Experimental Data Analysis

Course Description:

This course provides a comprehensive introduction to the principles and techniques of experimental data analysis, incorporating industry-standard tools like R, SQL, and Tableau. Students will learn how to effectively collect, organize, visualize, and interpret data from scientific experiments, leveraging statistical methods, error analysis, and computational tools. The course will also emphasize the integration of AI assistance for enhanced data exploration and analysis.

Course Objectives:

Upon successful completion of this course, students will be able to:

• Understand the fundamental principles of experimental design and data collection.
• Apply appropriate statistical methods for analyzing experimental data using R.
• Perform error analysis and quantify uncertainties in measurements.
• Utilize data visualization techniques in Tableau and Python to effectively communicate results.
• Employ SQL for data querying and management.
• Leverage AI assistance (e.g., code generation, data insights) for data processing and analysis.
• Interpret and draw meaningful conclusions from experimental data.
• Write clear and concise reports summarizing experimental findings.

Target Audience:

Undergraduate or graduate students in science, engineering, data science, or related fields.

Prerequisites:

• Basic understanding of calculus and linear algebra.
• Introductory statistics course (recommended).
• Basic programming skills (recommended).

Course Structure:

The course will consist of lectures, hands-on computer labs (R, Python, SQL, Tableau), data analysis projects, and AI-assisted exercises.

Course Outline:

Module 1: Introduction to Experimental Data and Measurement

• Introduction to the scientific method and experimental design.
• Types of data (quantitative vs. qualitative, continuous vs. discrete).
• Measurement and units.
• Sources of error and uncertainty.
• Significant figures and rounding.
• Data collection and organization.

Module 2: Error Analysis and Uncertainty

• Types of errors (systematic vs. random).
• Propagation of errors.
• Statistical methods for error estimation.
• Confidence intervals.
• Least squares fitting and error estimation of fitting parameters (R).

Module 3: Descriptive Statistics (R)

• Measures of central tendency (mean, median, mode).
• Measures of dispersion (variance, standard deviation, range).
• Histograms and frequency distributions (R).
• Probability distributions (normal, Poisson, binomial) (R).
• Skewness and Kurtosis (R).

Module 4: Data Visualization (Tableau and Python)

• Principles of effective data visualization.
• Scatter plots, line graphs, bar charts, histograms (Tableau and Matplotlib).
• Error bars and data uncertainty.
• Choosing appropriate graph types.
• Interactive dashboards creation using Tableau.

Module 5: Statistical Inference (R)

• Hypothesis testing (R).
• T-tests, chi-square tests, ANOVA (R).
• Correlation and regression analysis (R).
• Statistical significance.
• Non-parametric tests (R).

Module 6: Data Analysis with Computational Tools (Python & AI Assistance)

• Introduction to Python for data analysis.
• NumPy for numerical computation.
• Pandas for data manipulation and analysis.
• SciPy for statistical functions.
• Using AI tools like code generation assistants to create python code for data analysis.
• Using AI tools for initial data insights.

Module 7: Relational Databases and SQL

• Introduction to relational databases.
• SQL for data querying and manipulation.
• Data extraction, transformation, and loading (ETL).
• Joining tables and aggregating data.
• Connecting python and R to SQL databases.

Module 8: Regression and Curve Fitting (R & Python)

• Linear regression (R & Python).
• Non-linear regression (R & Python).
• Goodness of fit (R-squared, chi-squared).
• Model selection.
• Polynomial regression.
• Using AI to help select appropriate regression models.

Module 9: Advanced Topics & AI Applications (Select from the following based on course level and time constraints)

• Time series analysis (R & Python).
• Fourier analysis (R & Python).
• Signal processing (R & Python).
• Machine learning for data analysis (e.g., clustering, classification) (R & Python).
• Bayesian statistics (R).
• Analysis of variance (ANOVA) in more detail (R).
• Using AI tools for anomaly detection.
• Using AI tools for automated reporting.

Assessment:

• Homework assignments (problem sets, data analysis exercises in R, Python, and SQL).
• Lab reports (analysis of experimental data using R, Python, and Tableau).
• Midterm examination.
• Final project (data analysis project and report, including R, SQL, Tableau, and AI assistance).
• Class Participation.

Recommended Textbooks:

• "R for Data Science" by Hadley Wickham and Garrett Grolemund.
• "SQL for Data Analysis: Perform Fast and Efficient Data Analysis with SQL" by Cathy Tanimura.
• "Practical Tableau: 100 Tips, Techniques, & Strategies to Build and Share Actionable Insights" by Ryan Sleeper.
• "Python Data Science Handbook: Essential Tools for Working with Data" by Jake VanderPlas.
• Various online documentation for AI assistance tools.

Software:

• R and RStudio.
• Python (Anaconda distribution recommended).
• Jupyter Notebooks.
• Libraries: NumPy, SciPy, Pandas, Matplotlib, Seaborn.
• SQL database (MySQL).
• Tableau Desktop/Public.
• Access to an AI code generation tool.

Note:

This outline emphasizes the practical application of R, SQL, and Tableau, and integrates AI assistance to enhance the learning experience.