Essentials of Statistics
Publisher: Bookboon
Published: 2013
ISBN-13: 9788776814083
Table of contents: title: Preface; title: Basic concepts of probability theory; title: Probability space, probability function, sample space, event; title: Conditional probability; title: Independent events; title: The Inclusion-Exclusion Formula; title: Binomial coefficients; title: Multinomial coefficients; title: Random variables; title: Random variables, definition; title: The distribution function; title: Discrete random variables, point probabilities; title: Continuous random variables, density function; title: Continuous random variables, distribution function; title: Independent random variables; title: Random vector, simultaneous density and distribution function; title: Expected value and variance; title: Expected value of random variables; title: Variance and standard deviation of random variables; title: Example (computation of expected value, variance and standard deviation); title: Estimation of expected value µ and standard deviation s by eye; title: Addition and multiplication formulas for expected value and variance; title: Covariance and correlation coefficient; title: The Law of Large Numbers; title: Chebyshev’s Inequality; title: The Law of Large Numbers; title: The Central Limit Theorem; title: Example (distribution functions converge to F); title: Descriptive statistics; title: Median and quartiles; title: Mean value; title: Empirical variance and empirical standard deviation; title: Empirical covariance and empirical correlation coefficient; title: Statistical hypothesis testing; title: Null hypothesis and alternative hypothesis; title: Significance probability and significance level; title: Errors of type I and II; title: Example; title: The binomial distribution Bin(n, p); title: Parameters; title: Description; title: Point probabilities; title: Expected value and variance; title: Significance probabilities for tests in the binomial distribution; title: The normal approximation to the binomial distribution; title: Estimators; title: Confidence intervals; title: The Poisson distribution Pois(?); title: Parameters; title: Description; title: Point probabilities; title: Expected value and variance; title: Addition formula; title: Significance probabilities for tests in the Poisson distribution; title: Example (significant increase in sale of Skodas); title: The binomial approximation to the Poisson distribution; title: The normal approximation to the Poisson distribution; title: Example (significant decrease in number of complaints); title: Estimators; title: Confidence intervals; title: The geometrical distribution Geo(p); title: Parameters; title: Description; title: Point probabilities and tail probabilities; title: Expected value and variance; title: The hypergeometrical distribution HG(n, r,N); title: Parameters; title: Description; title: Point probabilities and tail probabilities; title: Expected value and variance; title: The binomial approximation to the hypergeometrical distribution; title: The normal approximation to the hypergeometrical distribution; title: The multinomial distribution Mult(n, p1, . . . , pr); title: Parameters; title: Description; title: Point probabilities; title: Estimatorer; title: The negative binomial distribution NB(n, p); title: Parameters; title: Description; title: Point probabilities; title: Expected value and variance; title: Estimatorer; title: The exponential distribution Exp(?); title: Parameters; title: Description; title: Density and distribution function; title: Expected value and variance; title: The normal distribution; title: Parameters; title: Description; title: Density and distribution function; title: The standard normal distribution; title: Properties of F; title: Estimation of the expected value µ; title: Estimation of the variance s2; title: Confidence intervals for the expected value µ; title: Confidence intervals for the variance s2 and the standard deviation s; title: Addition formula; title: Distributions connected with the normal distribution; title: The ?2-distribution; title: Student’s t-distribution; title: Fisher’s F-distribution; title: Tests in the normal distribution; title: One sample, known variance, H0 : µ = µ0; title: One sample, unknown variance, H0 : µ = µ0 (Student’s t-test); title: One sample, unknown expected value, H0 : s2 = s2 0; title: Example; title: Two samples, known variances, H0 : µ1 = µ2; title: Two samples, unknown variances, H0 : µ1 = µ2 (Fisher-Behrens); title: samples, unknown expected values, H0 : s2 1 = s2 2; title: Two samples, unknown common variance, H0 : µ1 = µ2; title: Example (comparison of two expected values); title: Analysis of Variance (ANOVA); title: Aim and motivation; title: k samples, unknown common variance, H0 : µ1 = · · · = µk; title: Two examples (comparison of mean values from 3 samples); title: The chi-square test (or ?2-test); title: ?2-test for equality of distribution; title: The assumption of normal distribution; title: Standardised residuals; title: Example (women with 5 children); title: Example (election); title: Example (deaths in the Prussian cavalry); title: Contingency tables; title: Definition, method; title: Standardised residuals; title: Example (students’ political orientation); title: ?2-test for 2 × 2 tables; title: Fisher’s exact test for 2 × 2 tables; title: Example (Fisher’s exact test); title: Distribution free tests; title: Wilcoxon’s test for one set of observations; title: Example; title: The normal approximation to Wilcoxon’s test for one set of observations; title: Wilcoxon’s test for two sets of observations; title: The normal approximation to Wilcoxon’s test for two sets of observations; title: Linear regression; title: The model; title: Estimation of the parameters ß0 and ß1; title: The distribution of the estimators; title: Predicted values ˆyi and residuals ˆei; title: Estimation of the variance s2; title: Confidence intervals for the parameters ß0 and ß1; title: The determination coefficient R2; title: Predictions and prediction intervals; title: Overview of formulas; title: Example; title: A Overview of discrete distributions; title: B Tables; title: B.1 How to read the tables; title: B.2 The standard normal distribution; title: B.3 The ?2-distribution (values x with F?2(x) = 0.500 etc.); title: B.4 Student’s t-distribution (values x with FStudent(x) = 0.600 etc.); title: B.5 Fisher’s F-distribution (values x with FFisher(x) = 0.90); title: B.6 Fisher’s F-distribution (values x with FFisher(x) = 0.95); title: B.7 Fisher’s F-distribution (values x with FFisher(x) = 0.99); title: B.8 Wilcoxon’s test for one set of observations; title: B.9 Wilcoxon’s test for two sets of observations, a = 5%; title: C Explanation of symbols; title: D Index