Fundamentals of Statistics

TEACHING UNIT 1. Basic Concepts and Data Organization 1. Introduction to Statistics 2. Concept and Functions of Statistics 2.1. Descriptive Statistics 2.2. Inferential Statistics 3. Measurement and Measurement Scales 3.1. Nominal Scale 3.2. Ordinal Scale 3.3. Interval Scale 3.4. Ratio Scale 4. Variables: Classification and Notation 5. Frequency Distribution 5.1. Frequency Distribution by Intervals 6. Graphical Representations Glossary TEACHING UNIT 2. Basic Descriptive Statistics and Inference 1. Descriptive Statistics 1.1. Description of a Qualitative Variable 1.2. Description of a Quantitative Variable 2. Inferential Statistics 2.1. Prerequisite Concepts 2.2. Sampling Methods 2.3. Key Measures Glossary TEACHING UNIT 3. Probability Distributions 1. Prerequisite Concepts in Probability 2. Discrete Probability Variables 2.1. Probability Function 2.2. Distribution Function 2.3. Mean and Variance of a Random Variable 3. Discrete Probability Distributions 3.1. The Binomial Distribution 3.2. Other Discrete Distributions 4. Normal Distribution 5. Distributions Associated with the Normal Distribution 5.1. Pearson’s “Chi-Square” Distribution 5.2. Student’s “t” Distribution Glossary TEACHING UNIT 4. Central Limit Theorem 1. Introduction to the Central Limit Theorem 2. Normal approximation to the binomial distribution 2.1. First version of the Central Limit Theorem 2.2. Use of the normal approximation to the binomial distribution 3. Laplace’s Central Limit Theorem 4. The Central Limit Theorem and Early Rigorous Proofs 4.1. Liapunov’s Central Limit Theorem 4.2. Lindeberg’s Central Limit Theorem 4.3. Lindeberg–Lévy Central Limit Theorem 4.4. Lindeberg–Feller Central Limit Theorem 5. Generalizations of the Central Limit Theorem Glossary TEACHING UNIT 5. Hypothesis Testing 1. Introduction to Statistical Hypotheses 2. Hypothesis Testing 3. Parametric Hypothesis Testing 3.1. Hypotheses in Parametric Tests 3.2. Test Statistic 3.3. Power of a Test 3.4. Properties of the Test 4. Types of Errors 5. Nonparametric Tests 5.1. Chi-Square Glossary TEACHING UNIT 6. Linear Regression 1. Introduction to Regression Models 2. Regression Models: Applicability 3. Variables to Include in the Regression Model 3.1. Types of Variables to Include in the Model 4. Building the Regression Model 4.1. Selecting Model Variables 4.2. Methods for Building the Regression Model 4.3. Obtaining and Validating the Most Appropriate Model 5. Linear Regression Model 6. Logistic regression model 7. Confounding factors 8. Interpretation of regression model results Glossary