1 The statistical evaluation
2 The detection of real phenomena
2.1 Overall considerations on the statistical method
2.2 Concepts underlying the statistical language: real phenomenon,
population, statistical unit , character and modality
2.3 Classification of statistical characters
2.3.1 The measure of a qualitative character
2.3.2 The measure of a quantitative character
2.4 The measure of a latent variable
2.5 The measurement of uncertainty: the probability
2.5.1 The event space
2.5.2 The probability
2.5.3 The conditioned probability
2.5.4 The Bayes' theorem
2.5.5 The random variables
2.5.6 Moments of random variables
2.5.7 The moment-generating function
2.6 The measurement scales
3 The statistical survey
3.1 The stages of a statistical survey
3.2 The tools of a statistical survey
3.3 The questionnaire
3.4 The sample or partial surveys
4 The distribution of a statistical character
4.1 The data for a statistical survey
4.2 Univariate and frequency distributions
4.3 Empirical methods for the subdivision in classes of a discrete or
continuous character
5 Univariate analysis of statistical characters measured on different
kind of scales
5.1 Sinthesis and variability
5.2 Shape
6 The evaluation of a character measured on nominal scale
6.1 Synthesis
6.1.1 The mode
6.2 Variability
6.2.1 The absolute homogeneity or heterogeneity
6.3 The relative indexes
6.4 The relative indexes of homogeneity or heterogeneity
6.5 The dissimilarity index
6.6 Graphic representations of characters measured on nominal scale
6.6.1 The pie chart
6.6.2 Bar diagrams
6.6.3 Figurative graph or pictogram
7 Characters measured on qualitative orderable scale
7.1 The cumulative frequency
7.2 The retro-cumulative frequency
7.3 Synthesis
7.4 Variability
7.5 Shape
7.5.1 The indexes of asymmetry
7.6 Graphic representations
7.6.1 The Box-plot
8 The evaluation of a quantitative character
8.1 Graphic representations of quantitative characters
8.2 Synthesis
8.2.1 The median class
8.2.2 The concept of mean
8.3 Variability
8.3.1 The Range and the interquartile range
8.3.2 The relative variability
8.4 The shape indices: asymmetry and kurtosis
9 Theoretical distributions
9.1 The parametric approach
9.1.1 The moments of a theoretical distribution
9.1.2 Most-used theoretical distributions
9.1.3 Binomial distribution
9.2 Theoretical models for continuous variables
9.2.1 Uniform distribution
9.2.2 Normal or Gaussian distribution
9.2.4 Chi-squared distribution
9.3 Analytic interpolation
9.3.1 The method of least squares
10 Analysis of the relationships between two variables
10.1 Contingency table
10.2 Contingency table: joint, marginal and conditional distributions
10.2.1 Conditional distribution
10.2.2 Marginal and conditional means and variances
10.2.3 Dependency and independency between two variables
10.2.4 Statistical independence
10.2.5 Dependence
10.3 Measures of association in a contingency table: the Chi-square
Index
10.3.1 The normalised Chi-square Index
10.4.1 Covariance as measure of linear interdependence
10.4.2 The linear correlation coefficient 10.5 The regression
10.5.1 The goodness of fit of the regression line to the observations
12 Inference
12.1 Estimate and estimator
12.2 Properties of estimators (with the exception of the sufficiency)
12.3 Model based inference, an approach based on the likelihood
function
12.3.1 Classical inference
12.4 Properties of maximum likelihood estimators
12.5 Interval estimation
12.7 Hypothesis verification
12.8 Inference for finite population
12.8.1 Simple random sampling
12.8.2 Estimation of the total and of the mean
12.9 Other sampling schemes
12.9.1 The stratified sampling
12.9.2 The bunch sampling
12.9.3 The systematic sampling