This 2nd edition compendium contains and explains essential statistical formulas within an economic context. Expanded by more than 100 pages compared to the 1st edition, the compendium has been supplemented with numerous additional practical examples, which will help readers to better understand the formulas and their practical applications. This statistical formulary is presented in a practice-oriented, clear, and understandable manner, as it is needed for meaningful and relevant application in global business, as well as in the academic setting and economic practice.
The topics presented include, but are not limited to: statistical signs and symbols, descriptive statistics, empirical distributions, ratios and index figures, correlation analysis, regression analysis, inferential statistics, probability calculation, probability distributions, theoretical distributions, statistical estimation methods, confidence intervals, statistical testing methods, the Peren-Clement index, and the usual statistical tables.
Given its scope, the book offers an indispensable reference guide and is a must-read for undergraduate and graduate students, as well as managers, scholars, and lecturers in business, politics, and economics.
Author(s): Franz W. Peren
Edition: 2
Publisher: Springer
Year: 2022
Language: English
Pages: 324
City: Cham
Preface
Preface to the 2nd edition
Preface to the 1st edition
Contents
About the Author
List of Abbreviations
Chapter 1 Statistical Signs and Symbols
General
Set Theory
Chapter 2 Descriptive Statistics
2.1 Empirical Distributions
2.1.1 Frequencies
2.1.2 Cumulative Frequencies
2.2 Mean Values and Measures of Dispersion
2.2.1 Mean Values
2.2.2 Measures of Dispersion
2.3 Ratios and Index Figures
2.3.1 Ratios
2.3.2 Index Figures
2.3.3 Peren-Clement Index (PCI)
2.4 Correlation Analysis
2.5 Regression Analysis
2.5.1 Simple Linear Regression
2.5.1.1 Confidence Intervals for the Regression Coefficients of a Simple Linear Regression Function
2.5.1.2 Student’s t-Tests for the Regression Coefficients of a Simple Linear Regression Function
2.5.2 Multiple Linear Regression
2.5.2.1 Confidence Intervals for the Regression Coefficients of a Multiple Linear Regression Function
2.5.2.2 Student’s t-Tests for the Regression Coefficients of a Multiple Linear Regression Function
2.5.3 Double Linear Regression
2.5.3.1 Confidence Intervals for the Regression Coefficients of a Double Linear Regression Function
2.5.3.2 Student’s t-Tests for the Regression Coefficients of a Double Linear Regression Function
Chapter 3 Inferential Statistics
3.1 Probability Calculation
3.1.1 Fundamental Terms/Definitions
3.1.2 Theorems of Probability Theory
3.2 Probability Distributions
3.2.1 Concept of Random Variables
3.2.2 Probability, Distribution and Density Function
3.2.2.1 Discrete Random Variables Probability Function
3.2.2.2 Continuous Random Variables
3.2.3 Parameters for Probability Distributions
3.3 Theoretical Distributions
3.3.1 Discrete Distributions
3.3.2 Continuous Distributions
3.4 Statistical Estimation Methods (Confidence Intervals)
3.4.1 Confidence Interval for the Arithmetic Mean of the Population μ
3.4.2 Confidence Interval for the Variance of the Population σ2
3.4.3 Confidence Interval for the Share Value in the Population θ
3.4.4 Confidence Interval for the Difference of the Mean Values of Two Populations μ1 and μ2
3.4.5 Conficence Interval for the Difference of the Share Values of Two Populations θ1 and θ2
3.5 Determination of the Required Sample Size
3.5.1 Determination of the Required Sample Size for an Estimation of the Arithmetic Mean μ
3.5.2 Determination of the Required Sample Size for an Estimation of the Share Value θ
3.6 Statistical Testing Methods
3.6.1 Parameter Tests
3.6.1.1 Arithmetic Mean with Known Variance of the Population | One Sample Test
3.6.1.2 Arithmetic Mean with Unknown Variance of the Population | One Sample Test
3.6.1.3 Share Value | One Sample Test
3.6.1.4 Variance | One Sample Test
3.6.1.5 Difference of Two Arithmetic Means with Known Variances of the Population | Two Samples Test
3.6.1.6 Difference of Two Arithmetic Means with Unknown Variances of the Populations under the Assumption that their Variances are Unequal | Two Samples Test
3.6.1.7 Difference of Two Arithmetic Means with Unknown Variances of the Populations under the Assumption that their Variances are Equal | Two Samples Test
3.6.1.8 Difference of Two Share Values | Two Samples Test
3.6.1.9 Quotients of Two Variances | Two Samples Test
3.6.2 Distribution Tests (Chi-Squared Tests)
3.6.2.1 Chi-Squared Goodness of Fit Test
3.6.2.2 Chi-Squared Independence Test
3.6.2.3 Chi-Squared Homogeneity Test
3.6.3 Yates’s Correction
Chapter 4 Probability Calculation
4.1 Terms and Definitions
4.2 Definitions of Probability
4.2.1 The Classical Definition of Probabilty
4.2.2 The Statistical Definition of Probability
4.2.3 The Subjective Definition of Probability
4.2.4 Axioms of Probability Calculation
4.3 Theorems of Probability Calculation
4.3.1 Theorem of Complementary Events
4.3.2 The Multiplication Theorem with Independence of Events
4.3.3 The Addition Theorem
4.3.4 Conditional Probability
4.3.5 Stochastic Independence
4.3.6 The Multiplication Theorem in General Form
4.3.7 The Theorem of Total Probability
4.3.8 Bayes’ Theorem (Bayes’ Rule)
4.3.9 Overview of the Probability Calculation of Mutually Exclusive and Non-Exclusive Events
4.4 Random Variable
4.4.1 The Concept of Random Variables
4.4.2 The Probability Function of Discrete Random Variables
4.4.3 The Distribution Function of Discrete Random Variables
4.4.4 Probability Density and Distribution Function of Continuous Random Variables
4.4.5 Expected Value and Variance of Random Variables
Appendix A Statistical Tables
Appendix B Bibliography
Index
