98993 - Statistical Analysis

Learning outcomes

At the end of the course the student will be able to handle fundamental concepts of error analysis, probability distributions and statistical tools that are used to handle experimental data.

Course contents

1. Fundamental Concepts & Descriptive Statistics
• Data Types: Understanding categorical (nominal, ordinal) and quantitative (interval, ratio) data.
• Data Summarisation: Calculating measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation).
• Visualisation: Creating graphs and plots, including histograms, box plots, scatter plots, and bar charts.


2. Probability and Probability Distributions
• Basic Rules: Understanding sample spaces, events, and conditional probability.
• Distributions:Discrete and Continuous
• Central Limit Theorem: Understanding how sample means approximate a normal distribution, which is foundational for inference.


3. Inferential Statistics & Hypothesis Testing
• Sampling: Techniques for drawing samples from a population and understanding bias.
• Estimation: Using confidence intervals to estimate population parameters.
Hypothesis Testing: Defining null and alternative hypotheses, selecting significance levels (a), and calculating p-values.


• Statistical Tests:
◦ t-tests: For comparing means (one-sample, two-sample, paired).
◦ ANOVA (Analysis of Variance): For comparing means across three or more groups.
◦ Chi-square Tests: For testing relationships between categorical variables.


4. Regression Analysis & Modelling
• Correlation: Analysing the strength and direction of relationships between variables.
• Simple Linear Regression: Modelling relationships with one predictor variable (y=ax+b).
• Multiple Regression: Using multiple independent variables to predict an outcome.
• Logistic Regression: Modelling binary outcomes.
• Diagnostic Checking: Testing model assumptions (e.g., linearity,
normality, homoscedasticity).

5. Lagrange Multipliers

Readings/Bibliography

1. John R. Taylor, An Introduction to Error Analysis: The Study of Uncertainties in Physical measurements, 2^nd Edition, University Science Books Sausalito, California (1997).

2) A Modern Introduction to Probability and Statistics: Understanding Why and How by F.M. Dekking C. Kraaikamp, H.P.
Lopuhaa, and L.E. Meester.

3) Lecture Notes

Teaching methods

Teaching in classroom.

Assessment methods

Written examination at the end of the semester, with theoretical questions and problems to solve (each one corresponding to a specific maximum score if correctly answered, for a total of 33 points equivalent to a final mark of 30 with Lode). The exam is passed with a minimum score of 18/30.

Teaching tools

Lessons and exercises in the classroom for the theory (3 CFU).

Office hours

See the website of Evangelos Bakalis