amazon
Citing this foreword:
Having read Professor Mynbaev's previous books and research articles I was not surprised with his clear writing and precision. However, I was surprised with an informal and almost conversational one-on-one style of writing which should please most students. The informality belies a careful presentation where great care has been taken to present the material in a pedagogical manner. This will be useful for both student and instructor.
Carlos Martins-Filho
Professor of Economics
University of Colorado at Boulder
Boulder, USA
Chapter 1
Unit 1.1. The structure of mathematics
Unit 1.2. Studying a definition
Units 1.3 and 1.4. Ways to think about things, and questions for repetition
Chapter 2
Unit 2.1. Classification of variables
Unit 2.2. Frequencies and distributions
Unit 2.3. Visualizing statistical data
Unit 2.4. Questions for repetition
Chapter 3
Unit 3.1. Three representations of data: raw, ordered and frequency
Unit 3.2. Measures of central tendency
Unit 3.3. Shape of the distribution
Unit 3.4. Measures of variability
Unit 3.5. Measures of relationships
Unit 3.6. Questions for repetition
Chapter 4
Unit 4.3. Set versus probabilistic terminology
Unit 4.5. Ways to find probabilities
Unit 4.7. All about joint events
Unit 4.8. Conditional probabilities
Unit 4.9. Problem solving strategy
Unit 4.10. Questions for repetition
Chapter 5
Unit 5.2. General properties of means
Unit 5.3. Linear combinations of random variables
Unit 5.5. Independence and its consequences
Unit 5.9. Correlation coefficient
Unit 5.12. An obvious and handy result
Unit 5.13. Distribution of the binomial variable
Unit 5.14. Distribution function
Unit 5.15. Poisson distribution
Unit 5.16. Poisson approximation to the binomial
Unit 5.18. Questions for repetition
Chapter 6
Unit 6.1. Properties of integrals
Unit 6.3. Mean value of a continuous random variable
Unit 6.4. Mean, covariance, variance and correlation
Unit 6.5. The uniform distribution
Unit 6.6. The normal distribution
Unit 6.7. Normal approximation to the binomial
Unit 6.8. Joint distribution and independence
Unit 6.9. Exponential distribution and link to Poisson
Unit 6.10. Questions for repetition
Chapter 7
Unit 7.1. Sampling distribution
Unit 7.2. Sampling distribution of sample variance
Unit 7.3. Monte Carlo simulations
Unit 7.4. Questions for repetition
Chapter 8
Unit 8.1. Unbiasedness and efficiency
Unit 8.3.1. Confidence interval for the population mean. Case of a known variance
Unit 8.3.2. Confidence interval for the population mean. Case of an unknown variance
Unit 8.3.3. Confidence interval for population proportion
Unit 8.4.2. Independent samples. Case I
Unit 8.4.3. Independent samples. Case II
Unit 8.4.4. Independent samples. Case III (Satterthwaite's formula)
Unit 8.4.5. Difference between two population proportions
Unit 8.5. Questions for repetition
Chapter 9
Unit 9.1. Concepts of hypothesis testing
Unit 9.2. Tradeoff between Type I and Type II errors
Unit 9.3. Confidence intervals and hypothesis testing
Unit 9.6. Testing for equality of two sample variances
Unit 9.7. Questions for repetition
Chapter 10
Unit 10.1. Algebra of sample means
Unit 10.3.
Sections 10.3.1-10.3.2. Ordinary Least Squares (OLS): definition and derivation
Section 10.3.3. Unbiasedness of OLS estimators
Section 10.3.4. Variances of OLS estimators
Section 10.3.5. Statistics for testing hypotheses
Unit 10.4. Orthogonality and its consequences
Unit 10.6. Questions for repetition
Chapter 11
Unit 11.1. Main idea and algorithm
Unit 11.2. Exponential and Bernoulli distributions
Unit 11.3. Application to the linear model
Unit 11.4. Questions for repetition
Chapter 12
Unit 12.1. One-way ANOVA: setup and the SST decomposition
Unit 12.2. One-way ANOVA: distributions and the F-test
Unit 12.3. Two-way ANOVA: setup and population model
Unit 12.4. Two-way ANOVA: decompositions and F-tests
Unit 12.5. Questions for repetition
Chapter 13
Unit 13.1. Problems with LSE econometrics
Unit 13.2. How to read Dougherty's book
Unit 13.3. Model with two regressors
Unit 13.4. Linear dependence of vectors
Unit 13.5. Criterion of linear dependence and the dummy variable trap
Unit 13.6. Questions for repetition
Chapter 14
Unit 14.1. Excel functions for distributions
Unit 14.2. Excel functions for critical values
Miscellaneous
AP Statistics the Genghis Khan way 1
AP Statistics the Genghis Khan way 2
Descriptive statistics and inferential statistics
Numerical versus categorical variable
Uniform distribution definition, with examples
Using graphs to describe data
What should you hate about AP Statistics? The TI-83+ and TI-84 graphing calculators are terrible
How to prevent cheating with TI-83+ and TI-84
Minitab is overpriced. Use Excel instead
The stem-and-leaf plot is an archaism - it's time to leave it behind
Histogram versus time series plot, with video
Comparing histogram, Pareto chart and times series plot
Using statistical tables for normal distribution
Probability
Little tricks for AP Statistics
What is probability. Includes sample space; elementary, impossible, sure events; completeness axiom, de Morgan’s laws, link between logic and geometry
Independence of events. Includes conditional probability, multiplication rule and visual illustration of independence
Law of total probability - you could have invented this
Significance level and power of test
Reevaluating probabilities based on piece of evidence
Using numerical measures to describe data
What is a median, with an exercise
Using financial examples to explain properties of sample means
What is a mean value. All means in one place: population mean, sample mean, grouped data formula, mean of a continuous random variable
Unbiasedness definition, with intuition
Marginal probabilities and densities
All properties of variance in one place
Variance of a vector: motivation and visualization
Different faces of vector variance: again visualization helps
Inductive introduction to Chebyshev inequality
Properties of standard deviation
Correlation coefficient: the last block of statistical foundation
Statistical measures and their geometric roots
Population mean versus sample mean: summary comparison
Mean plus deviation-from-mean decomposition
What is a z score: the scientific explanation
What is a binomial random variable - analogy with market demand
Active learning - away from boredom of lectures, with Excel file and video. How to simulate several random variables at the same time.
From independence of events to independence of random variables. Includes multiplicativity of means and additivity of variance
Definitions of chi-square, t statistic and F statistic
Distribution function
Distribution function properties
Examples of distribution functions
Distribution and density functions of a linear transformation
Binary choice models: theoretical obstacles
Maximum likelihood
Maximum likelihood: idea and life of a bulb
Maximum likelihood: application to linear model
Conditioning
Properties of conditional expectation
Conditional expectation generalized to continuous random variables
Conditional variance properties
Simulation of random variables
Generating the Bernoulli random variable (coin), with Excel file
Simulating the binomial variable in Excel and deriving its distribution, with Excel file
Creating frequency table and histogram and using Excel macros, with Excel file
Modeling a sample from a normal distribution, with Excel file
Modeling a pair of random variables and scatterplot definition, with video
Sampling distributions
Law of large numbers and central limit theorem
All about the law of large numbers. Includes convergence in probability, preservation of arithmetic operations and application to simple regression