Basic statistics

• Population vs Sample
• Mean, median and mode
• The geometric mean
• Weighted mean
• Variables and scales
• Range, interquartile range and box plots
• How to identify and deal with outliers
• Standard deviations and error bars
• Why we divide by n-1 and not n when we calculate the SD
• The normal distribution
• The central limit theorem 
• The standard error of the mean (SEM)
• Confidence intervals
• The t-distribution – why we need it
• The one-sample t-test and p-values
• t-test VS confidence intervals
• The degrees of freedom
• The basic steps of hypothesis testing
• The unpaired t-test (independent samples t-test)
• How to check normal distribution
• One-way ANOVA: the basics
• One-way ANOVA: the calculations
• The paired t-test
• Paired vs unpaired t-test
• The repeated-measures ANOVA
• One-proportion Z-test and the corresponding confidence interval
• The Chi-square goodness of fit test and the difference to the one-proportion Z-test
• The two proportion z-test and the Chi-square test of homogeneity
• The Chi-square test of independence VS homogeneity and goodness of fit
• McNemar test
• A deeper understanding of p-values

Non-parametric tests

• The Mann Whitney U test (Wilcoxon Mann Whitney test) part 1/2
• The Mann Whitney U test (Wilcoxon Mann Whitney test) part 2/2 | exact p-value
• The Wilcoxon signed-rank test & the sign test

Type 1 and 2 errors and power

• The basics of type 1 and 2 errors
• The probability of making a type 1 error
• The probability of making a type 2 error (part 1/2)
• The probability of making a type 2 error (part 2/2)
• Statistical power and sample size calculations
• Statistical power – Parametric vs Nonparametric test

Correlation

• Correlation – the basics | Pearson correlation
• Correlation | hypothesis testing | assumptions
• Spearman’s rank correlation | Pearson VS Spearman

Linear regression

• Linear regression – the basics
• Linear regression – least squares
• Linear regression – hypothesis testing
• Linear regression – R2
• Multiple linear regression
• Linear regression – assumptions

How to select an appropriate statistical test

• How to choose an appropriate statistical test

Regression vs ANOVA vs t-test

• Regression vs ANOVA vs t-test

Two-way ANOVA

• Two-way ANOVA – the basics
• Within-Within, Between-Between
• Two-way ANOVA by hand

Post-hoc tests

• The familywise error rate (FWER)
• Fisher’s LSD method
• Bonferroni
• Holm
• Tukey’s test and Dunnett’s test
• How to select an appropriate post-hoc test

Tests based on the false discovery rate (FDR)

• The basics of the FDR
• The Benjamini-Hochberg method
• Storey’s method and q values

Generalized linear models (GLMs)

• Probability vs likelihood
• Maximum likelihood vs ordinary least squares

Logistic regression

• Logistic regression 1: the basics
• Logistic regression 2: classification
• Logistic regression 3: Likelihood and deviance
• Logistic regression 4: Likelihood ratio test and AIC

Poisson regression

• The Poisson distribution vs the normal distribution
• Poisson regression 1 – the basics
• Poisson regression 2 – rates and the offset
• Poisson regression 3 – categorical variables
• Poisson regression 4 – how to calculate the likelihood and the deviance 
• Poisson regression 5 – compare models with the likelihood ratio test and AIC
• Quasi-Poisson and negative binomial regression models
• Zero-inflated Poisson (ZIP) regression

Linear mixed-effect models

• Linear mixed effect models – the basics
• Linear mixed effect models – random slope and intercept

Bayesian statistics

• The basics

Introduction to multivariate statistics

To understand the methods that are used in multivariate statistics, you need to understand some basic linear algebra. For example, you need to understand things like matrix operations, eigenvectors and eigenvalues. You also need to understand the meaning of covariance and different distances in space.

Linear algebra

• Matrices and matrix operations – part 1
• Matrices and matrix operations – part 2
• Eigenvectors and eigenvalues – the basics
• Eigenvectors and eigenvalues – the math

Covariance and distances

• Covariance, correlation matrix 
• Distances in space (Euclidean and Mahalanobis distance)

Once you know the basics in the above videos, you can start to learn about multivariate statistical methods. I recommend that you start to learn about PCA.

PCA

• PCA 1: the basics
• PCA 2: the math
• PCA 3: standardization and extract
• PCA 4: interpret the weights and Varimax rotation

LDA

• LDA – the basics
• LDA – how to use it as a classifier

Multivariate statistical methods

• Multivariate analysis of variance (MANOVA) 
• Hotelling’s T-square test

Metrics used for binary classification and validation

• Sensitivity and specificity
• The positive and negative predictive values
• The ROC curve
• Validation (cross-validation, hold-out, LOOCV) 
• Likelihood ratio

Classification methods

Logistic regression

• Logistic regression 1: the basics
• Logistic regression 2: classification

Linear discriminant analysis

• LDA – the basics
• LDA – how to use it as a classifier

k-nearest neighbors and Mahalanobis distance

• KNN
• Classify based on the Mahalanobis distance

Decision trees and random forest

• Decision trees
• Random forest

Support vector machines

• SVM

Gaussian naive Bayes

• Gaussian naive Bayes

Clustering methods

• Hierarchical clustering
• Cluster heatmaps
• k-means clustering

Partial least squares regression

• Principal component regression (PCR)
• Partial least squares regression (PLSR)
• PLS-DA

Canonical correlation analysis

• Canonical correlation analysis

Artificial Neural Networks (ANN)

• ANN – the basics
• ANN vs regression
• Image classification with ANN, CNN, Decision trees, Logistic regression…

Survival analysis

• Kaplan Meier curve
• Comparing Kaplan-Meier curves – the Log-rank test
• The Cox proportional hazards model explained

Gene set analysis

In gene set analysis, one usually uses Fisher’s exact test to identify an overrepresented set of genes. To understand Fisher’s exact test, we first need to understand a few things about permutations and combinations.

• Permutations Combinations and the Hypergeometric distribution
• Fisher’s test and how to calculate the exact p-value
• Gene set analysis

Model selection

• Model selection with AIC and AICc
• Forward and backward selection, best subset selection
• Lasso regression

Statistics in epidemiology

• Odds vs probability
• Relative risk
• Odds ratio
• The Mantel-Haenszel method
• Meta-analysis

Additional videos

• Bootstrap confidence intervals

Mathematical and computational biology/ systems biology

Some basic math

• Understanding the equation of a straight line
• Logarithms
• Derivatives – the basics
• Second and partial derivatives
• Numerical differentiation
• Why do we use Euler’s number e?
• Exponential growth
• Doubling time with examples
• Exponential decay – a cup of coffee
• Ordinary differential equations (ODE)
• Euler’s method
• How to solve ordinary differential equations (ODEs) in R (deSolve)
• How to build a system of differential equations (ODEs)
• Receptor ligand kinetics
• The SIR model | the math of epidemics

Optimization – find the minimum value of a function

• Gradient descent
• Newton’s method | Newton-Raphson
• The Gauss Newton Method

Nonlinear regression

• Nonlinear regression – the basics
• Nonlinear regression – comparing models with F test and AIC
• Nonlinear regression – how to fit a dose-response curve in R
• Nonlinear regression – how to fit a logistic growth model to data
• Nonlinear mixed effects models (NLME)

Cellular automata – spatial modeling

• Cellular automata tutorial – the basics
• Cellular automata tutorial – applications
• Cellular automata tutorial – implementation in R