Essentials of Statistics
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About the book
Reviews
Mohadeseh Savadkoohi ★★★★★
Practices at all levels with a good book
IDOWU KUNLE ★★★★★
Its a very comrehensive and expalanatory book, cover the most essaential aspects anyone learing Statistics should know
Description
Many students find that the obligatory Statistics course comes as a shock. The set textbook is difficult, the curriculum is vast, and secondaryschool maths feels infinitely far away. "Statistics" offers friendly instruction on the core areas of these subjects. The focus is overview. And the numerous examples give the reader a "recipe" for solving all the common types of exercise.
This free eBook can be read in combination with and in some cases instead of the following textbooks:
 Essential Statistics, by David More
 Essential Statistics, by Robert Gould & Colleen N. Ryan
 Statistics, by James T McClave & Terry Sincich
 Statistics 4th edition, by David Freedman, Robert Pisani & Roger Purves
 Elementary Statistics 11th edition, by Mario F Triola
 Statistics 3rd edition, by Alan Agresti, Christine Franklin, Christine A Franklin & Joseph Blitzstein
 Essentials of Statistics 4th edition, by Mario F Triola
 Elementary Statistics 8th edition, by Allan G Bluman
 Understanding Basic Statistics, by Charles Henry Brase & Corrinne Pellillo Brase
 Understandable Statistics 10th edition, by Charles Henry Brase & Corrinne Pellillo Brase
Preface
Many students find that the obligatory Statistics course comes as a shock. The set textbook is difficult, the curriculum is vast, and secondaryschool maths feels infinitely far away.
“Statistics” offers friendly instruction on the core areas of these subjects. The focus is overview. And the numerous examples give the reader a “recipe” for solving all the common types of exercise. You can download this book free of charge.
Content
 Preface
 Basic concepts of probability theory
 Probability space, probability function, sample space, event
 Conditional probability
 Independent events
 The InclusionExclusion Formula
 Binomial coefficients
 Multinomial coefficients
 Random variables
 Random variables, definition
 The distribution function
 Discrete random variables, point probabilities
 Continuous random variables, density function
 Continuous random variables, distribution function
 Independent random variables
 Random vector, simultaneous density and distribution function
 Expected value and variance
 Expected value of random variables
 Variance and standard deviation of random variables
 Example (computation of expected value, variance and standard deviation)
 Estimation of expected value µ and standard deviation s by eye
 Addition and multiplication formulas for expected value and variance
 Covariance and correlation coefficient
 The Law of Large Numbers
 Chebyshev’s Inequality
 The Law of Large Numbers
 The Central Limit Theorem
 Example (distribution functions converge to F)
 Descriptive statistics
 Median and quartiles
 Mean value
 Empirical variance and empirical standard deviation
 Empirical covariance and empirical correlation coefficient
 Statistical hypothesis testing
 Null hypothesis and alternative hypothesis
 Significance probability and significance level
 Errors of type I and II
 Example
 The binomial distribution Bin(n, p)
 Parameters
 Description
 Point probabilities
 Expected value and variance
 Significance probabilities for tests in the binomial distribution
 The normal approximation to the binomial distribution
 Estimators
 Confidence intervals
 The Poisson distribution Pois(?)
 Parameters
 Description
 Point probabilities
 Expected value and variance
 Addition formula
 Significance probabilities for tests in the Poisson distribution
 Example (significant increase in sale of Skodas)
 The binomial approximation to the Poisson distribution
 The normal approximation to the Poisson distribution
 Example (significant decrease in number of complaints)
 Estimators
 Confidence intervals
 The geometrical distribution Geo(p)
 Parameters
 Description
 Point probabilities and tail probabilities
 Expected value and variance
 The hypergeometrical distribution HG(n, r,N)
 Parameters
 Description
 Point probabilities and tail probabilities
 Expected value and variance
 The binomial approximation to the hypergeometrical distribution
 The normal approximation to the hypergeometrical distribution
 The multinomial distribution Mult(n, p1, . . . , pr)
 Parameters
 Description
 Point probabilities
 Estimatorer
 The negative binomial distribution NB(n, p)
 Parameters
 Description
 Point probabilities
 Expected value and variance
 Estimatorer
 The exponential distribution Exp(?)
 Parameters
 Description
 Density and distribution function
 Expected value and variance
 The normal distribution
 Parameters
 Description
 Density and distribution function
 The standard normal distribution
 Properties of F
 Estimation of the expected value µ
 Estimation of the variance s2
 Confidence intervals for the expected value µ
 Confidence intervals for the variance s2 and the standard deviation s
 Addition formula
 Distributions connected with the normal distribution
 The ?2distribution
 Student’s tdistribution
 Fisher’s Fdistribution
 Tests in the normal distribution
 One sample, known variance, H0 : µ = µ0
 One sample, unknown variance, H0 : µ = µ0 (Student’s ttest)
 One sample, unknown expected value, H0 : s2 = s2 0
 Example
 Two samples, known variances, H0 : µ1 = µ2
 Two samples, unknown variances, H0 : µ1 = µ2 (FisherBehrens)
 samples, unknown expected values, H0 : s2 1 = s2 2
 Two samples, unknown common variance, H0 : µ1 = µ2
 Example (comparison of two expected values)
 Analysis of Variance (ANOVA)
 Aim and motivation
 k samples, unknown common variance, H0 : µ1 = · · · = µk
 Two examples (comparison of mean values from 3 samples)
 The chisquare test (or ?2test)
 ?2test for equality of distribution
 The assumption of normal distribution
 Standardised residuals
 Example (women with 5 children)
 Example (election)
 Example (deaths in the Prussian cavalry)
 Contingency tables
 Definition, method
 Standardised residuals
 Example (students’ political orientation)
 ?2test for 2 × 2 tables
 Fisher’s exact test for 2 × 2 tables
 Example (Fisher’s exact test)
 Distribution free tests
 Wilcoxon’s test for one set of observations
 Example
 The normal approximation to Wilcoxon’s test for one set of observations
 Wilcoxon’s test for two sets of observations
 The normal approximation to Wilcoxon’s test for two sets of observations
 Linear regression
 The model
 Estimation of the parameters ß0 and ß1
 The distribution of the estimators
 Predicted values ˆyi and residuals ˆei
 Estimation of the variance s2
 Confidence intervals for the parameters ß0 and ß1
 The determination coefficient R2
 Predictions and prediction intervals
 Overview of formulas
 Example
 A Overview of discrete distributions
 B Tables
 B.1 How to read the tables
 B.2 The standard normal distribution
 B.3 The ?2distribution (values x with F?2(x) = 0.500 etc.)
 B.4 Student’s tdistribution (values x with FStudent(x) = 0.600 etc.)
 B.5 Fisher’s Fdistribution (values x with FFisher(x) = 0.90)
 B.6 Fisher’s Fdistribution (values x with FFisher(x) = 0.95)
 B.7 Fisher’s Fdistribution (values x with FFisher(x) = 0.99)
 B.8 Wilcoxon’s test for one set of observations
 B.9 Wilcoxon’s test for two sets of observations, a = 5%
 C Explanation of symbols
 D Index
About the Author
Author website: www.davidbrink.dk