This course introduces chemometrics and statistics for analytical methods, focusing on how raw separation and detector signals are processed into reliable quantitative results. Core topics include method-performance metrics (accuracy, precision, sensitivity, selectivity, robustness), data exploration and visualization, statistical inference and hypothesis testing, and calibration for both univariate and multivariate data. Students also learn practical signal-processing workflows (e.g., baseline correction, peak detection, integration) and gain hands-on skills in software-based data analysis using a higher programming language, with attention to design-of-experiments and validation.
Chemometrics & Statistics #
This online course is based on the academic curriculum taught within the UvA-VU joint degree Master’s programme in Chemistry, Analytical Sciences. The online course contains contributions from Dr. Bob Pirok, Dr. Johan Westerhuis and Prof. Dr. Peter Schoenmakers. While it cannot fully replace the in-person lectures and tutorials, it offers wider access to core concepts and practices through this web-based platform.
Whether you are a student, educator, or professional aiming to deepen your understanding of separation science, this course provides a structured pathway through the textbook. It offers guided reading, supplementary materials, and exercises designed to support a rigorous and comprehensive learning experience.
Learning Goals #
After this course, you will be able to
- Propose suitable methods to data processing and statistical analysis.
- Evaluate whether the applied statistical method led to a useful answer to the analytical question.
- Examine the quality of analytical methods (e.g. accuracy and precision, sensitivity, selectivity, robustness).
- Find the main characteristics of signals obtained by instrumental analytical techniques.
- Optionally: Write scripts to perform statistical computations.
How to use this course #
This course assumes active reading of the accompanying book Analytical Separation Science. Throughout the course, you will be guided to specific modules of the book such as is shown in the example below.
READ SECTION 9.4.2
Outlier testing
Most of the images will feature interactive options that help you to explore what the graph is displaying, just like we would explain you in a lecture room in class.
Some concepts are exclusively explained through such images or the interactive exercises that we provide.
Programming #
Many of the concepts in this course are computational. Where possible, simple Excel methods will be provided for you to apply these concepts. However, it is difficult to process, for example, modern LC-MS datasets with a spreadsheet processor. We therefore also provide programming scripts, currently in MATLAB and Julia.
If you are unfamiliar with programming, there is an introduction course.
% Significance Level
p = 1-alpha/2;
% Calculation
t_crit = icdf('T',p,x_dof);
x_range = t_crit*(x_std/sqrt(n));
% Confidence Interval
x_CI = [x_mean - x_range, x_mean + x_range];
The T.INV() function can be used to compute the ICDF for the t-distribution for a given probability and number of degrees of freedom.
using Distributions, Statistics
# Significance level
p = 1 - alpha / 2
# Define the T distribution with degrees of freedom
t_dist = TDist(x_dof)
# Calculation
t_crit = quantile(t_dist, p)
x_range = t_crit * (x_std / sqrt(n))
# Confidence interval
x_CI = [x_mean - x_range, x_mean + x_range]
Course Overview #
At the current stage, this course contains the following components.
- Introduction to Chemometrics
- Statistics of Repeated Measurements
- Confidence Intervals
- Hypothesis Testing
- Comparing Two Means
- Power Analysis
- Comparing Variances
- Comparing Several Means (ANOVA)
- Pre-testing
- Robust Statistics
- Least Squares Regression
- Calibration & Model Variance
- Model Validation
- Error Propagation
- Design of Experiments (DoE)
- Introduction to Multivariate Statistics
Advanced Chemometrics & Statistics #
A second course is planned entitled Advanced Chemometrics & Statistics. Featuring lectures including:
- Non-linear Regression
- Weighted Regression
- Bootstrapping
- Decision Trees & Random Forests
- SVMs and k-means Clustering
- Optimization Strategies I
- Optimization Strategies II
- Reinforcement Learning
- Bayesian Statistics
