The purpose of this manual is to present the basic principles of Statistics in a methodical and explanatory manner, avoiding specific mathematical difficulties, while also providing the reader with the opportunity to become familiar with the use of computers when applying them.
The first two chapters deal with introductory concepts of statistics, specifically descriptive statistics. Understanding these is helpful for the easier learning of the concepts in the subsequent chapters. In Chapters 3, 4, and 5, a brief introduction to probabilities is given, and the basic theoretical distributions are studied.
Chapter 6 provides an introduction to multivariate distributions, emphasizing the study of independent random variables. In Chapter 7, we analyze the concept of the normal approximation as well as its relationship with the broader term of statistical research and sampling.
The remaining chapters formulate and develop the primary methods for drawing statistical conclusions regarding the parameters that characterize a population, always based on a random sample taken from it. Thus, Chapter 8 presents the necessary technical tools that will assist us in drawing these conclusions.
In Chapter 9, various Estimation Methods for the parameters of a population are developed, while in Chapter 10, the estimation is done with the help of Confidence Intervals. Other methods for drawing statistical conclusions involve Hypothesis Testing, provided in Chapter 11.
In Chapters 9, 10, and 11, we always assume that the population we are studying follows a Normal distribution, something we can statistically test. The latter is achieved in Chapter 12 with the help of Goodness-of-Fit Tests. Additionally, in the same chapter, other statistical problems are developed, such as the Independence Test between two qualitative characteristics.
In Chapter 13, with the help of Simple Regression, we study the joint behavior of two variables, estimating the Regression Line, the degree of dependency of the variables, and providing the statistical effectiveness of our conclusions regarding it.
With the basic principles of Analysis of Variance, provided in Chapter 14, we compare the means of several populations. Chapter 15 generalizes Chapter 13 and deals with Multivariate Regression.
In Chapter 16, the basic principles of a Time Series are presented, and we then briefly provide the time series models according to Box and Jenkins. The main Non-parametric tests are presented in Chapter 16.
All examples and exercises are applications of Statistics, useful for economists and business executives.
Finally, all the Statistical Methodology developed in the book, along with its examples, is also presented using Excel and is included at the end of the book as an independent chapter titled "Excel Usage Guide". The major contribution to the writing of the Excel section was made by mathematics graduate Mr. K. Petridis, to whom I express my heartfelt thanks.
